TSTP Solution File: GRP291-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP291-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:46:42 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP291-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n016.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 00:37:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 815 clauses, backtracked 369 clauses, performed 12 splits and kept 696 clauses.
% 0.20/0.48 SPASS allocated 63595 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 345 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.48 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.48 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.48 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 8[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 10[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 21[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.48 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 23[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 25[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.48 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 30[1:Spt:26.3,26.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.48 31[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.48 33[2:SpL:31.0,30.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.20/0.48 34[3:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 36[4:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 40[5:Spt:5.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 42[6:Spt:3.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 45[3:SpR:34.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 46[4:SpR:36.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.48 47[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c6) -> .
% 0.20/0.48 54[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 55[5:SpR:40.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.48 57[3:SpR:45.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.48 58[4:SpR:46.0,29.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.20/0.48 60[3:Rew:27.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.48 61[4:Rew:27.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.20/0.48 62[0:Rew:27.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 66[5:SpR:40.0,60.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 72[6:SpR:42.0,61.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 76[6:SpL:72.0,30.1] || equal(inverse(sk_c7),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.48 77[6:Obv:76.1] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.20/0.48 79[0:SpR:62.0,62.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 81[2:SpR:31.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.48 83[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 86[3:SpR:45.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.48 88[5:SpR:66.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.48 89[4:SpR:46.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.20/0.48 91[6:SpR:72.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.48 97[5:Rew:81.0,88.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 99[5:Rew:97.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 100[5:Rew:97.0,34.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 103[5:Rew:97.0,45.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.48 109[5:Rew:97.0,86.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.48 113[5:Rew:97.0,55.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.48 121[6:Rew:97.0,91.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.48 122[6:Rew:28.0,121.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 123[6:Rew:122.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 127[6:Rew:122.0,103.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.20/0.48 134[6:Rew:123.0,127.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.48 135[6:Rew:134.0,100.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 137[6:MRR:135.0,77.0] || -> .
% 0.20/0.48 160[6:Spt:137.0,3.0,42.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.20/0.48 161[6:Spt:137.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 163[5:Rew:89.0,109.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.48 167[6:Rew:97.0,160.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.20/0.48 168[0:Rew:79.0,83.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 169[4:Rew:168.0,89.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.20/0.48 177[5:Rew:97.0,13.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.48 178[6:MRR:177.1,167.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 181[5:Rew:163.0,113.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.48 184[5:Rew:97.0,8.1,97.0,8.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.48 185[6:MRR:184.0,167.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.48 192[4:SpR:169.0,62.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.20/0.48 216[6:SpR:185.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.20/0.48 218[6:Rew:99.0,216.0,178.0,216.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 225[6:Rew:218.0,181.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.48 231[6:Rew:192.0,225.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 232[6:Rew:231.0,46.0] || -> equal(identity,sk_c3)**.
% 0.20/0.48 240[6:Rew:232.0,27.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 248[6:UnC:240.0,167.0] || -> .
% 0.20/0.48 250[5:Spt:248.0,5.0,40.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.48 251[5:Spt:248.0,5.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 252[3:Rew:168.0,86.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 253[3:Rew:252.0,81.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.48 254[5:Rew:253.0,250.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.48 258[3:Rew:253.0,15.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.20/0.48 259[5:MRR:258.1,254.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 260[3:Rew:252.0,33.0] || equal(sk_c4,sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.20/0.48 263[3:Rew:253.0,10.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 264[5:MRR:263.0,254.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 265[4:Rew:36.0,47.0,169.0,47.0] || equal(sk_c7,sk_c7) equal(identity,sk_c6)** -> .
% 0.20/0.48 266[4:Obv:265.0] || equal(identity,sk_c6)** -> .
% 0.20/0.48 268[5:SpR:251.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.48 270[5:Rew:169.0,268.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.20/0.48 273[3:SpR:252.0,62.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.48 302[5:SpR:264.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.48 304[5:Rew:251.0,302.0,259.0,302.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 315[5:Rew:304.0,270.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.48 340[5:SpR:315.0,29.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.48 344[5:Rew:192.0,340.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 345[5:Rew:344.0,45.0] || -> equal(identity,sk_c4)**.
