TSTP Solution File: GRP212-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP212-1 : 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 11:46:21 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
% 0.00/0.12 % Problem : GRP212-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 : Mon Jun 13 22:40:24 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 1079 clauses, backtracked 353 clauses, performed 10 splits and kept 737 clauses.
% 0.19/0.49 SPASS allocated 63763 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.03 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 4, length 410 :
% 0.19/0.49 % SZS output start Refutation
% 0.19/0.49 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.49 4[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.49 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.49 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 7[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c1),sk_c2).
% 0.19/0.49 8[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c2).
% 0.19/0.49 9[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 10[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 11[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c2).
% 0.19/0.49 13[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 14[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.49 16[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.49 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.49 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 19[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c3),sk_c8).
% 0.19/0.49 20[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 21[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 22[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 23[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 25[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.49 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.49 28[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c3,sk_c7),sk_c8).
% 0.19/0.49 31[0:Inp] || equal(multiply(u,v),sk_c8)** equal(inverse(u),v) equal(multiply(v,sk_c7),sk_c8)** equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(inverse(sk_c8),sk_c7) equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.19/0.49 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.49 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.49 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.49 35[0:Con:31.6] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),y)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** -> .
% 0.19/0.49 36[1:Spt:35.0,35.4,35.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.49 37[2:Spt:7.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.49 39[3:Spt:19.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 41[4:Spt:1.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 43[4:SpL:41.0,36.1] || equal(inverse(sk_c1),sk_c2) equal(sk_c8,sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 44[4:Obv:43.1] || equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 45[4:Rew:37.0,44.0] || equal(sk_c2,sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 46[4:Obv:45.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 47[4:MRR:18.1,46.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 48[4:MRR:14.1,46.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 49[4:MRR:13.1,46.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 50[4:MRR:17.1,46.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 51[4:MRR:16.1,46.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 52[4:MRR:15.1,46.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 64[4:SpL:52.0,36.1] || equal(inverse(sk_c4),sk_c7) equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 65[4:Obv:64.1] || equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 66[4:Rew:48.0,65.0] || equal(sk_c8,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 68[1:SpL:32.0,36.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 71[3:SpR:39.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.19/0.49 72[4:SpR:47.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.49 73[4:SpR:48.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.49 74[4:SpR:49.0,33.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.49 75[1:SpL:33.0,36.1] || equal(inverse(inverse(u)),u) equal(sk_c8,identity) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 78[4:SpR:52.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.49 83[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.49 85[0:Rew:32.0,83.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.49 93[3:SpL:71.0,36.1] || equal(inverse(sk_c8),sk_c3) equal(sk_c8,identity) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.49 96[4:SpR:72.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.49 99[4:Rew:32.0,96.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.49 107[4:SpR:74.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.19/0.49 110[4:Rew:32.0,107.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 127[4:SpR:50.0,99.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 129[4:Rew:51.0,127.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 135[4:Rew:129.0,49.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 137[4:Rew:129.0,51.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 142[4:Rew:129.0,73.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.49 143[4:Rew:129.0,74.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.49 150[4:Rew:129.0,66.0] || equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 160[4:Rew:129.0,78.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 163[4:Rew:129.0,110.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.49 170[4:Obv:150.0] || equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 171[4:Rew:143.0,170.0,129.0,170.0] || equal(identity,sk_c7)** -> .
% 0.19/0.49 218[0:SpR:85.0,85.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.49 221[0:SpR:33.0,85.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.49 228[4:SpR:137.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 231[4:SpR:142.0,85.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.19/0.49 242[4:Rew:143.0,228.0,135.0,228.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 246[4:Rew:242.0,171.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.49 250[4:Rew:242.0,143.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 271[4:Rew:135.0,231.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.19/0.49 272[4:Rew:242.0,271.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.19/0.49 273[4:Rew:137.0,272.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.49 277[4:Rew:273.0,160.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 290[4:Rew:163.0,277.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 294[4:Rew:290.0,250.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 295[4:MRR:294.0,246.0] || -> .
% 0.19/0.49 301[4:Spt:295.0,1.1,41.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.19/0.49 302[4:Spt:295.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 304[0:Rew:218.0,221.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.49 305[4:MRR:6.1,301.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 306[4:MRR:2.1,301.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 307[4:MRR:5.1,301.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 308[4:MRR:4.1,301.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 309[4:MRR:3.1,301.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 310[4:Rew:302.0,93.0] || equal(sk_c3,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.49 322[3:SpR:71.0,85.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.19/0.49 324[4:Rew:302.0,322.0] || -> equal(multiply(sk_c7,identity),sk_c3)**.
