TSTP Solution File: GRP374-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP374-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:47:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP374-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Tue Jun 14 03:32:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 887 clauses, backtracked 421 clauses, performed 12 splits and kept 813 clauses.
% 0.19/0.49 SPASS allocated 63664 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.07 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 5, length 414 :
% 0.19/0.49 % SZS output start Refutation
% 0.19/0.49 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 3[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.19/0.49 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 5[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.19/0.49 7[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 8[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 9[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 10[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 11[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 15[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.49 22[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.49 23[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.49 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 25[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.49 26[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.49 27[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.49 31[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 32[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 33[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.49 34[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 35[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 36[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.49 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_c6),sk_c7)** equal(inverse(v),sk_c6) 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) -> .
% 0.19/0.49 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.49 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.49 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.49 41[0:Con:37.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.19/0.49 42[1:Spt:41.0,41.4,41.7] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.19/0.49 44[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 46[3:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 48[4:Spt:31.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.49 50[5:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 53[1:SpL:38.0,42.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.49 54[6:Spt:25.1] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.49 56[7:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 62[2:SpR:44.0,39.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.49 63[4:SpR:48.0,39.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.19/0.49 64[5:SpR:50.0,39.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.19/0.49 73[2:SpR:62.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.19/0.49 74[3:SpR:46.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.49 76[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.49 77[6:SpR:54.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.49 78[4:SpR:63.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.49 80[2:Rew:38.0,73.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 81[4:Rew:38.0,78.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.49 82[0:Rew:38.0,76.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.49 85[5:SpR:64.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.49 86[5:Rew:38.0,85.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.19/0.49 89[3:SpR:46.0,80.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 90[5:SpR:64.0,80.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.19/0.49 92[3:SpR:89.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 94[5:SpR:90.0,40.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.19/0.49 96[5:Rew:38.0,94.0] || -> equal(multiply(sk_c7,u),multiply(sk_c1,u))**.
% 0.19/0.49 97[5:Rew:96.0,90.0] || -> equal(multiply(sk_c1,identity),sk_c1)**.
% 0.19/0.49 98[5:Rew:96.0,89.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.49 99[5:Rew:96.0,80.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),u)**.
% 0.19/0.49 100[5:Rew:96.0,62.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.19/0.49 101[5:Rew:96.0,92.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 103[5:Rew:96.0,74.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c1,u))**.
% 0.19/0.49 104[6:Rew:96.0,77.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c1,u))**.
% 0.19/0.49 105[7:Rew:56.0,100.0] || -> equal(sk_c7,identity)**.
% 0.19/0.49 107[7:Rew:105.0,44.0] || -> equal(inverse(sk_c8),identity)**.
% 0.19/0.49 110[7:Rew:105.0,56.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.19/0.49 114[7:Rew:105.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),identity)** -> .
% 0.19/0.49 116[7:Rew:105.0,96.0] || -> equal(multiply(identity,u),multiply(sk_c1,u))**.
% 0.19/0.49 117[7:Rew:105.0,98.0] || -> equal(multiply(sk_c1,identity),sk_c6)**.
% 0.19/0.49 118[7:Rew:97.0,117.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.49 122[7:Rew:118.0,97.0] || -> equal(multiply(sk_c6,identity),sk_c6)**.
% 0.19/0.49 123[7:Rew:118.0,110.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.19/0.49 124[7:Rew:118.0,99.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.19/0.49 125[7:Rew:38.0,116.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.49 126[7:Rew:118.0,125.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 127[7:Rew:126.0,63.0] || -> equal(identity,sk_c2)**.
% 0.19/0.49 128[7:Rew:126.0,124.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 129[7:Rew:126.0,123.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 130[7:Rew:126.0,122.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 133[7:Rew:127.0,39.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.49 135[7:Rew:127.0,107.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.19/0.49 138[7:Rew:127.0,129.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.49 140[7:Rew:138.0,127.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 142[7:Rew:130.0,140.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 146[7:Rew:142.0,130.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 147[7:Rew:138.0,135.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 153[7:Rew:138.0,133.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.49 166[7:Rew:128.0,114.2,146.0,114.2,147.0,114.0,146.0,114.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.49 167[7:Obv:166.1] || equal(u,sk_c8)* -> .
% 0.19/0.49 168[7:UnC:167.0,153.0] || -> .
% 0.19/0.49 171[7:Spt:168.0,7.1,56.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.19/0.49 172[7:Spt:168.0,7.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 173[7:Rew:100.0,171.0] || equal(sk_c7,identity)** -> .
