TSTP Solution File: GRP381-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP381-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP381-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 11:50:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 675 clauses, backtracked 342 clauses, performed 11 splits and kept 632 clauses.
% 0.19/0.45 SPASS allocated 63557 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.05 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 5, length 324 :
% 0.19/0.45 % SZS output start Refutation
% 0.19/0.45 1[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.45 3[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.45 5[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 8[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.19/0.45 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 11[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 15[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 16[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.45 20[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 23[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 25[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 26[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 28[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 29[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 30[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.45 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.45 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.45 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.45 35[1:Spt:31.2,31.7] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.45 36[2:Spt:1.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 38[3:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.45 40[4:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.45 43[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c7) -> .
% 0.19/0.45 44[5:Spt:5.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 46[6:Spt:3.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 48[6:SpL:46.0,35.1] || equal(inverse(sk_c3),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 49[6:Obv:48.1] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.19/0.45 50[6:Rew:40.0,49.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.45 52[3:SpR:38.0,33.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.45 53[4:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.45 54[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c7) -> .
% 0.19/0.45 59[2:SpR:36.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.45 60[3:SpR:52.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.45 62[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.45 65[3:Rew:32.0,60.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.45 66[0:Rew:32.0,62.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.45 68[4:SpR:53.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.45 70[4:Rew:32.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.45 73[5:SpR:44.0,65.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.45 83[0:SpR:66.0,66.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.45 86[2:SpR:36.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.45 88[3:SpR:65.0,66.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c4,u))**.
% 0.19/0.45 89[5:SpR:73.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.45 91[0:SpR:33.0,66.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.45 95[4:SpR:70.0,66.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c3,u))**.
% 0.19/0.45 99[5:Rew:86.0,89.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 103[3:Rew:88.0,86.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.45 104[5:Rew:44.0,103.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 105[6:MRR:104.0,50.0] || -> .
% 0.19/0.45 107[0:Rew:83.0,91.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.45 109[6:Spt:105.0,3.1,46.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.45 110[6:Spt:105.0,3.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 112[5:Rew:99.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.45 125[6:Rew:99.0,110.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 126[6:Rew:125.0,95.0] || -> equal(multiply(sk_c3,u),multiply(sk_c7,u))**.
% 0.19/0.45 128[6:Rew:99.0,109.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.45 130[6:Rew:126.0,128.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.45 131[6:Rew:112.0,130.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.45 135[6:Rew:112.0,28.1,99.0,28.1,126.0,28.1,99.0,28.0] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c5,sk_c7).
% 0.19/0.45 136[6:MRR:135.1,131.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.45 145[6:Rew:99.0,23.1,112.0,23.0,99.0,23.0,126.0,23.0] || -> equal(sk_c5,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.45 146[6:MRR:145.0,131.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.45 181[6:SpR:146.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.19/0.45 183[6:Rew:112.0,181.0,136.0,181.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 184[6:MRR:183.0,131.0] || -> .
% 0.19/0.45 185[5:Spt:184.0,5.1,44.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.45 186[5:Spt:184.0,5.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 187[5:Rew:103.0,185.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.45 188[5:Rew:186.0,95.0] || -> equal(multiply(sk_c3,u),multiply(sk_c6,u))**.
% 0.19/0.45 189[5:Rew:188.0,70.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.45 192[3:Rew:103.0,30.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.19/0.45 193[5:MRR:192.1,187.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 194[3:Rew:103.0,20.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.45 195[5:MRR:194.1,187.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.45 199[3:Rew:103.0,25.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 200[5:MRR:199.0,187.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 201[3:Rew:103.0,15.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 202[5:MRR:201.0,187.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 205[5:SpR:186.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 207[5:Rew:59.0,205.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 213[5:SpR:195.0,66.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.45 215[3:SpR:103.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.45 224[5:SpR:200.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 226[5:Rew:193.0,224.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.45 227[5:Rew:36.0,226.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 230[5:Rew:227.0,207.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 235[5:Rew:230.0,189.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 250[5:Rew:235.0,213.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.45 262[5:Rew:250.0,202.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 263[5:MRR:262.0,187.0] || -> .