% 0.19/0.49 325[4:Rew:304.0,324.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.49 327[4:Rew:325.0,71.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.49 330[4:Rew:325.0,310.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.49 332[4:Obv:330.0] || equal(sk_c8,identity) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.49 333[4:Rew:325.0,332.1] || equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 336[4:SpR:307.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 338[4:Rew:305.0,336.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 339[4:Rew:308.0,338.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 340[4:Rew:339.0,302.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 342[4:Rew:339.0,306.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.49 345[4:Rew:339.0,308.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 346[4:Rew:339.0,309.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 347[4:Rew:339.0,333.0] || equal(identity,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.49 359[4:Rew:339.0,327.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.49 362[4:Rew:359.0,347.1,339.0,347.1] || equal(identity,sk_c7)** equal(identity,sk_c7)** -> .
% 0.19/0.49 363[4:Obv:362.0] || equal(identity,sk_c7)** -> .
% 0.19/0.49 391[4:SpR:345.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 393[4:Rew:340.0,391.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 394[4:Rew:359.0,393.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 395[4:Rew:394.0,363.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.49 402[4:Rew:394.0,359.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 407[4:SpR:346.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 409[4:Rew:342.0,407.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 410[4:Rew:402.0,409.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 411[4:MRR:410.0,395.0] || -> .
% 0.19/0.49 412[3:Spt:411.0,19.1,39.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.19/0.49 413[3:Spt:411.0,19.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 414[3:MRR:24.1,412.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 415[3:MRR:20.1,412.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 416[3:MRR:23.0,412.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 417[3:MRR:22.0,412.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 418[3:MRR:21.0,412.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 422[3:SpR:413.0,85.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 434[3:SpR:416.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 436[3:Rew:414.0,434.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 437[3:Rew:417.0,436.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 438[3:Rew:437.0,413.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 439[3:Rew:437.0,414.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.49 440[3:Rew:437.0,415.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.49 443[3:Rew:437.0,417.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 444[3:Rew:437.0,418.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 447[3:Rew:437.0,75.2] || equal(inverse(inverse(u)),u) equal(sk_c8,identity) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 451[3:Rew:437.0,422.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.49 457[3:Rew:437.0,447.1] || equal(inverse(inverse(u)),u) equal(identity,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 472[3:SpR:443.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.49 473[3:SpR:443.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 475[3:Rew:438.0,473.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 477[3:SpR:444.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 479[3:Rew:440.0,477.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 480[3:Rew:475.0,479.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 484[3:Rew:480.0,472.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 486[3:Rew:451.0,484.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 505[0:SpR:33.0,85.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.49 506[0:SpR:33.0,304.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.49 510[3:SpR:439.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.19/0.49 515[3:Rew:486.0,510.0] || -> equal(identity,sk_c5)**.
% 0.19/0.49 517[3:Rew:515.0,304.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.49 520[3:Rew:515.0,457.1] || equal(inverse(inverse(u)),u) equal(sk_c5,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 522[3:Rew:515.0,506.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.19/0.49 524[3:Rew:439.0,522.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.49 527[3:Rew:524.0,515.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 534[3:Rew:524.0,517.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 541[3:Rew:534.0,505.0,527.0,505.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.49 550[3:Rew:534.0,520.2,524.0,520.1,541.0,520.0] || equal(u,u)* equal(sk_c7,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.49 551[3:Obv:550.1] || equal(u,sk_c7)* -> .
% 0.19/0.49 552[3:UnC:551.0,480.0] || -> .
% 0.19/0.49 553[2:Spt:552.0,7.1,37.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.19/0.49 554[2:Spt:552.0,7.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 555[0:Rew:304.0,505.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.49 556[2:MRR:12.1,553.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 557[2:MRR:8.1,553.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 559[2:MRR:11.0,553.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 560[2:MRR:10.0,553.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 561[2:MRR:9.0,553.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 563[1:Rew:506.0,68.0] || equal(identity,u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 566[2:SpR:554.0,85.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 576[2:SpR:559.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 578[2:Rew:556.0,576.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 579[2:Rew:560.0,578.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 580[2:Rew:579.0,554.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 582[2:Rew:579.0,557.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.49 584[2:Rew:579.0,560.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 585[2:Rew:579.0,561.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 586[2:Rew:579.0,563.1] || equal(identity,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 590[2:Rew:579.0,566.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.49 595[2:Rew:579.0,586.2] || equal(identity,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 609[2:SpR:584.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.49 610[2:SpR:584.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 612[2:Rew:580.0,610.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 614[2:SpR:585.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 616[2:Rew:582.0,614.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 617[2:Rew:612.0,616.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 621[2:Rew:617.0,609.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 623[2:Rew:590.0,621.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 638[2:SpR:580.0,33.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.49 641[2:Rew:623.0,638.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 645[2:Rew:641.0,304.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 647[2:Rew:641.0,595.0] || equal(sk_c7,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 662[2:Obv:647.0] || equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 663[2:Rew:645.0,662.1] || equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.49 664[2:Obv:663.0] || equal(u,sk_c7)* -> .
