TSTP Solution File: GRP383-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP383-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP383-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 22:53:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 825 clauses, backtracked 414 clauses, performed 11 splits and kept 759 clauses.
% 0.18/0.47 SPASS allocated 63695 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.47 0:00:00.03 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.07 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 321 :
% 0.18/0.47 % SZS output start Refutation
% 0.18/0.47 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.18/0.47 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c8),sk_c7).
% 0.18/0.47 5[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 6[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 8[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.18/0.47 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 10[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.18/0.47 11[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 16[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 18[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.18/0.47 23[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.18/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 28[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 33[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.47 36[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c8)** equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,w),sk_c7)** equal(inverse(v),w) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(inverse(y),sk_c7) equal(multiply(y,sk_c6),sk_c7)** -> .
% 0.18/0.47 37[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.47 38[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.47 39[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.47 40[0:Con:36.8] || equal(inverse(u),v) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c7)**+ equal(multiply(w,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.18/0.47 41[1:Spt:40.0,40.4,40.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.18/0.47 42[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 44[2:SpL:42.0,41.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c6,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.18/0.47 45[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 47[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 49[5:Spt:5.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 51[5:SpL:49.0,41.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 52[5:Obv:51.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 53[5:Rew:45.0,52.0] || equal(sk_c6,sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 55[1:SpL:37.0,41.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.18/0.47 56[6:Spt:3.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 62[3:SpR:45.0,38.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.18/0.47 63[4:SpR:47.0,38.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.18/0.47 66[3:SpL:62.0,41.1] || equal(inverse(sk_c7),sk_c5) equal(identity,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.18/0.47 71[2:SpR:42.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.18/0.47 74[0:SpR:38.0,39.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.47 76[3:SpR:62.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.18/0.47 77[4:SpR:63.0,39.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.47 79[3:Rew:37.0,76.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 80[4:Rew:37.0,77.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.18/0.47 81[0:Rew:37.0,74.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.47 85[5:SpR:49.0,79.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 96[6:SpR:56.0,80.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 109[0:SpR:81.0,81.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.47 111[2:SpR:42.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 114[0:SpR:38.0,81.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.47 116[3:SpR:62.0,81.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.18/0.47 118[5:SpR:85.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 119[4:SpR:63.0,81.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.18/0.47 121[6:SpR:96.0,81.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.47 123[3:SpR:45.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 128[5:Rew:111.0,118.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 130[5:Rew:128.0,42.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 137[6:Rew:128.0,96.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 142[5:Rew:128.0,116.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.18/0.47 145[5:Rew:128.0,53.0] || equal(sk_c6,sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 156[6:Rew:130.0,137.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 159[6:Rew:128.0,121.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 160[6:Rew:38.0,159.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 180[6:Rew:160.0,114.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.47 188[6:Rew:109.0,180.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 195[6:Rew:156.0,145.1,188.0,145.1,128.0,145.1,156.0,145.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 196[6:Obv:195.1] || -> .
% 0.18/0.47 214[6:Spt:196.0,3.1,56.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 215[6:Spt:196.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 216[6:Rew:128.0,215.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 217[6:Rew:216.0,119.0] || -> equal(multiply(sk_c8,identity),sk_c4)**.
% 0.18/0.47 219[6:Rew:217.0,142.0,216.0,142.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.47 223[6:Rew:128.0,214.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.18/0.47 224[0:Rew:109.0,114.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.47 225[6:Rew:224.0,217.0] || -> equal(sk_c4,sk_c8)**.
% 0.18/0.47 228[6:Rew:225.0,219.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 230[6:Rew:225.0,223.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.18/0.47 237[6:Rew:130.0,230.0] || equal(sk_c6,sk_c8)** -> .
% 0.18/0.47 238[6:Rew:128.0,123.0,228.0,123.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.18/0.47 243[6:Rew:130.0,28.1,225.0,28.1,128.0,28.1] || -> equal(inverse(sk_c2),sk_c3)** equal(sk_c6,sk_c8).