% 0.19/0.45 269[4:Spt:263.0,2.0,40.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.45 270[4:Spt:263.0,2.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 271[4:MRR:27.0,269.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 273[4:MRR:22.0,269.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 275[4:MRR:7.0,269.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 276[4:SpR:270.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 278[4:Rew:59.0,276.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 280[4:Rew:278.0,215.0] || -> equal(multiply(sk_c4,u),multiply(sk_c7,u))**.
% 0.19/0.45 282[4:Rew:280.0,88.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c7,u))**.
% 0.19/0.45 297[3:SpR:52.0,66.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.45 299[4:Rew:107.0,297.0,282.0,297.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.45 301[4:Rew:299.0,52.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.45 303[4:Rew:36.0,301.0] || -> equal(identity,sk_c5)**.
% 0.19/0.45 304[4:Rew:303.0,107.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.45 309[4:Rew:303.0,54.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c5,sk_c7) -> .
% 0.19/0.45 310[4:Rew:304.0,275.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 311[4:Rew:310.0,270.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 312[4:Rew:310.0,271.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.45 313[4:Rew:310.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.45 317[4:Rew:310.0,273.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.45 325[4:Rew:311.0,309.0,311.0,309.0,310.0,309.0] || equal(sk_c7,sk_c7) equal(sk_c5,sk_c7)** -> .
% 0.19/0.45 326[4:Obv:325.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.45 342[4:SpR:317.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.19/0.45 344[4:Rew:313.0,342.0,312.0,342.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 345[4:MRR:344.0,326.0] || -> .
% 0.19/0.45 346[3:Spt:345.0,4.0,38.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.45 347[3:Spt:345.0,4.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 348[3:MRR:29.0,346.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 350[3:MRR:24.0,346.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 352[3:MRR:9.0,346.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 353[3:SpR:347.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 355[3:Rew:59.0,353.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 357[3:SpR:348.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.45 366[3:SpR:350.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 368[3:Rew:36.0,366.0,348.0,366.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 371[3:Rew:368.0,352.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.45 372[3:Rew:368.0,355.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 373[3:Rew:372.0,371.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 375[3:Rew:372.0,357.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.45 378[3:Rew:373.0,348.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.45 381[3:Rew:373.0,43.0] || equal(inverse(identity),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.45 391[3:Rew:373.0,381.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 392[3:Obv:391.1] || equal(inverse(identity),sk_c7)** -> .
% 0.19/0.45 417[3:SpR:375.0,107.0] || -> equal(identity,sk_c2)**.
% 0.19/0.45 420[3:Rew:417.0,392.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.45 425[3:Rew:378.0,420.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 426[3:Obv:425.0] || -> .
% 0.19/0.45 429[2:Spt:426.0,1.1,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.45 430[2:Spt:426.0,1.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 431[2:MRR:26.1,429.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 432[2:MRR:16.1,429.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.45 433[2:MRR:21.0,429.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 434[2:MRR:11.0,429.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 435[2:MRR:6.0,429.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 443[2:SpR:433.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 445[2:Rew:431.0,443.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.45 452[2:SpR:435.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.19/0.45 455[2:SpR:445.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.45 457[2:Rew:33.0,455.0] || -> equal(identity,sk_c7)**.
% 0.19/0.45 458[2:Rew:457.0,107.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 463[2:Rew:457.0,54.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 464[2:Rew:458.0,434.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.45 465[2:Rew:458.0,452.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.45 466[2:Rew:464.0,432.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.45 469[2:Rew:465.0,466.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 473[2:Rew:469.0,465.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.45 488[2:Obv:463.1] || equal(inverse(inverse(sk_c6)),sk_c6)** -> .
% 0.19/0.45 489[2:Rew:473.0,488.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.45 490[2:Rew:430.0,489.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.45 491[2:Obv:490.0] || -> .
