TSTP Solution File: GRP372-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP372-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:47:04 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP372-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n029.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jun 14 05:28:25 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.41
% 0.14/0.41 SPASS V 3.9
% 0.14/0.41 SPASS beiseite: Proof found.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 SPASS derived 888 clauses, backtracked 454 clauses, performed 12 splits and kept 817 clauses.
% 0.14/0.41 SPASS allocated 63641 KBytes.
% 0.14/0.41 SPASS spent 0:00:00.12 on the problem.
% 0.14/0.41 0:00:00.03 for the input.
% 0.14/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.41 0:00:00.00 for inferences.
% 0.14/0.41 0:00:00.00 for the backtracking.
% 0.14/0.41 0:00:00.06 for the reduction.
% 0.14/0.41
% 0.14/0.41
% 0.14/0.41 Here is a proof with depth 5, length 385 :
% 0.14/0.41 % SZS output start Refutation
% 0.14/0.41 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 3[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.14/0.41 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 5[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.14/0.41 7[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 8[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 9[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 10[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 11[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 15[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.14/0.41 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.14/0.41 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.14/0.41 22[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.14/0.41 23[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.14/0.41 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.14/0.41 25[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.14/0.41 31[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 32[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 33[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.14/0.41 34[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 35[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 36[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.14/0.41 37[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(v,sk_c7),sk_c6)** equal(inverse(v),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.14/0.41 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.14/0.41 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.14/0.41 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.14/0.41 41[0:Con:37.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) 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_c8,sk_c6),sk_c7) -> .
% 0.14/0.41 42[1:Spt:41.0,41.3,41.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.14/0.41 44[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.14/0.41 46[3:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.14/0.41 48[4:Spt:31.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.14/0.41 50[5:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.14/0.41 53[1:SpL:38.0,42.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.14/0.41 54[6:Spt:25.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.14/0.41 56[7:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 62[2:SpR:44.0,39.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.14/0.41 63[4:SpR:48.0,39.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.14/0.41 64[5:SpR:50.0,39.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.14/0.41 73[2:SpR:62.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.14/0.41 74[3:SpR:46.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.14/0.41 76[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.14/0.41 78[4:SpR:63.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.14/0.41 80[2:Rew:38.0,73.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.14/0.41 81[4:Rew:38.0,78.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.14/0.41 82[0:Rew:38.0,76.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.14/0.41 85[5:SpR:64.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.14/0.41 86[5:Rew:38.0,85.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.14/0.41 89[3:SpR:46.0,80.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.14/0.41 90[5:SpR:64.0,80.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.14/0.41 95[5:SpR:90.0,40.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.14/0.41 96[5:Rew:38.0,95.0] || -> equal(multiply(sk_c7,u),multiply(sk_c1,u))**.
% 0.14/0.41 97[5:Rew:96.0,90.0] || -> equal(multiply(sk_c1,identity),sk_c1)**.
% 0.14/0.41 98[5:Rew:96.0,89.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.14/0.41 100[5:Rew:96.0,63.0] || -> equal(multiply(sk_c1,sk_c2),identity)**.
% 0.14/0.41 101[5:Rew:96.0,62.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.14/0.41 103[5:Rew:96.0,81.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.14/0.41 105[5:Rew:96.0,74.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c1,u))**.
% 0.14/0.41 107[7:Rew:56.0,101.0] || -> equal(sk_c7,identity)**.
% 0.14/0.41 109[7:Rew:107.0,44.0] || -> equal(inverse(sk_c8),identity)**.
% 0.14/0.41 113[7:Rew:107.0,56.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.14/0.41 117[7:Rew:107.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),identity)** -> .
% 0.14/0.41 119[7:Rew:107.0,96.0] || -> equal(multiply(identity,u),multiply(sk_c1,u))**.
% 0.14/0.41 120[7:Rew:107.0,98.0] || -> equal(multiply(sk_c1,identity),sk_c6)**.