% 0.18/0.47 244[6:MRR:243.1,237.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.47 250[6:Rew:128.0,33.1,130.0,33.0,225.0,33.0,128.0,33.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.18/0.47 251[6:MRR:250.0,237.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.18/0.47 252[6:Rew:128.0,23.1,130.0,23.0,225.0,23.0,128.0,23.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.18/0.47 253[6:MRR:252.0,237.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.18/0.47 287[6:SpR:251.0,39.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.18/0.47 291[6:SpR:253.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.18/0.47 293[6:Rew:251.0,291.0,244.0,291.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.47 299[6:Rew:293.0,287.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.18/0.47 305[6:Rew:238.0,299.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 306[6:Rew:305.0,130.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 312[6:MRR:306.0,237.0] || -> .
% 0.18/0.47 315[5:Spt:312.0,5.1,49.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 316[5:Spt:312.0,5.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 317[5:Rew:224.0,119.0,316.0,119.0] || -> equal(sk_c4,sk_c7)**.
% 0.18/0.47 318[5:Rew:317.0,47.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.47 320[5:Rew:224.0,116.0,318.0,116.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 322[5:Rew:320.0,62.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.18/0.47 323[5:Rew:42.0,322.0] || -> equal(identity,sk_c6)**.
% 0.18/0.47 324[5:Rew:323.0,224.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.47 330[5:Rew:324.0,315.0,320.0,315.0] || equal(sk_c7,sk_c8)** -> .
% 0.18/0.47 355[5:Rew:324.0,10.1,320.0,10.0,324.0,10.0] || -> equal(sk_c7,sk_c8)** equal(sk_c7,sk_c8)**.
% 0.18/0.47 356[5:Obv:355.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 357[5:MRR:356.0,330.0] || -> .
% 0.18/0.47 369[4:Spt:357.0,2.0,47.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 370[4:Spt:357.0,2.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 371[3:Rew:224.0,116.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.47 372[3:Rew:371.0,111.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 375[4:MRR:12.0,369.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 378[4:MRR:17.0,369.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 379[4:MRR:7.0,369.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 381[3:Rew:371.0,66.0] || equal(sk_c5,sk_c5) equal(identity,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.18/0.47 382[3:Obv:381.0] || equal(identity,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.18/0.47 384[4:SpR:370.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 386[4:Rew:71.0,384.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 406[3:SpR:372.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 410[4:Rew:386.0,406.0] || -> equal(multiply(sk_c5,u),multiply(sk_c8,u))**.
% 0.18/0.47 415[4:Rew:410.0,382.1] || equal(identity,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.18/0.47 425[4:SpR:378.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.18/0.47 427[4:Rew:375.0,425.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 428[4:Rew:427.0,415.1] || equal(identity,sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.47 430[4:Obv:428.1] || equal(identity,sk_c7)** -> .
% 0.18/0.47 433[4:SpR:379.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.18/0.47 435[4:Rew:371.0,433.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.47 436[4:Rew:427.0,435.0,410.0,435.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 438[4:Rew:436.0,379.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.18/0.47 439[4:Rew:436.0,386.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 442[4:Rew:439.0,62.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 443[4:Rew:439.0,438.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 450[4:Rew:442.0,430.0] || equal(sk_c5,sk_c7)** -> .
% 0.18/0.47 456[4:Rew:443.0,370.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 458[4:Rew:443.0,371.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.18/0.47 471[4:Rew:443.0,450.0] || equal(sk_c5,sk_c8)** -> .
% 0.18/0.47 472[4:Rew:456.0,458.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 473[4:MRR:472.0,471.0] || -> .
% 0.18/0.47 496[3:Spt:473.0,4.0,45.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 497[3:Spt:473.0,4.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 499[3:MRR:14.0,496.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 502[3:MRR:19.0,496.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 503[3:MRR:9.0,496.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 504[3:SpR:497.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 506[3:Rew:71.0,504.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 524[3:SpR:502.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.18/0.47 526[3:Rew:499.0,524.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 527[3:Rew:526.0,44.2] || equal(inverse(sk_c7),sk_c8)** equal(sk_c6,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.18/0.47 528[3:Obv:527.2] || equal(inverse(sk_c7),sk_c8)** equal(sk_c6,sk_c7) -> .
% 0.18/0.47 529[3:SpR:503.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 532[3:Rew:506.0,529.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.18/0.47 534[3:Rew:532.0,42.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 539[3:Rew:526.0,534.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 541[3:Rew:539.0,506.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 542[3:Rew:539.0,528.1] || equal(inverse(sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.47 545[3:Rew:532.0,541.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 548[3:Rew:545.0,526.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 549[3:Rew:548.0,497.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 576[3:Obv:542.1] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.18/0.47 577[3:Rew:549.0,576.0,548.0,576.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 578[3:Obv:577.0] || -> .