% 0.20/0.48 346[5:Rew:344.0,273.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.48 350[5:Rew:345.0,266.0] || equal(sk_c4,sk_c6)** -> .
% 0.20/0.48 354[5:Rew:345.0,28.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.20/0.48 364[5:SpR:252.0,354.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.20/0.48 369[5:Rew:346.0,364.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 370[5:MRR:369.0,350.0] || -> .
% 0.20/0.48 374[4:Spt:370.0,2.0,36.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.48 375[4:Spt:370.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 376[4:MRR:22.0,374.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 377[4:MRR:12.0,374.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 378[4:MRR:17.0,374.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 379[4:MRR:7.0,374.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 381[4:SpR:375.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.48 401[4:SpR:378.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.20/0.48 403[4:Rew:376.0,401.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.48 405[4:SpR:379.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.48 407[4:Rew:375.0,405.0,377.0,405.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 413[4:Rew:407.0,260.1] || equal(sk_c4,sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.20/0.48 418[4:Rew:407.0,381.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 420[4:Rew:407.0,403.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 421[4:Rew:28.0,418.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 422[4:Rew:421.0,45.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 423[4:Rew:421.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 427[4:Rew:421.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 429[4:Rew:423.0,422.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 438[4:Rew:429.0,413.0] || equal(sk_c6,sk_c7)** equal(sk_c6,sk_c7)** -> .
% 0.20/0.48 439[4:Obv:438.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.48 457[4:SpR:420.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.48 459[4:Rew:427.0,457.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 460[4:MRR:459.0,439.0] || -> .
% 0.20/0.48 461[3:Spt:460.0,4.0,34.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.48 462[3:Spt:460.0,4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 463[3:MRR:24.0,461.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 464[3:MRR:14.0,461.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 465[3:MRR:19.0,461.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 466[3:MRR:9.0,461.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 468[3:SpR:462.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.48 478[3:SpR:465.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.20/0.48 480[3:Rew:463.0,478.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.48 482[3:SpR:466.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.48 484[3:Rew:462.0,482.0,464.0,482.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 486[3:Rew:484.0,463.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 488[3:Rew:484.0,465.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.48 493[3:Rew:484.0,33.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.20/0.48 494[3:Rew:484.0,468.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 496[3:Rew:484.0,480.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 497[3:Rew:28.0,494.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 498[3:Rew:497.0,168.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 500[3:Rew:497.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 516[3:SpR:496.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.48 518[3:Rew:500.0,516.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 524[3:Rew:518.0,498.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 528[3:Rew:518.0,493.0] || equal(inverse(sk_c7),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.20/0.48 529[3:Rew:524.0,488.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.48 531[3:Rew:529.0,486.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 544[3:Rew:518.0,528.1,531.0,528.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 545[3:Obv:544.1] || -> .
% 0.20/0.48 548[2:Spt:545.0,1.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.48 549[2:Spt:545.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 551[2:MRR:11.1,548.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 553[2:MRR:6.0,548.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 555[2:SpR:549.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.48 566[2:SpR:553.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.48 568[2:Rew:549.0,566.0,551.0,566.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 572[2:Rew:568.0,548.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.48 573[2:Rew:568.0,555.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 578[2:Rew:28.0,573.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 579[2:Rew:578.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 585[2:UnC:579.0,572.0] || -> .
% 0.20/0.48 587[1:Spt:585.0,26.0,26.1,26.2,26.4,26.5,26.6,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.48 589[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.48 590[2:Rew:589.0,587.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.48 592[2:Obv:590.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.48 595[2:SpR:589.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.48 597[3:Spt:2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 599[3:Rew:597.0,592.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(sk_c5,sk_c5) -> .
% 0.20/0.48 600[3:Obv:599.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 605[4:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 614[5:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 626[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 627[0:SpR:28.0,168.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.48 629[4:SpR:605.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 630[5:SpR:614.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.48 632[0:Rew:168.0,626.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.48 640[4:SpR:629.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.48 642[4:Rew:168.0,640.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 643[4:Rew:642.0,595.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.48 645[4:Rew:643.0,10.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 646[4:Rew:643.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 647[4:Rew:643.0,15.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.20/0.48 648[4:Rew:643.0,25.1] || -> equal(inverse(sk_c2),sk_c5)** equal(sk_c6,sk_c7).