% 0.19/0.49 665[2:UnC:664.0,617.0] || -> .
% 0.19/0.49 666[1:Spt:665.0,35.1,35.2,35.3,35.5,35.6,35.8] || 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_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.19/0.49 669[1:EqR:666.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 671[2:Spt:19.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.49 674[2:Rew:671.0,669.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 675[2:Obv:674.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 678[2:SpR:671.0,85.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.49 680[3:Spt:12.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 683[4:Spt:8.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 686[5:Spt:11.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 688[5:SpR:686.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 690[5:Rew:680.0,688.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 691[5:Rew:690.0,28.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.49 692[5:Rew:690.0,16.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 693[5:Rew:690.0,4.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 694[5:Rew:690.0,22.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.49 695[5:Rew:690.0,10.1] || -> equal(inverse(sk_c1),sk_c2)** equal(sk_c8,sk_c7).
% 0.19/0.49 696[5:Rew:694.1,21.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 697[5:Rew:695.1,9.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 698[5:Rew:691.0,27.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.49 705[5:SpR:690.0,85.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.49 707[5:Rew:671.0,705.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.49 708[5:SpR:707.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.19/0.49 711[5:Rew:678.0,708.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 714[0:SpR:555.0,85.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.49 717[2:SpR:671.0,555.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.49 718[3:SpR:680.0,555.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.49 719[4:SpR:683.0,555.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.49 722[3:Rew:671.0,718.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.49 727[4:Rew:671.0,719.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.49 732[5:Rew:727.0,698.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.49 733[5:Rew:727.0,697.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 734[5:Rew:727.0,696.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 755[2:SpR:671.0,33.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.49 758[2:SpR:717.0,33.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.49 759[5:Rew:707.0,755.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 762[5:Rew:759.0,304.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 765[5:Rew:759.0,758.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.49 812[6:Spt:694.1] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 813[6:Rew:812.0,671.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 814[6:Rew:812.0,707.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.49 818[6:Rew:812.0,675.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 821[6:Rew:812.0,734.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 822[6:Rew:812.0,732.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.49 826[6:Rew:814.0,733.1] || -> equal(inverse(sk_c1),sk_c2)** equal(sk_c6,sk_c7).
% 0.19/0.49 827[6:Rew:814.0,821.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.49 828[6:Rew:814.0,822.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.49 831[6:Rew:812.0,818.3,812.0,818.2,812.0,818.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 840[7:Spt:826.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 843[7:Rew:840.0,711.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 845[7:Rew:840.0,762.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 851[7:Rew:843.0,831.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 853[7:Con:851.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 854[7:Rew:845.0,853.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.49 879[7:SpL:813.0,854.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.49 880[7:Obv:879.1] || -> .
% 0.19/0.49 881[7:Spt:880.0,826.1,840.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.49 882[7:Spt:880.0,826.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.49 883[7:MRR:827.1,881.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.49 884[7:MRR:828.0,881.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.49 896[7:SpR:883.0,555.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.49 898[7:Rew:813.0,896.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.49 900[7:Rew:898.0,884.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 901[7:Rew:814.0,900.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 902[7:MRR:901.0,881.0] || -> .
% 0.19/0.49 904[6:Spt:902.0,694.1,812.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.49 905[6:Spt:902.0,694.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.49 906[6:MRR:695.1,904.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.49 908[6:MRR:692.0,904.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 909[6:MRR:693.0,904.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 925[6:SpR:906.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.49 928[6:SpR:908.0,85.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c7)**.
% 0.19/0.49 930[6:Rew:925.0,928.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 931[6:SpR:925.0,85.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.49 944[6:SpR:909.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.49 948[6:Rew:931.0,944.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 949[6:Rew:948.0,765.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 959[6:Rew:949.0,762.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 960[6:Rew:949.0,711.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 970[6:Rew:959.0,908.0] || -> equal(sk_c8,sk_c2)**.