% 0.18/0.47 584[2:Spt:578.0,1.1,42.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.47 585[2:Spt:578.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 586[2:MRR:26.1,584.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.47 587[2:MRR:11.1,584.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 589[2:MRR:21.0,584.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.18/0.47 590[2:MRR:16.0,584.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 602[2:SpR:589.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.18/0.47 604[2:Rew:586.0,602.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.18/0.47 613[2:SpR:604.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.18/0.47 615[2:Rew:38.0,613.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 616[2:Rew:615.0,224.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 619[2:Rew:615.0,55.0] || equal(inverse(sk_c7),u) equal(u,sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.18/0.47 622[2:Rew:616.0,590.0] || -> equal(sk_c1,sk_c8)**.
% 0.18/0.47 624[2:Rew:622.0,587.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 627[2:Rew:585.0,624.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 628[2:Rew:627.0,585.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 643[2:Rew:627.0,616.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 666[2:Rew:643.0,619.2,627.0,619.2,627.0,619.1,628.0,619.0,627.0,619.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.18/0.47 667[2:Obv:666.1] || equal(u,sk_c8)* -> .
% 0.18/0.47 668[2:UnC:667.0,81.0] || -> .
% 0.18/0.47 674[1:Spt:668.0,40.1,40.2,40.3,40.5,40.7,40.8,40.9] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.18/0.47 676[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 677[2:Rew:676.0,674.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(sk_c6,sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.18/0.47 679[2:Obv:677.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.18/0.47 681[2:SpR:676.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.18/0.47 682[2:SpR:676.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 684[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 685[3:SpR:684.0,81.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.18/0.47 687[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 688[4:SpR:687.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 690[5:Spt:3.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 692[5:SpR:690.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.18/0.47 694[5:Rew:684.0,692.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 695[6:Spt:5.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 697[6:SpR:695.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.18/0.47 699[6:Rew:687.0,697.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 704[5:SpR:694.0,81.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.47 707[6:SpR:699.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 709[6:Rew:682.0,707.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 710[6:Rew:709.0,676.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 711[6:Rew:709.0,687.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 713[6:Rew:709.0,695.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 714[6:Rew:709.0,694.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 717[6:Rew:709.0,679.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.18/0.47 718[6:Rew:709.0,682.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 725[6:Rew:710.0,714.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 727[6:Rew:725.0,713.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.18/0.47 729[6:Rew:38.0,718.0,725.0,718.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 731[6:Rew:729.0,224.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 735[6:Rew:731.0,727.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 737[6:Rew:735.0,711.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 747[6:Rew:709.0,717.5,731.0,717.5,725.0,717.5,731.0,717.4,709.0,717.4,731.0,717.3,725.0,717.3,709.0,717.3,737.0,717.2,709.0,717.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(sk_c8,sk_c8) equal(u,sk_c8) equal(v,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.18/0.47 748[6:Obv:747.5] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.18/0.47 749[6:Con:748.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 810[6:SpL:737.0,749.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 812[6:Obv:810.1] || -> .
% 0.18/0.47 813[6:Spt:812.0,5.1,695.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 814[6:Spt:812.0,5.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 815[6:Rew:814.0,704.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.18/0.47 821[6:MRR:10.0,813.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 826[6:SpR:814.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 828[6:Rew:681.0,826.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 854[6:SpR:815.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c7)**.
% 0.18/0.47 865[6:SpR:821.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.18/0.47 867[6:Rew:854.0,865.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 871[6:Rew:867.0,813.0] || equal(multiply(sk_c5,sk_c7),sk_c7)** -> .
% 0.18/0.47 874[6:Rew:867.0,828.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 875[6:Rew:874.0,815.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 879[6:Rew:874.0,688.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 905[6:Rew:879.0,871.0,875.0,871.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 906[6:Obv:905.0] || -> .
% 0.18/0.47 920[5:Spt:906.0,3.1,690.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 921[5:Spt:906.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 923[5:MRR:13.1,920.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 926[5:MRR:18.0,920.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 927[5:MRR:8.0,920.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 932[5:SpR:921.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 934[5:Rew:681.0,932.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 954[5:SpR:926.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.18/0.47 956[5:Rew:923.0,954.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 957[5:SpR:927.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 960[5:Rew:934.0,957.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.18/0.47 962[5:Rew:960.0,676.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 968[5:Rew:956.0,962.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 972[5:Rew:968.0,934.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 975[5:Rew:960.0,972.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 977[5:Rew:975.0,956.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 979[5:Rew:975.0,685.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.18/0.47 985[5:Rew:977.0,920.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.18/0.47 998[5:Rew:979.0,985.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 999[5:Obv:998.0] || -> .