% 0.19/0.45 492[1:Spt:491.0,31.0,31.1,31.3,31.4,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.45 494[2:Spt:1.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 495[2:Rew:494.0,492.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.45 497[2:Obv:495.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.45 499[2:SpR:494.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.45 500[2:SpR:494.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.45 502[3:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.45 503[3:SpR:502.0,66.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.45 505[4:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.45 506[4:SpR:505.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.45 508[5:Spt:3.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 510[5:SpR:508.0,66.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.19/0.45 512[5:Rew:502.0,510.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.45 514[5:SpR:512.0,66.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.45 516[6:Spt:5.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 518[6:SpR:516.0,66.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.19/0.45 520[6:Rew:505.0,518.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.45 522[6:SpR:520.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.45 524[6:Rew:500.0,522.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 525[6:Rew:524.0,494.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.45 526[6:Rew:524.0,505.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.45 528[6:Rew:524.0,512.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.45 529[6:Rew:524.0,516.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.45 532[6:Rew:524.0,497.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.45 533[6:Rew:524.0,500.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.19/0.45 540[6:Rew:525.0,528.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 542[6:Rew:540.0,529.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.45 544[6:Rew:33.0,533.0,540.0,533.0] || -> equal(identity,sk_c7)**.
% 0.19/0.45 546[6:Rew:544.0,107.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 550[6:Rew:546.0,542.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.45 552[6:Rew:550.0,526.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 562[6:Rew:524.0,532.7,546.0,532.7,540.0,532.7,546.0,532.6,524.0,532.6,546.0,532.5,524.0,532.5,546.0,532.4,540.0,532.4,524.0,532.4,552.0,532.3,524.0,532.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.45 563[6:Obv:562.7] || 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) -> .
% 0.19/0.45 564[6:Con:563.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 608[6:SpL:552.0,564.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 610[6:Obv:608.1] || -> .
% 0.19/0.45 611[6:Spt:610.0,5.1,516.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.45 612[6:Spt:610.0,5.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 613[6:Rew:612.0,514.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.45 614[6:MRR:30.1,611.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 616[6:MRR:25.0,611.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 623[6:SpR:612.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 625[6:Rew:499.0,623.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 636[6:SpR:616.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 638[6:Rew:614.0,636.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.45 639[6:Rew:494.0,638.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 642[6:Rew:639.0,611.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.19/0.45 646[6:Rew:639.0,625.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 649[6:Rew:646.0,613.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 653[6:Rew:646.0,506.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.45 666[6:Rew:653.0,642.0,649.0,642.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 667[6:Obv:666.0] || -> .
% 0.19/0.45 675[5:Spt:667.0,3.1,508.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.45 676[5:Spt:667.0,3.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 677[5:MRR:28.1,675.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 679[5:MRR:23.0,675.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 681[5:MRR:8.0,675.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 686[5:SpR:676.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 688[5:Rew:499.0,686.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 689[5:Rew:688.0,499.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 701[5:SpR:679.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 703[5:Rew:494.0,701.0,677.0,701.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 706[5:Rew:703.0,681.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.45 709[5:Rew:703.0,688.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 710[5:Rew:709.0,706.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 713[5:Rew:709.0,689.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 719[5:Rew:710.0,675.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.45 724[5:Rew:713.0,503.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.45 726[5:Rew:724.0,719.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 727[5:Obv:726.0] || -> .
% 0.19/0.45 733[4:Spt:727.0,4.0,505.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.45 734[4:Spt:727.0,4.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 735[4:MRR:29.0,733.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 737[4:MRR:24.0,733.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 739[4:MRR:9.0,733.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 740[4:Rew:739.0,497.7,734.0,497.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 741[4:Obv:740.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 744[4:SpR:734.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 746[4:Rew:499.0,744.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 747[4:Rew:746.0,499.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 748[4:SpR:735.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.45 757[4:SpR:737.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 759[4:Rew:494.0,757.0,735.0,757.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 762[4:Rew:759.0,739.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.45 763[4:Rew:759.0,741.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 765[4:Rew:759.0,746.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 766[4:Rew:765.0,762.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 768[4:Rew:765.0,748.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.45 769[4:Rew:765.0,747.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 770[4:Rew:766.0,734.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 781[4:Rew:766.0,763.5,766.0,763.4,766.0,763.3,766.0,763.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.45 782[4:Con:781.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.45 805[4:SpR:768.0,107.0] || -> equal(identity,sk_c2)**.