% 0.20/0.48 649[4:Rew:647.1,13.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.48 650[4:Rew:648.1,23.1] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.48 651[4:Rew:645.0,8.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 655[4:SpR:642.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.20/0.48 658[5:SpR:630.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.20/0.48 660[5:Rew:168.0,658.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.20/0.48 663[6:Spt:647.1] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 664[6:Rew:663.0,589.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 668[6:Rew:663.0,642.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.48 670[6:Rew:663.0,600.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 675[6:Rew:663.0,651.1] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.48 676[6:Rew:663.0,655.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.20/0.48 678[6:Rew:660.0,668.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.48 683[6:Rew:678.0,676.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.20/0.48 685[6:Rew:683.0,650.1] || -> equal(inverse(sk_c2),sk_c5)** equal(identity,sk_c7).
% 0.20/0.48 686[6:Rew:683.0,649.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.20/0.48 689[6:Rew:683.0,675.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.48 690[6:Rew:663.0,670.4,663.0,670.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 695[5:SpR:660.0,28.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.20/0.48 706[7:Spt:685.1] || -> equal(identity,sk_c7)**.
% 0.20/0.48 707[7:Rew:706.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 710[7:Rew:706.0,627.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 713[7:Rew:660.0,710.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.48 714[7:Rew:713.0,614.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 721[7:Rew:707.0,664.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 723[7:Rew:707.0,690.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c7)** equal(v,sk_c7) equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 731[7:Rew:707.0,723.5,721.0,723.5,707.0,723.3,721.0,723.3,721.0,723.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.20/0.48 732[7:Con:731.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.48 771[7:SpL:714.0,732.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 773[7:Obv:771.1] || -> .
% 0.20/0.48 774[7:Spt:773.0,685.1,706.0] || equal(identity,sk_c7)** -> .
% 0.20/0.48 775[7:Spt:773.0,685.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 776[7:MRR:686.1,774.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 778[7:MRR:689.0,774.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.48 794[7:SpR:776.0,632.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 796[7:Rew:660.0,794.0] || -> equal(sk_c1,sk_c3)**.
% 0.20/0.48 798[7:Rew:796.0,778.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.48 799[7:Rew:683.0,798.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 800[7:MRR:799.0,774.0] || -> .
% 0.20/0.48 802[6:Spt:800.0,647.1,663.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.48 803[6:Spt:800.0,647.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 804[6:MRR:648.1,802.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 805[6:MRR:645.0,802.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 806[6:MRR:646.0,802.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 808[6:SpR:803.0,632.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 810[6:Rew:660.0,808.0] || -> equal(sk_c1,sk_c3)**.
% 0.20/0.48 812[6:Rew:810.0,805.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.48 813[6:Rew:695.0,812.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 816[6:Rew:813.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 821[6:Rew:813.0,695.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.48 831[6:Rew:816.0,589.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 834[6:Rew:831.0,804.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 835[6:Rew:831.0,806.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.48 858[6:SpR:834.0,632.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.20/0.48 860[6:Rew:660.0,858.0] || -> equal(sk_c2,sk_c3)**.
% 0.20/0.48 862[6:Rew:860.0,835.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.48 863[6:Rew:821.0,862.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 864[6:MRR:863.0,802.0] || -> .
% 0.20/0.48 866[5:Spt:864.0,22.0,614.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.48 867[5:Spt:864.0,22.1] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 868[5:MRR:12.0,866.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 869[5:MRR:17.0,866.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 870[5:MRR:7.0,866.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 872[5:SpR:867.0,632.0] || -> equal(inverse(sk_c5),sk_c2)**.