% 0.19/0.49 176[5:Rew:100.0,9.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c7,identity).
% 0.19/0.49 178[5:Rew:96.0,101.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),multiply(sk_c6,u))**.
% 0.19/0.49 183[5:Rew:100.0,8.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c7,identity).
% 0.19/0.49 185[7:SpR:172.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 187[7:Rew:86.0,185.0,96.0,185.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 189[7:Rew:187.0,103.0] || -> equal(multiply(sk_c1,u),multiply(sk_c8,u))**.
% 0.19/0.49 190[7:Rew:187.0,104.0] || -> equal(multiply(sk_c2,u),multiply(sk_c1,u))**.
% 0.19/0.49 191[7:Rew:187.0,81.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.49 192[7:Rew:187.0,63.0] || -> equal(identity,sk_c2)**.
% 0.19/0.49 193[7:Rew:192.0,100.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.19/0.49 195[7:Rew:192.0,97.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.19/0.49 198[7:Rew:192.0,173.0] || equal(sk_c7,sk_c2)** -> .
% 0.19/0.49 201[7:Rew:191.0,54.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.49 203[7:Rew:201.0,44.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.49 212[7:Rew:201.0,198.0] || equal(sk_c2,sk_c6)** -> .
% 0.19/0.49 213[7:Rew:189.0,193.0] || -> equal(multiply(sk_c8,sk_c8),sk_c2)**.
% 0.19/0.49 217[7:Rew:189.0,195.0] || -> equal(multiply(sk_c8,sk_c2),sk_c1)**.
% 0.19/0.49 219[7:Rew:191.0,190.0,189.0,190.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 220[7:Rew:219.0,213.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.49 222[7:Rew:219.0,217.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.49 228[7:Rew:220.0,212.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.49 230[7:Rew:220.0,222.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.49 231[7:Rew:230.0,50.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 234[7:Rew:203.0,231.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 235[7:MRR:234.0,228.0] || -> .
% 0.19/0.49 246[6:Spt:235.0,25.1,54.0] || equal(multiply(sk_c2,sk_c6),sk_c7)** -> .
% 0.19/0.49 247[6:Spt:235.0,25.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 251[5:Rew:176.1,27.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c6),identity)**.
% 0.19/0.49 257[5:Rew:183.1,26.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),identity)**.
% 0.19/0.49 258[6:SpR:247.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 260[6:Rew:86.0,258.0,96.0,258.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 261[6:Rew:260.0,103.0] || -> equal(multiply(sk_c1,u),multiply(sk_c8,u))**.
% 0.19/0.49 262[6:Rew:260.0,178.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.19/0.49 263[6:Rew:260.0,81.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.49 264[6:Rew:260.0,63.0] || -> equal(identity,sk_c2)**.
% 0.19/0.49 266[6:Rew:264.0,97.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.19/0.49 268[6:Rew:264.0,100.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.19/0.49 269[6:Rew:264.0,39.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.49 270[6:Rew:264.0,183.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c7,sk_c2).
% 0.19/0.49 273[6:Rew:264.0,176.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c7,sk_c2).
% 0.19/0.49 275[6:Rew:264.0,257.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c2)**.
% 0.19/0.49 278[6:Rew:264.0,251.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c2)**.
% 0.19/0.49 282[6:Rew:263.0,246.0] || equal(sk_c7,sk_c6)** -> .
% 0.19/0.49 283[6:Rew:261.0,268.0] || -> equal(multiply(sk_c8,sk_c8),sk_c2)**.
% 0.19/0.49 284[6:Rew:261.0,266.0] || -> equal(multiply(sk_c8,sk_c2),sk_c1)**.
% 0.19/0.49 286[6:Rew:261.0,96.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.19/0.49 289[6:Rew:261.0,262.0,261.0,262.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.19/0.49 290[6:Rew:263.0,278.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c2,sk_c6).
% 0.19/0.49 291[6:Rew:290.1,273.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c7,sk_c6).
% 0.19/0.49 292[6:MRR:291.1,282.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 296[6:Rew:263.0,275.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c2,sk_c6).
% 0.19/0.49 297[6:Rew:296.1,270.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c7,sk_c6).
% 0.19/0.49 298[6:MRR:297.1,282.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 321[6:SpR:298.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.49 323[6:Rew:286.0,321.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.19/0.49 339[6:SpR:292.0,269.0] || -> equal(multiply(sk_c8,sk_c3),sk_c2)**.