% 0.14/0.41 121[7:Rew:97.0,120.0] || -> equal(sk_c1,sk_c6)**.
% 0.14/0.41 126[7:Rew:121.0,100.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.14/0.41 127[7:Rew:121.0,113.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.14/0.41 129[7:Rew:121.0,103.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.14/0.41 130[7:Rew:38.0,119.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.14/0.41 131[7:Rew:121.0,130.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 132[7:Rew:131.0,129.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.14/0.41 134[7:Rew:131.0,127.0] || -> equal(identity,sk_c8)**.
% 0.14/0.41 135[7:Rew:131.0,126.0] || -> equal(identity,sk_c2)**.
% 0.14/0.41 138[7:Rew:134.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.14/0.41 140[7:Rew:134.0,109.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 144[7:Rew:134.0,135.0] || -> equal(sk_c2,sk_c8)**.
% 0.14/0.41 150[7:Rew:144.0,132.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 165[7:Rew:150.0,117.2,134.0,117.2,140.0,117.0,134.0,117.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.14/0.41 166[7:Obv:165.1] || equal(u,sk_c8)* -> .
% 0.14/0.41 167[7:UnC:166.0,138.0] || -> .
% 0.14/0.41 170[7:Spt:167.0,7.1,56.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.14/0.41 171[7:Spt:167.0,7.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 172[7:Rew:101.0,170.0] || equal(sk_c7,identity)** -> .
% 0.14/0.41 175[5:Rew:101.0,9.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c7,identity).
% 0.14/0.41 176[7:MRR:175.1,172.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 182[5:Rew:101.0,8.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c7,identity).
% 0.14/0.41 183[7:MRR:182.1,172.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 184[7:SpR:171.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 186[7:Rew:86.0,184.0,96.0,184.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 188[7:Rew:186.0,105.0] || -> equal(multiply(sk_c1,u),multiply(sk_c8,u))**.
% 0.14/0.41 190[7:Rew:188.0,96.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.14/0.41 191[7:Rew:188.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.14/0.41 196[7:Rew:188.0,97.0] || -> equal(multiply(sk_c8,identity),sk_c1)**.
% 0.14/0.41 197[7:Rew:188.0,100.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.14/0.41 198[7:Rew:188.0,101.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.14/0.41 220[7:SpR:183.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.14/0.41 222[7:Rew:190.0,220.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.14/0.41 242[7:SpR:176.0,39.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.14/0.41 253[0:SpR:82.0,82.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.14/0.41 262[7:SpR:197.0,82.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.14/0.41 264[7:SpR:242.0,82.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.14/0.41 270[0:SpR:39.0,82.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.14/0.41 293[7:Rew:44.0,262.0] || -> equal(multiply(sk_c7,identity),sk_c2)**.
% 0.14/0.41 294[7:Rew:190.0,293.0] || -> equal(multiply(sk_c8,identity),sk_c2)**.
% 0.14/0.41 295[7:Rew:196.0,294.0] || -> equal(sk_c2,sk_c1)**.
% 0.14/0.41 296[7:Rew:295.0,48.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.14/0.41 297[7:Rew:295.0,54.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.14/0.41 301[7:Rew:50.0,296.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 302[7:Rew:301.0,171.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 303[7:Rew:301.0,172.0] || equal(identity,sk_c8)** -> .
% 0.14/0.41 304[7:Rew:301.0,44.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 305[7:Rew:301.0,46.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.14/0.41 313[7:Rew:188.0,297.0,301.0,297.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 314[7:Rew:198.0,313.0] || -> equal(identity,sk_c6)**.
% 0.14/0.41 322[7:Rew:314.0,303.0] || equal(sk_c6,sk_c8)** -> .
% 0.14/0.41 334[7:Rew:305.0,264.0,304.0,264.0,314.0,264.0] || -> equal(sk_c3,sk_c8)**.
% 0.14/0.41 336[7:Rew:334.0,222.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.14/0.41 359[7:Rew:191.0,336.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 361[7:Rew:359.0,302.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 362[7:MRR:361.0,322.0] || -> .