% 0.20/0.48 878[5:SpR:868.0,62.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.48 879[5:SpR:868.0,632.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 888[5:SpR:872.0,62.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.20/0.48 891[5:SpR:879.0,62.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.20/0.48 912[5:SpR:869.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.48 916[5:Rew:888.0,912.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 917[5:Rew:916.0,878.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 919[5:Rew:916.0,597.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 922[5:Rew:916.0,891.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 929[5:Rew:919.0,600.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 936[5:Rew:917.0,870.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 937[5:Rew:936.0,605.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 938[5:Rew:936.0,642.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.48 939[5:Rew:936.0,655.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.20/0.48 943[5:Rew:936.0,919.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 944[5:Rew:879.0,938.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.48 946[5:Rew:944.0,879.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.48 948[5:Rew:944.0,922.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.48 954[5:Rew:948.0,939.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 955[5:Rew:954.0,627.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 956[5:Rew:954.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 959[5:Rew:946.0,955.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.48 961[5:Rew:959.0,937.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 974[5:Rew:956.0,929.5,943.0,929.5,956.0,929.4,936.0,929.4,956.0,929.3,943.0,929.3,936.0,929.3,936.0,929.2,936.0,929.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.20/0.48 975[5:Con:974.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.48 1000[5:SpL:961.0,975.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 1001[5:Obv:1000.1] || -> .
% 0.20/0.48 1002[4:Spt:1001.0,24.0,605.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.48 1003[4:Spt:1001.0,24.1] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 1004[4:MRR:14.0,1002.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 1005[4:MRR:19.0,1002.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.48 1006[4:MRR:9.0,1002.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 1008[4:SpR:1003.0,632.0] || -> equal(inverse(sk_c5),sk_c2)**.
% 0.20/0.48 1015[4:SpR:1004.0,632.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 1018[4:SpR:1008.0,62.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.20/0.48 1021[4:SpR:1015.0,62.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.20/0.48 1031[4:SpR:1005.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.48 1035[4:Rew:1018.0,1031.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 1036[4:Rew:1035.0,597.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 1039[4:Rew:1035.0,1021.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 1046[4:Rew:1036.0,595.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.48 1048[4:Rew:1036.0,600.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.20/0.48 1053[4:Rew:1039.0,1006.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 1055[4:Rew:1053.0,1036.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 1063[4:Rew:28.0,1046.0,1053.0,1046.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 1064[4:Rew:1063.0,627.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 1066[4:Rew:1063.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 1068[4:Rew:1015.0,1064.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.48 1069[4:Rew:1068.0,1004.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 1078[4:Rew:1066.0,1048.5,1055.0,1048.5,1066.0,1048.4,1053.0,1048.4,1066.0,1048.3,1055.0,1048.3,1053.0,1048.3,1053.0,1048.2,1053.0,1048.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.20/0.48 1079[4:Con:1078.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.48 1119[4:SpL:1069.0,1079.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 1120[4:Obv:1119.1] || -> .
% 0.20/0.48 1121[3:Spt:1120.0,2.1,597.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.48 1122[3:Spt:1120.0,2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 1123[3:MRR:4.1,1121.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 1125[3:MRR:5.1,1121.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 1134[3:SpR:1123.0,632.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 1136[3:Rew:1134.0,595.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.48 1138[3:Rew:1125.0,1136.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 1140[3:Rew:1138.0,589.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.49 1141[3:Rew:1138.0,1121.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.20/0.49 1149[3:Rew:1140.0,1141.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.49 1150[3:Obv:1149.0] || -> .
% 0.20/0.49 1153[2:Spt:1150.0,1.0,589.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.49 1154[2:Spt:1150.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 1155[2:MRR:21.1,1153.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.49 1156[2:MRR:11.1,1153.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 1157[2:MRR:16.0,1153.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.49 1158[2:MRR:6.0,1153.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 1163[2:SpR:1155.0,632.0] || -> equal(inverse(sk_c5),sk_c2)**.
% 0.20/0.49 1165[2:SpR:1156.0,62.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.49 1169[2:SpR:1157.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 1173[2:SpR:1163.0,62.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.20/0.49 1176[2:Rew:1169.0,1173.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 1177[2:Rew:1176.0,1154.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.49 1179[2:Rew:1176.0,1165.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 1184[2:Rew:1177.0,1153.0] || equal(multiply(sk_c6,sk_c7),sk_c6)** -> .
% 0.20/0.49 1188[2:Rew:1179.0,1158.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 1196[2:Rew:1176.0,1184.0,1188.0,1184.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 1197[2:Obv:1196.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 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_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.20/0.49
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