% 0.18/0.47 1009[4:Spt:999.0,4.0,687.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 1010[4:Spt:999.0,4.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 1012[4:MRR:14.0,1009.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 1015[4:MRR:19.0,1009.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 1016[4:MRR:9.0,1009.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 1017[4:Rew:1016.0,679.5,1010.0,679.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.18/0.47 1018[4:Obv:1017.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.18/0.47 1021[4:SpR:1010.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 1023[4:Rew:681.0,1021.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 1041[4:SpR:1015.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.18/0.47 1043[4:Rew:1012.0,1041.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 1044[4:SpR:1016.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 1047[4:Rew:1023.0,1044.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.18/0.47 1049[4:Rew:1047.0,676.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 1054[4:Rew:1043.0,1049.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 1056[4:Rew:1054.0,1018.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.18/0.47 1058[4:Rew:1054.0,1023.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 1061[4:Rew:1047.0,1058.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 1062[4:Rew:1061.0,1043.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 1066[4:Rew:1062.0,1010.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 1088[4:Rew:1062.0,1056.3,1062.0,1056.2,1062.0,1056.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.47 1089[4:Con:1088.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.18/0.47 1112[4:SpR:1061.0,224.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 1115[4:Rew:1112.0,224.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 1118[4:Rew:1115.0,1089.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 1155[4:SpL:1066.0,1118.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 1156[4:Obv:1155.1] || -> .
% 0.18/0.47 1157[3:Spt:1156.0,2.0,684.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 1158[3:Spt:1156.0,2.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 1160[3:MRR:12.0,1157.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 1163[3:MRR:17.0,1157.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.47 1164[3:MRR:7.0,1157.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 1165[3:Rew:1164.0,679.5,1158.0,679.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.18/0.47 1166[3:Obv:1165.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.18/0.47 1169[3:SpR:1158.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.47 1171[3:Rew:681.0,1169.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 1189[3:SpR:1163.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.18/0.47 1191[3:Rew:1160.0,1189.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 1192[3:SpR:1164.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 1195[3:Rew:1171.0,1192.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.18/0.47 1197[3:Rew:1195.0,676.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 1202[3:Rew:1191.0,1197.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 1204[3:Rew:1202.0,1166.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.18/0.47 1206[3:Rew:1202.0,1171.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 1209[3:Rew:1195.0,1206.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 1210[3:Rew:1209.0,1191.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 1213[3:Rew:1210.0,1158.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 1234[3:Rew:1210.0,1204.3,1210.0,1204.2,1210.0,1204.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.47 1235[3:Con:1234.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.18/0.47 1258[3:SpR:1209.0,224.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 1260[3:Rew:1258.0,224.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 1264[3:Rew:1260.0,1235.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 1300[3:SpL:1213.0,1264.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 1301[3:Obv:1300.1] || -> .
% 0.18/0.47 1302[2:Spt:1301.0,1.1,676.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.47 1303[2:Spt:1301.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.18/0.47 1304[2:MRR:26.1,1302.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.47 1307[2:MRR:21.0,1302.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.18/0.47 1309[2:MRR:6.0,1302.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.18/0.47 1320[2:SpR:1307.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.18/0.47 1322[2:Rew:1304.0,1320.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.18/0.47 1331[2:SpR:1322.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.18/0.47 1333[2:Rew:38.0,1331.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 1334[2:Rew:1333.0,37.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 1338[2:Rew:1334.0,1309.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 1344[2:Rew:1334.0,1302.0] || equal(sk_c6,sk_c8)** -> .
% 0.18/0.48 1346[2:Rew:1338.0,1344.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.48 1347[2:Obv:1346.0] || -> .
% 0.18/0.48 % SZS output end Refutation
% 0.18/0.48 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_16 prove_this_17 prove_this_18 prove_this_19 prove_this_21 prove_this_23 prove_this_26 prove_this_28 prove_this_33 prove_this_36 left_identity left_inverse associativity
% 0.18/0.48
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