% 0.14/0.41 372[6:Spt:362.0,25.1,54.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.14/0.41 373[6:Spt:362.0,25.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 380[0:Rew:253.0,270.0] || -> equal(multiply(u,identity),u)**.
% 0.14/0.41 395[6:SpR:373.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 399[6:Rew:86.0,395.0,96.0,395.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 400[6:Rew:399.0,105.0] || -> equal(multiply(sk_c1,u),multiply(sk_c8,u))**.
% 0.14/0.41 403[6:Rew:400.0,96.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.14/0.41 408[6:Rew:400.0,100.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.14/0.41 409[6:Rew:400.0,101.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.14/0.41 420[3:SpR:46.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.14/0.41 430[5:SpR:64.0,82.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.14/0.41 432[5:Rew:44.0,430.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.14/0.41 433[6:Rew:380.0,432.0,403.0,432.0] || -> equal(sk_c1,sk_c8)**.
% 0.14/0.41 434[6:Rew:433.0,50.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 437[6:Rew:44.0,434.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 438[6:Rew:437.0,373.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 440[6:Rew:437.0,44.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 442[6:Rew:437.0,372.0] || equal(multiply(sk_c2,sk_c8),sk_c6)** -> .
% 0.14/0.41 456[6:Rew:409.0,438.0] || -> equal(identity,sk_c6)**.
% 0.14/0.41 460[6:Rew:456.0,380.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.14/0.41 461[6:Rew:456.0,408.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.14/0.41 462[6:Rew:456.0,409.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 485[6:SpR:461.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c2)**.
% 0.14/0.41 487[6:Rew:440.0,485.0] || -> equal(multiply(sk_c8,sk_c6),sk_c2)**.
% 0.14/0.41 488[6:Rew:460.0,487.0] || -> equal(sk_c2,sk_c8)**.
% 0.14/0.41 489[6:Rew:488.0,442.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.14/0.41 493[6:Rew:462.0,489.0] || equal(sk_c6,sk_c6)* -> .
% 0.14/0.41 494[6:Obv:493.0] || -> .
% 0.14/0.41 496[5:Spt:494.0,13.0,50.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.14/0.41 497[5:Spt:494.0,13.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 499[5:MRR:18.1,496.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 500[5:MRR:15.1,496.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 501[5:MRR:17.0,496.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 502[5:MRR:16.0,496.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 503[5:MRR:14.0,496.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 504[5:SpR:497.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 524[2:SpR:62.0,82.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c8)**.
% 0.14/0.41 526[2:Rew:380.0,524.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.14/0.41 531[2:SpR:526.0,82.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.14/0.41 533[5:Rew:504.0,531.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 534[5:Rew:533.0,420.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.14/0.41 537[5:Rew:534.0,62.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.14/0.41 546[5:SpR:501.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 548[5:Rew:499.0,546.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 549[5:Rew:502.0,548.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 550[5:Rew:549.0,497.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 551[5:Rew:549.0,44.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 556[5:Rew:549.0,503.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.41 559[5:Rew:549.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 563[5:Rew:537.0,550.0] || -> equal(identity,sk_c6)**.
% 0.14/0.41 568[5:Rew:563.0,537.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 571[5:Rew:563.0,559.0] || equal(inverse(sk_c6),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 589[5:SpR:556.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.41 591[5:Rew:500.0,589.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.14/0.41 592[5:Rew:568.0,591.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 595[5:Rew:592.0,533.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 600[5:Rew:592.0,571.0] || equal(inverse(sk_c8),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 628[5:Rew:551.0,600.0] || equal(sk_c8,sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 629[5:Obv:628.0] || equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 630[5:Rew:595.0,629.1] || equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.14/0.41 631[5:Obv:630.0] || equal(u,sk_c8)* -> .
% 0.14/0.41 632[5:UnC:631.0,549.0] || -> .