% 0.19/0.45 807[4:Rew:805.0,107.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.45 810[4:Rew:805.0,33.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.45 817[4:SpR:502.0,810.0] || -> equal(multiply(sk_c7,sk_c3),sk_c2)**.
% 0.19/0.45 819[4:SpR:770.0,810.0] || -> equal(multiply(sk_c7,sk_c7),sk_c2)**.
% 0.19/0.45 821[4:Rew:769.0,817.0] || -> equal(sk_c2,sk_c3)**.
% 0.19/0.45 826[4:Rew:821.0,807.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.45 830[4:Rew:769.0,819.0,821.0,819.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.45 837[4:Rew:830.0,826.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 838[4:Rew:837.0,782.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 866[4:SpL:770.0,838.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 867[4:Obv:866.1] || -> .
% 0.19/0.45 868[3:Spt:867.0,2.0,502.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.45 869[3:Spt:867.0,2.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 870[3:MRR:27.0,868.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 871[3:MRR:17.0,868.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.45 872[3:MRR:22.0,868.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 874[3:MRR:7.0,868.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 875[3:Rew:874.0,497.7,869.0,497.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 876[3:Obv:875.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 879[3:SpR:869.0,66.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 881[3:Rew:499.0,879.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 882[3:Rew:881.0,499.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 892[3:SpR:872.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 894[3:Rew:494.0,892.0,870.0,892.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.45 897[3:Rew:894.0,874.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.45 898[3:Rew:894.0,876.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 900[3:Rew:894.0,881.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.45 901[3:Rew:900.0,897.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 904[3:Rew:900.0,882.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 905[3:Rew:901.0,869.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 914[3:Rew:901.0,898.5,901.0,898.4,901.0,898.3,901.0,898.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.45 915[3:Con:914.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.45 938[0:SpR:33.0,107.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.45 940[3:SpR:871.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.45 944[3:Rew:904.0,940.0] || -> equal(identity,sk_c1)**.
% 0.19/0.45 946[3:Rew:944.0,107.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.45 948[3:Rew:944.0,938.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.45 949[3:Rew:871.0,948.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.45 959[3:Rew:949.0,946.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 960[3:Rew:959.0,915.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 986[3:SpL:905.0,960.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 987[3:Obv:986.1] || -> .
% 0.19/0.45 988[2:Spt:987.0,1.1,494.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.45 989[2:Spt:987.0,1.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 991[2:MRR:26.1,988.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.45 994[2:MRR:21.0,988.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.45 996[2:MRR:6.0,988.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.45 1007[2:SpR:994.0,66.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.45 1009[2:Rew:991.0,1007.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.45 1010[2:Rew:1009.0,988.0] || equal(sk_c5,sk_c6)** -> .
% 0.19/0.45 1016[2:SpR:996.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.19/0.45 1023[2:SpR:1009.0,66.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.45 1025[2:Rew:33.0,1023.0] || -> equal(identity,sk_c7)**.
% 0.19/0.45 1026[2:Rew:1025.0,938.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 1027[2:Rew:1025.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 1030[2:Rew:989.0,1026.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 1031[2:Rew:1030.0,989.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 1034[2:Rew:1030.0,1010.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.46 1043[2:Rew:1030.0,1016.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.46 1053[2:Rew:1027.0,1043.0,1031.0,1043.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 1054[2:MRR:1053.0,1034.0] || -> .
% 0.19/0.46 % SZS output end Refutation
% 0.19/0.46 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_11 prove_this_15 prove_this_16 prove_this_17 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.46
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