% 0.19/0.49 971[6:Rew:970.0,904.0] || equal(sk_c7,sk_c2)** -> .
% 0.19/0.49 973[6:Rew:970.0,671.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.49 975[6:Rew:970.0,930.0] || -> equal(multiply(sk_c1,sk_c2),sk_c7)**.
% 0.19/0.49 978[6:Rew:925.0,973.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.49 986[6:Rew:978.0,971.0] || equal(sk_c2,sk_c1)** -> .
% 0.19/0.49 988[6:Rew:978.0,960.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.49 991[6:Rew:988.0,975.0,978.0,975.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.49 992[6:MRR:991.0,986.0] || -> .
% 0.19/0.49 1000[5:Spt:992.0,11.1,686.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.19/0.49 1001[5:Spt:992.0,11.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.49 1002[5:Rew:755.0,1000.0,722.0,1000.0] || equal(identity,sk_c6)** -> .
% 0.19/0.49 1006[3:Rew:755.0,5.0,722.0,5.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 1007[5:MRR:1006.0,1002.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.49 1008[3:Rew:755.0,17.0,722.0,17.0] || -> equal(identity,sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 1009[5:MRR:1008.0,1002.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 1014[5:SpR:1001.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.49 1036[5:SpR:1014.0,85.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.49 1044[5:SpR:1007.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.49 1048[5:Rew:1036.0,1044.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 1050[5:Rew:1048.0,758.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 1054[5:Rew:1048.0,675.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.49 1056[5:Rew:1050.0,506.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 1058[5:Rew:1050.0,304.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 1062[5:Rew:717.0,1056.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 1063[5:Rew:1062.0,671.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 1066[5:Rew:1062.0,1009.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.49 1071[5:Rew:1058.0,1066.0] || -> equal(sk_c7,sk_c2)**.
% 0.19/0.49 1077[5:Rew:1071.0,1062.0] || -> equal(sk_c8,sk_c2)**.
% 0.19/0.49 1078[5:Rew:1071.0,1063.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.49 1080[5:Rew:1071.0,1058.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.49 1082[5:Rew:1014.0,1078.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.49 1083[5:Rew:1082.0,1001.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.49 1087[5:Rew:1082.0,1071.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.49 1092[5:Rew:1082.0,1077.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.49 1098[5:Rew:1082.0,1080.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.49 1103[5:Rew:1098.0,1054.3,1092.0,1054.3,1087.0,1054.3,1098.0,1054.2,1087.0,1054.2,1092.0,1054.2,1092.0,1054.1,1092.0,1054.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.19/0.49 1104[5:Con:1103.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.49 1163[5:SpL:1083.0,1104.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.49 1164[5:Obv:1163.1] || -> .
% 0.19/0.49 1165[4:Spt:1164.0,8.0,683.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.49 1166[4:Spt:1164.0,8.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.49 1168[4:MRR:2.0,1165.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.50 1169[4:MRR:14.0,1165.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.50 1172[4:SpR:1166.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.50 1173[4:SpR:1166.0,714.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.50 1214[4:SpR:1168.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.50 1218[4:Rew:1173.0,1214.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1219[4:Rew:1218.0,758.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1224[4:Rew:1218.0,675.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.50 1225[4:Rew:1219.0,506.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1228[4:Rew:1219.0,304.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1231[4:Rew:717.0,1225.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1232[4:Rew:1231.0,717.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1236[4:Rew:1231.0,1169.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.50 1241[4:Rew:1228.0,1236.0] || -> equal(sk_c7,sk_c2)**.
% 0.19/0.50 1245[4:Rew:1241.0,1231.0] || -> equal(sk_c8,sk_c2)**.
% 0.19/0.50 1246[4:Rew:1241.0,1232.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.50 1248[4:Rew:1241.0,1228.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.50 1251[4:Rew:1172.0,1246.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.50 1252[4:Rew:1251.0,1166.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.50 1256[4:Rew:1251.0,1241.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.50 1260[4:Rew:1251.0,1245.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.50 1265[4:Rew:1251.0,1248.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.50 1271[4:Rew:1265.0,1224.3,1260.0,1224.3,1256.0,1224.3,1265.0,1224.2,1256.0,1224.2,1260.0,1224.2,1260.0,1224.1,1260.0,1224.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.19/0.50 1272[4:Con:1271.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.50 1321[4:SpL:1252.0,1272.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.50 1322[4:Obv:1321.1] || -> .