% 0.14/0.41 635[4:Spt:632.0,31.0,48.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.14/0.41 636[4:Spt:632.0,31.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 637[4:MRR:36.1,635.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 638[4:MRR:33.1,635.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 639[4:MRR:35.0,635.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 640[4:MRR:34.0,635.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 641[4:MRR:32.0,635.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 642[4:SpR:636.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 646[4:Rew:531.0,642.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 648[4:Rew:646.0,420.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.14/0.41 653[4:Rew:648.0,62.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.14/0.41 673[4:SpR:639.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 675[4:Rew:637.0,673.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 676[4:Rew:640.0,675.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 677[4:Rew:676.0,636.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 678[4:Rew:676.0,526.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 683[4:Rew:676.0,641.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.41 684[4:Rew:676.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 690[4:Rew:653.0,677.0] || -> equal(identity,sk_c6)**.
% 0.14/0.41 695[4:Rew:690.0,653.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 697[4:Rew:690.0,684.0] || equal(inverse(sk_c6),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 714[4:SpR:683.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.41 716[4:Rew:638.0,714.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.14/0.41 717[4:Rew:695.0,716.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 720[4:Rew:717.0,646.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 725[4:Rew:717.0,697.0] || equal(inverse(sk_c8),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 748[4:Rew:678.0,725.0] || equal(sk_c8,sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 749[4:Obv:748.0] || equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.14/0.41 750[4:Rew:720.0,749.1] || equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.14/0.41 751[4:Obv:750.0] || equal(u,sk_c8)* -> .
% 0.14/0.41 752[4:UnC:751.0,676.0] || -> .
% 0.14/0.41 755[3:Spt:752.0,19.1,46.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.14/0.41 756[3:Spt:752.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 757[3:MRR:24.1,755.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 759[3:MRR:23.1,755.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 760[3:MRR:22.1,755.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 781[3:SpR:759.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 783[3:Rew:757.0,781.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 784[3:Rew:760.0,783.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 785[3:Rew:784.0,756.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 788[3:Rew:784.0,62.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.14/0.41 789[3:Rew:784.0,755.0] || equal(multiply(sk_c8,sk_c6),sk_c8)** -> .
% 0.14/0.41 800[3:Rew:785.0,788.0] || -> equal(identity,sk_c6)**.
% 0.14/0.41 802[3:Rew:800.0,380.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.14/0.41 805[3:Rew:802.0,789.0] || equal(sk_c8,sk_c8)* -> .
% 0.14/0.41 806[3:Obv:805.0] || -> .
% 0.14/0.41 809[2:Spt:806.0,1.0,44.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.14/0.41 810[2:Spt:806.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 811[2:MRR:6.1,809.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 812[2:MRR:3.1,809.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 813[2:MRR:5.0,809.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 814[2:MRR:4.0,809.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 815[2:MRR:2.0,809.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 817[2:SpR:810.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.14/0.41 824[2:SpR:813.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 826[2:Rew:811.0,824.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 827[2:Rew:814.0,826.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 828[2:Rew:827.0,810.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 829[2:Rew:827.0,809.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.14/0.41 830[2:Rew:827.0,814.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 831[2:Rew:827.0,815.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.41 837[2:Rew:827.0,817.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.14/0.41 844[2:SpR:830.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.14/0.41 846[2:Rew:39.0,844.0] || -> equal(identity,sk_c5)**.
% 0.14/0.41 847[2:Rew:846.0,380.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.14/0.41 849[2:Rew:846.0,39.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.14/0.41 857[2:SpR:831.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.41 859[2:Rew:828.0,857.0,812.0,857.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 861[2:Rew:859.0,837.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.14/0.41 863[2:Rew:849.0,861.0] || -> equal(sk_c5,sk_c8)**.
% 0.14/0.41 864[2:Rew:863.0,813.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.14/0.41 866[2:Rew:863.0,847.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.14/0.41 873[2:Rew:866.0,864.0] || -> equal(sk_c4,sk_c8)**.