% 0.19/0.49 355[0:SpR:82.0,82.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.49 361[6:SpR:283.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c2),sk_c8)**.
% 0.19/0.49 364[6:SpR:339.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c2),sk_c3)**.
% 0.19/0.49 383[6:Rew:44.0,361.0] || -> equal(multiply(sk_c7,sk_c2),sk_c8)**.
% 0.19/0.49 384[6:Rew:286.0,383.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.19/0.49 385[6:Rew:284.0,384.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.49 386[6:Rew:385.0,50.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 390[6:Rew:44.0,386.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 391[6:Rew:390.0,247.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 392[6:Rew:390.0,282.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.49 393[6:Rew:390.0,44.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 394[6:Rew:390.0,46.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 403[6:Rew:283.0,391.0] || -> equal(sk_c2,sk_c6)**.
% 0.19/0.49 406[6:Rew:403.0,283.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 418[6:Rew:394.0,364.0,393.0,364.0,403.0,364.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 420[6:Rew:418.0,323.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.19/0.49 448[6:Rew:289.0,420.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 449[6:Rew:448.0,406.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 451[6:MRR:449.0,392.0] || -> .
% 0.19/0.49 458[5:Spt:451.0,13.0,50.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.49 459[5:Spt:451.0,13.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 461[5:MRR:18.1,458.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 462[5:MRR:15.1,458.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 463[5:MRR:17.0,458.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 464[5:MRR:16.0,458.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 465[5:MRR:14.0,458.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 494[5:SpR:463.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 496[5:Rew:461.0,494.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 497[5:Rew:464.0,496.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 498[5:Rew:497.0,459.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 502[5:Rew:497.0,62.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.19/0.49 507[5:Rew:497.0,465.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 511[5:Rew:497.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 517[5:Rew:498.0,502.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 518[5:Rew:517.0,63.0] || -> equal(multiply(sk_c6,sk_c2),sk_c6)**.
% 0.19/0.49 519[5:Rew:517.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 522[5:Rew:519.0,518.0] || -> equal(sk_c2,sk_c6)**.
% 0.19/0.49 524[5:Rew:522.0,48.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.49 534[5:Rew:524.0,511.0,517.0,511.0] || equal(sk_c6,sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 564[5:SpR:507.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 566[5:Rew:498.0,564.0,462.0,564.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 573[5:Rew:566.0,519.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 576[5:Rew:566.0,534.0] || equal(sk_c8,sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 588[5:Obv:576.0] || equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 589[5:Rew:573.0,588.1] || equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.49 590[5:Obv:589.0] || equal(u,sk_c8)* -> .
% 0.19/0.49 591[5:UnC:590.0,497.0] || -> .
% 0.19/0.49 592[4:Spt:591.0,31.0,48.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.19/0.49 593[4:Spt:591.0,31.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 594[4:MRR:36.1,592.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 595[4:MRR:33.1,592.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 596[4:MRR:35.0,592.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 597[4:MRR:34.0,592.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 598[4:MRR:32.0,592.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 621[4:SpR:596.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 623[4:Rew:594.0,621.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 624[4:Rew:597.0,623.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 625[4:Rew:624.0,593.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 626[4:Rew:624.0,44.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 627[4:Rew:624.0,62.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.19/0.49 638[4:Rew:624.0,598.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 640[4:Rew:624.0,53.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 644[4:Rew:625.0,627.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 645[4:Rew:644.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 654[4:Rew:644.0,640.0] || equal(inverse(sk_c6),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 675[4:SpR:638.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 677[4:Rew:625.0,675.0,595.0,675.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 683[4:Rew:677.0,645.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 686[4:Rew:677.0,654.0] || equal(inverse(sk_c8),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 698[4:Rew:626.0,686.0] || equal(sk_c8,sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 699[4:Obv:698.0] || equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.49 700[4:Rew:683.0,699.1] || equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.49 701[4:Obv:700.0] || equal(u,sk_c8)* -> .
% 0.19/0.49 702[4:UnC:701.0,624.0] || -> .
% 0.19/0.49 703[3:Spt:702.0,19.1,46.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.49 704[3:Spt:702.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 705[3:MRR:24.1,703.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 707[3:MRR:23.1,703.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 708[3:MRR:22.1,703.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 711[3:SpR:704.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.49 713[3:Rew:44.0,711.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 725[3:SpR:707.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 727[3:Rew:705.0,725.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 728[3:Rew:708.0,727.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 734[3:Rew:728.0,703.0] || equal(multiply(sk_c8,sk_c6),sk_c8)** -> .