% 0.19/0.50 1323[3:Spt:1322.0,12.0,680.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.50 1324[3:Spt:1322.0,12.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.50 1326[3:MRR:6.0,1323.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.50 1327[3:MRR:18.0,1323.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.50 1331[3:SpR:1324.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.50 1332[3:SpR:1324.0,714.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.50 1372[3:SpR:1326.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.50 1376[3:Rew:1332.0,1372.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1377[3:Rew:1376.0,758.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1382[3:Rew:1376.0,675.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.50 1383[3:Rew:1377.0,506.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1385[3:Rew:1377.0,304.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1389[3:Rew:717.0,1383.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1390[3:Rew:1389.0,671.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1394[3:Rew:1389.0,1327.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.50 1399[3:Rew:1385.0,1394.0] || -> equal(sk_c7,sk_c2)**.
% 0.19/0.50 1402[3:Rew:1399.0,1389.0] || -> equal(sk_c8,sk_c2)**.
% 0.19/0.50 1403[3:Rew:1399.0,1390.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.50 1405[3:Rew:1399.0,1385.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.50 1408[3:Rew:1331.0,1403.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.50 1409[3:Rew:1408.0,1324.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.50 1413[3:Rew:1408.0,1399.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.50 1416[3:Rew:1408.0,1402.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.50 1421[3:Rew:1408.0,1405.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.50 1427[3:Rew:1421.0,1382.3,1416.0,1382.3,1413.0,1382.3,1421.0,1382.2,1413.0,1382.2,1416.0,1382.2,1416.0,1382.1,1416.0,1382.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.19/0.50 1428[3:Con:1427.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.50 1466[3:SpL:1409.0,1428.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.50 1467[3:Obv:1466.1] || -> .
% 0.19/0.50 1468[2:Spt:1467.0,19.0,671.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.50 1469[2:Spt:1467.0,19.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 1470[2:MRR:7.0,1468.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.50 1471[2:MRR:13.0,1468.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.50 1472[2:MRR:25.0,1468.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 1473[2:MRR:1.0,1468.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.50 1475[2:SpR:1469.0,555.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.19/0.50 1476[2:SpR:1469.0,714.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),u)**.
% 0.19/0.50 1478[2:Rew:1475.0,1468.0] || equal(sk_c3,sk_c7)** -> .
% 0.19/0.50 1486[2:SpR:1470.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.50 1487[2:SpR:1470.0,714.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.50 1502[2:SpR:1472.0,85.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.50 1504[2:Rew:1469.0,1502.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.50 1505[2:SpR:1473.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.50 1506[2:SpR:1473.0,85.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.50 1508[2:Rew:1470.0,1506.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.50 1509[2:Rew:1487.0,1505.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1510[2:Rew:1509.0,1504.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1511[2:Rew:1509.0,1476.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 1516[2:Rew:1510.0,1475.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.50 1517[2:Rew:1510.0,1471.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.50 1521[2:Rew:1510.0,1508.0] || -> equal(multiply(sk_c2,sk_c7),sk_c2)**.
% 0.19/0.50 1522[2:Rew:1510.0,1509.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1523[2:Rew:1517.0,1521.0] || -> equal(sk_c7,sk_c2)**.
% 0.19/0.50 1524[2:Rew:1523.0,1478.0] || equal(sk_c3,sk_c2)** -> .
% 0.19/0.50 1527[2:Rew:1523.0,1516.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 1531[2:Rew:1486.0,1527.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.50 1532[2:Rew:1531.0,1511.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.50 1533[2:Rew:1531.0,1524.0] || equal(sk_c2,sk_c1)** -> .
% 0.19/0.50 1535[2:Rew:1523.0,1522.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.50 1564[2:SpR:1470.0,33.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.19/0.50 1565[2:SpR:1486.0,33.0] || -> equal(multiply(sk_c1,sk_c2),identity)**.
% 0.19/0.50 1566[2:Rew:1535.0,1564.0] || -> equal(identity,sk_c1)**.
% 0.19/0.50 1574[2:Rew:1532.0,1565.0,1566.0,1565.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.50 1575[2:MRR:1574.0,1533.0] || -> .
% 0.19/0.50 % SZS output end Refutation
% 0.19/0.50 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_27 prove_this_28 prove_this_31 left_identity left_inverse associativity
% 0.19/0.50
%------------------------------------------------------------------------------