% 0.14/0.41 879[2:Rew:873.0,811.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 883[2:MRR:879.0,829.0] || -> .
% 0.14/0.41 894[1:Spt:883.0,41.1,41.2,41.4,41.6,41.7] || equal(inverse(u),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c7)**+ equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.14/0.41 896[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.14/0.41 897[2:Rew:896.0,894.1] || equal(inverse(u),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.14/0.41 899[2:Obv:897.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.14/0.41 901[2:SpR:896.0,82.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.14/0.41 903[3:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.14/0.41 905[3:Rew:903.0,899.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.14/0.41 906[3:Obv:905.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.14/0.41 912[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.14/0.41 913[4:SpR:912.0,82.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.14/0.41 918[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.14/0.41 920[5:SpR:918.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.14/0.41 922[5:Rew:912.0,920.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.14/0.41 924[5:Rew:922.0,906.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.14/0.41 930[5:SpR:922.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.14/0.41 932[5:Rew:896.0,930.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.14/0.41 934[5:SpR:932.0,82.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.14/0.41 936[5:Rew:39.0,934.0] || -> equal(identity,sk_c8)**.
% 0.14/0.41 937[5:Rew:936.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 938[5:Rew:936.0,380.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.14/0.41 941[5:Rew:937.0,922.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 942[5:Rew:937.0,903.0] || -> equal(sk_c7,sk_c6)**.
% 0.14/0.41 949[5:Rew:941.0,896.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 960[5:Rew:941.0,924.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(sk_c6,sk_c8) -> .
% 0.14/0.41 964[5:Rew:941.0,942.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 980[5:Rew:964.0,960.2,938.0,960.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.14/0.41 981[5:Obv:980.2] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.14/0.41 1027[5:SpL:949.0,981.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.14/0.41 1029[5:Obv:1027.1] || -> .
% 0.14/0.41 1030[5:Spt:1029.0,7.1,918.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.14/0.41 1031[5:Spt:1029.0,7.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 1032[5:MRR:12.1,1030.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 1033[5:MRR:9.1,1030.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 1034[5:MRR:11.1,1030.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 1035[5:MRR:10.1,1030.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 1036[5:MRR:8.1,1030.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 1041[5:SpR:1031.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 1063[5:SpR:1034.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 1065[5:Rew:1032.0,1063.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 1066[5:Rew:1035.0,1065.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 1067[5:Rew:1066.0,1031.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 1073[5:Rew:1066.0,1030.0] || equal(multiply(sk_c1,sk_c8),sk_c8)** -> .
% 0.14/0.41 1074[5:Rew:1066.0,901.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.14/0.41 1077[5:Rew:1066.0,1041.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.14/0.41 1080[5:Rew:1066.0,1036.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.41 1085[5:Rew:1074.0,1077.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.41 1109[5:SpR:1080.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.41 1111[5:Rew:1067.0,1109.0,1033.0,1109.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.41 1115[5:Rew:1111.0,1085.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.41 1122[5:Rew:1115.0,913.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.14/0.41 1123[5:UnC:1122.0,1073.0] || -> .
% 0.14/0.41 1124[4:Spt:1123.0,13.0,912.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.14/0.41 1125[4:Spt:1123.0,13.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.41 1126[4:MRR:18.1,1124.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.41 1127[4:MRR:15.1,1124.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.41 1128[4:MRR:17.0,1124.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.41 1129[4:MRR:16.0,1124.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.41 1130[4:MRR:14.0,1124.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.41 1131[4:Rew:1125.0,906.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.14/0.41 1132[4:Obv:1131.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.14/0.41 1135[4:SpR:1125.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.14/0.41 1153[4:SpR:1128.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.41 1155[4:Rew:1126.0,1153.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.41 1156[4:Rew:1129.0,1155.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.41 1157[4:Rew:1156.0,1125.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.41 1158[4:Rew:1156.0,896.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.41 1162[4:Rew:1156.0,901.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.14/0.41 1164[4:Rew:1156.0,1135.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.14/0.42 1167[4:Rew:1156.0,1130.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.42 1168[4:Rew:1156.0,1132.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.14/0.42 1172[4:Rew:1162.0,1164.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.42 1200[4:SpR:1167.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.42 1202[4:Rew:1157.0,1200.0,1127.0,1200.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.42 1206[4:Rew:1202.0,1172.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.42 1226[4:SpR:1206.0,380.0] || -> equal(identity,sk_c8)**.