% 0.19/0.49 742[3:Rew:728.0,713.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 748[3:Rew:742.0,734.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 749[3:Obv:748.0] || -> .
% 0.19/0.49 754[2:Spt:749.0,1.0,44.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.49 755[2:Spt:749.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 756[2:MRR:6.1,754.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 757[2:MRR:3.1,754.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 758[2:MRR:5.0,754.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 759[2:MRR:4.0,754.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 760[2:MRR:2.0,754.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 762[2:SpR:755.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.49 769[2:SpR:758.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 771[2:Rew:756.0,769.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 772[2:Rew:759.0,771.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 773[2:Rew:772.0,755.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 774[2:Rew:772.0,754.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.19/0.49 775[2:Rew:772.0,759.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 776[2:Rew:772.0,760.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 782[2:Rew:772.0,762.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.49 789[2:SpR:775.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.49 791[2:Rew:39.0,789.0] || -> equal(identity,sk_c5)**.
% 0.19/0.49 792[2:Rew:791.0,38.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.49 793[2:Rew:791.0,39.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.49 800[2:SpR:776.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 802[2:Rew:773.0,800.0,757.0,800.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 804[2:Rew:802.0,782.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.49 806[2:Rew:793.0,804.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.49 810[2:Rew:806.0,792.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 811[2:Rew:806.0,793.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.49 833[2:SpR:757.0,811.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.49 838[2:Rew:810.0,833.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 839[2:Rew:838.0,757.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 841[2:MRR:839.0,774.0] || -> .
% 0.19/0.49 847[1:Spt:841.0,41.1,41.2,41.3,41.5,41.6,41.8,41.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.19/0.49 849[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 850[2:Rew:849.0,847.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.19/0.49 852[2:Obv:850.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) -> .
% 0.19/0.49 854[2:SpR:849.0,82.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 856[3:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 858[3:Rew:856.0,852.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.49 859[3:Obv:858.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.49 865[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 866[4:SpR:865.0,82.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.19/0.49 871[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 873[5:SpR:871.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.19/0.49 875[5:Rew:865.0,873.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.49 877[5:Rew:875.0,859.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.19/0.49 883[5:SpR:875.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.49 885[5:Rew:849.0,883.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.49 887[5:SpR:885.0,82.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.49 889[5:Rew:39.0,887.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 890[5:Rew:889.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 891[5:Rew:889.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.49 892[5:Rew:890.0,875.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 893[5:Rew:890.0,856.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.49 900[5:Rew:892.0,849.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 909[5:Rew:892.0,877.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.19/0.49 913[5:Rew:892.0,893.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 930[5:Rew:913.0,909.4,892.0,909.3,913.0,909.2,913.0,909.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.49 931[5:Obv:930.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 932[5:Con:931.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.49 949[5:SpR:891.0,82.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.19/0.49 960[5:Rew:355.0,949.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 961[5:Rew:960.0,932.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.49 973[5:SpL:900.0,961.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 974[5:Obv:973.1] || -> .
% 0.19/0.49 975[5:Spt:974.0,7.1,871.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.19/0.49 976[5:Spt:974.0,7.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 977[5:MRR:12.1,975.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 978[5:MRR:9.1,975.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 979[5:MRR:11.1,975.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 980[5:MRR:10.1,975.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 981[5:MRR:8.1,975.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 986[5:SpR:976.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 1001[5:SpR:979.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 1003[5:Rew:977.0,1001.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 1004[5:Rew:980.0,1003.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1005[5:Rew:1004.0,976.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 1010[5:Rew:1004.0,975.0] || equal(multiply(sk_c1,sk_c8),sk_c8)** -> .
% 0.19/0.49 1011[5:Rew:1004.0,854.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.19/0.49 1013[5:Rew:1004.0,986.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.19/0.49 1016[5:Rew:1004.0,981.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 1021[5:Rew:1011.0,1013.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 1051[5:SpR:1016.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 1053[5:Rew:1005.0,1051.0,978.0,1051.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 1058[5:Rew:1053.0,1021.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 1066[5:Rew:1058.0,866.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.49 1067[5:UnC:1066.0,1010.0] || -> .