% 0.14/0.42 1229[4:Rew:1226.0,380.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.14/0.42 1233[4:Rew:1229.0,1168.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.14/0.42 1262[4:SpL:1158.0,1233.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.14/0.42 1263[4:Obv:1262.1] || -> .
% 0.14/0.42 1264[3:Spt:1263.0,19.1,903.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.14/0.42 1265[3:Spt:1263.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.42 1266[3:MRR:24.1,1264.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.42 1268[3:MRR:23.1,1264.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.42 1269[3:MRR:22.1,1264.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.42 1272[3:SpR:1265.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.14/0.42 1274[3:Rew:896.0,1272.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.14/0.42 1282[3:SpR:1268.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.42 1284[3:Rew:1266.0,1282.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.42 1285[3:Rew:1269.0,1284.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.42 1288[3:Rew:1285.0,1264.0] || equal(multiply(sk_c8,sk_c6),sk_c8)** -> .
% 0.14/0.42 1292[3:Rew:1285.0,1274.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.14/0.42 1294[3:Rew:1292.0,1288.0] || equal(sk_c8,sk_c8)* -> .
% 0.14/0.42 1295[3:Obv:1294.0] || -> .
% 0.14/0.42 1297[2:Spt:1295.0,1.0,896.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.14/0.42 1298[2:Spt:1295.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.14/0.42 1299[2:MRR:6.1,1297.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.14/0.42 1300[2:MRR:3.1,1297.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.14/0.42 1301[2:MRR:5.0,1297.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.14/0.42 1302[2:MRR:4.0,1297.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.14/0.42 1303[2:MRR:2.0,1297.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.14/0.42 1305[2:SpR:1298.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.14/0.42 1312[2:SpR:1301.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.14/0.42 1314[2:Rew:1299.0,1312.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.42 1315[2:Rew:1302.0,1314.0] || -> equal(sk_c7,sk_c8)**.
% 0.14/0.42 1316[2:Rew:1315.0,1298.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.14/0.42 1317[2:Rew:1315.0,1297.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.14/0.42 1318[2:Rew:1315.0,1302.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.42 1319[2:Rew:1315.0,1303.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.42 1320[2:Rew:1315.0,1305.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.14/0.42 1327[2:SpR:1318.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.14/0.42 1329[2:Rew:39.0,1327.0] || -> equal(identity,sk_c5)**.
% 0.14/0.42 1330[2:Rew:1329.0,380.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.14/0.42 1333[2:Rew:1329.0,39.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.14/0.42 1338[2:SpR:1319.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.14/0.42 1340[2:Rew:1316.0,1338.0,1300.0,1338.0] || -> equal(sk_c6,sk_c8)**.
% 0.14/0.42 1342[2:Rew:1340.0,1320.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.14/0.42 1344[2:Rew:1333.0,1342.0] || -> equal(sk_c5,sk_c8)**.
% 0.14/0.42 1345[2:Rew:1344.0,1301.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.14/0.42 1347[2:Rew:1344.0,1330.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.14/0.42 1352[2:Rew:1347.0,1345.0] || -> equal(sk_c4,sk_c8)**.
% 0.14/0.42 1355[2:Rew:1352.0,1299.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.42 1359[2:MRR:1355.0,1317.0] || -> .
% 0.14/0.42 % SZS output end Refutation
% 0.14/0.42 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_22 prove_this_23 prove_this_24 prove_this_25 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.14/0.42
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