% 0.19/0.49 1070[4:Spt:1067.0,13.0,865.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.49 1071[4:Spt:1067.0,13.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 1072[4:MRR:18.1,1070.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 1073[4:MRR:15.1,1070.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 1074[4:MRR:17.0,1070.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 1075[4:MRR:16.0,1070.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 1076[4:MRR:14.0,1070.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 1077[4:Rew:1071.0,859.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.49 1078[4:Obv:1077.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.49 1081[4:SpR:1071.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.49 1099[4:SpR:1074.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 1101[4:Rew:1072.0,1099.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 1102[4:Rew:1075.0,1101.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1103[4:Rew:1102.0,1071.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 1104[4:Rew:1102.0,849.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 1108[4:Rew:1102.0,854.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.19/0.49 1110[4:Rew:1102.0,1081.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.19/0.49 1113[4:Rew:1102.0,1076.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 1114[4:Rew:1102.0,1078.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.49 1118[4:Rew:1108.0,1110.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 1121[4:Rew:1102.0,1114.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1142[4:SpR:1113.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 1144[4:Rew:1103.0,1142.0,1073.0,1142.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 1148[4:Rew:1144.0,1118.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 1149[4:Rew:1144.0,1121.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1156[4:Rew:1144.0,1149.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1157[4:Con:1156.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.49 1168[0:SpR:39.0,82.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.49 1170[4:SpR:1072.0,39.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.49 1171[4:SpR:1073.0,39.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.19/0.49 1172[4:SpR:1104.0,39.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.19/0.49 1173[4:Rew:1148.0,1170.0] || -> equal(identity,sk_c4)**.
% 0.19/0.49 1177[4:Rew:1148.0,1171.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1178[4:Rew:1173.0,1177.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 1181[4:Rew:1178.0,1173.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1182[4:Rew:1148.0,1172.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 1183[4:Rew:1181.0,1182.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 1187[4:Rew:1183.0,1181.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 1193[4:Rew:355.0,1168.0,1187.0,1168.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1194[4:Rew:1193.0,1157.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.49 1245[4:SpL:1104.0,1194.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 1247[4:Obv:1245.1] || -> .
% 0.19/0.49 1248[3:Spt:1247.0,19.1,856.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.49 1249[3:Spt:1247.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 1250[0:Rew:355.0,1168.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.49 1251[3:MRR:24.1,1248.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 1254[3:MRR:23.1,1248.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 1255[3:MRR:22.1,1248.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 1258[3:SpR:1249.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.49 1260[3:Rew:849.0,1258.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 1268[3:SpR:1254.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 1270[3:Rew:1251.0,1268.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 1271[3:Rew:1255.0,1270.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1274[3:Rew:1271.0,1248.0] || equal(multiply(sk_c8,sk_c6),sk_c8)** -> .
% 0.19/0.49 1278[3:Rew:1271.0,1260.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 1280[3:Rew:1278.0,1274.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 1281[3:Obv:1280.0] || -> .
% 0.19/0.49 1283[2:Spt:1281.0,1.0,849.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.49 1284[2:Spt:1281.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 1285[2:MRR:6.1,1283.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 1286[2:MRR:3.1,1283.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 1287[2:MRR:5.0,1283.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.49 1288[2:MRR:4.0,1283.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.49 1289[2:MRR:2.0,1283.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.49 1291[2:SpR:1284.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.49 1298[2:SpR:1287.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.49 1300[2:Rew:1285.0,1298.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 1301[2:Rew:1288.0,1300.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1302[2:Rew:1301.0,1284.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.49 1303[2:Rew:1301.0,1283.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.19/0.49 1304[2:Rew:1301.0,1288.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.49 1305[2:Rew:1301.0,1289.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.49 1306[2:Rew:1301.0,1291.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.49 1313[2:SpR:1304.0,82.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.49 1315[2:Rew:39.0,1313.0] || -> equal(identity,sk_c5)**.
% 0.19/0.49 1317[2:Rew:1315.0,39.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.49 1319[2:Rew:1315.0,1250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.49 1324[2:SpR:1305.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.49 1326[2:Rew:1302.0,1324.0,1286.0,1324.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.49 1328[2:Rew:1326.0,1306.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.49 1330[2:Rew:1317.0,1328.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.49 1331[2:Rew:1330.0,1287.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.49 1334[2:Rew:1330.0,1319.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1341[2:Rew:1334.0,1331.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.49 1343[2:Rew:1341.0,1285.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 1345[2:MRR:1343.0,1303.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 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_18 prove_this_19 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 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
% 0.19/0.49
%------------------------------------------------------------------------------