TSTP Solution File: GRP387-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP387-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:47:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP387-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 : Tue Jun 14 08:11:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 893 clauses, backtracked 344 clauses, performed 11 splits and kept 689 clauses.
% 0.19/0.46 SPASS allocated 63622 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 341 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 1[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 2[0:Inp] || -> equal(inverse(sk_c2),sk_c7)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.46 3[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 4[0:Inp] || -> equal(inverse(sk_c3),sk_c6)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.46 5[0:Inp] || -> equal(inverse(sk_c4),sk_c5)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.46 6[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 7[0:Inp] || -> equal(multiply(sk_c2,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.19/0.46 8[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.46 9[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.19/0.46 10[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.46 11[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.46 12[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.19/0.46 13[0:Inp] || -> equal(multiply(sk_c2,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.46 15[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.46 17[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.46 18[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.46 21[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 22[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 23[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 24[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 27[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 28[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 29[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 30[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 31[0:Inp] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c7),sk_c5)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 35[1:Spt:31.3,31.8] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.46 36[2:Spt:5.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 38[3:Spt:17.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.46 40[4:Spt:11.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.46 43[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.46 44[5:Spt:23.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 46[6:Spt:29.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 48[6:SpL:46.0,35.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 49[6:Obv:48.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 50[6:Rew:44.0,49.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 51[6:Obv:50.0] || -> .
% 0.19/0.46 52[6:Spt:51.0,29.1,46.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.19/0.46 53[6:Spt:51.0,29.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 54[6:MRR:28.1,52.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 56[6:MRR:30.1,52.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 57[6:MRR:27.1,52.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 68[2:SpR:36.0,33.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.46 70[6:SpR:53.0,33.0] || -> equal(multiply(sk_c5,sk_c4),identity)**.
% 0.19/0.46 73[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.46 81[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 87[0:Rew:32.0,81.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 102[0:SpR:87.0,87.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 104[6:SpR:57.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 105[3:SpR:38.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.46 106[4:SpR:40.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.19/0.46 108[0:SpR:33.0,87.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 111[2:SpR:68.0,87.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c7)**.
% 0.19/0.46 122[6:Rew:40.0,104.0,54.0,104.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 124[6:Rew:122.0,36.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 131[6:Rew:122.0,68.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.46 135[6:Rew:122.0,73.0] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.46 143[6:Rew:131.0,105.0,124.0,105.0,122.0,105.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 144[6:Rew:143.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 147[6:Rew:143.0,70.0] || -> equal(multiply(sk_c5,sk_c4),sk_c5)**.
% 0.19/0.46 153[6:Rew:144.0,147.0] || -> equal(sk_c4,sk_c5)**.
% 0.19/0.46 155[6:Rew:153.0,56.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.46 157[6:Rew:144.0,155.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 160[6:Rew:157.0,143.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 212[6:Rew:160.0,135.1,124.0,135.0,124.0,135.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 213[6:Obv:212.1] || -> .
% 0.19/0.46 217[5:Spt:213.0,23.1,44.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 218[5:Spt:213.0,23.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 220[0:Rew:102.0,108.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 221[2:Rew:220.0,111.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 222[4:Rew:221.0,106.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 223[5:MRR:22.1,217.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 225[5:MRR:24.0,217.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 226[5:MRR:21.0,217.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 233[2:SpR:221.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.46 257[5:SpR:225.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.19/0.46 259[5:Rew:218.0,257.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 265[5:SpR:226.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 267[5:Rew:40.0,265.0,223.0,265.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 268[5:Rew:267.0,36.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 271[5:Rew:267.0,68.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.46 281[5:Rew:267.0,43.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 287[5:Rew:222.0,271.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 288[5:Rew:287.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 292[5:Rew:288.0,259.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 299[5:Rew:292.0,287.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 323[5:Obv:281.1] || equal(inverse(identity),sk_c7)** -> .
% 0.19/0.46 324[5:Rew:268.0,323.0,299.0,323.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 325[5:Obv:324.0] || -> .
% 0.19/0.46 329[4:Spt:325.0,11.1,40.0] || equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 330[4:Spt:325.0,11.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 331[4:MRR:10.1,329.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 332[4:MRR:8.1,329.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 334[4:MRR:9.1,329.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 335[4:MRR:7.1,329.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 344[4:SpR:332.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.46 364[4:SpR:334.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 366[4:Rew:331.0,364.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 367[4:Rew:366.0,329.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 369[4:SpR:335.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.19/0.46 371[4:Rew:332.0,369.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 379[4:SpR:366.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 381[4:Rew:221.0,379.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 382[4:Rew:371.0,381.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 389[4:Rew:382.0,366.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 399[4:Rew:68.0,389.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 401[4:Rew:399.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 407[4:Rew:401.0,233.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 418[4:Rew:407.0,344.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 421[4:Rew:418.0,335.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 422[4:MRR:421.0,367.0] || -> .
% 0.19/0.46 431[3:Spt:422.0,17.1,38.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.46 432[3:Spt:422.0,17.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 433[3:MRR:16.1,431.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 434[3:MRR:14.1,431.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 436[3:MRR:15.1,431.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 437[3:MRR:13.1,431.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 454[3:SpR:436.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 456[3:Rew:433.0,454.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 458[3:SpR:437.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.19/0.46 460[3:Rew:434.0,458.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 465[3:SpR:456.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 467[3:Rew:221.0,465.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 468[3:Rew:460.0,467.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 473[3:Rew:468.0,456.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 480[3:Rew:68.0,473.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 481[3:Rew:480.0,68.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 482[3:Rew:480.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 486[3:Rew:480.0,43.0] || equal(inverse(sk_c6),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.46 488[3:Rew:482.0,481.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 493[3:Rew:488.0,221.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 523[3:Rew:488.0,486.1,493.0,486.0,488.0,486.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 524[3:Obv:523.1] || -> .
% 0.19/0.46 527[2:Spt:524.0,5.1,36.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.46 528[2:Spt:524.0,5.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 529[2:MRR:4.1,527.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 530[2:MRR:2.1,527.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 531[2:MRR:6.0,527.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 532[2:MRR:3.0,527.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 533[2:MRR:1.0,527.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 541[2:SpR:531.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.19/0.46 543[2:Rew:528.0,541.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 545[2:SpR:532.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 547[2:Rew:529.0,545.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 549[2:SpR:533.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.19/0.46 551[2:Rew:530.0,549.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 556[2:SpR:547.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 558[2:Rew:33.0,556.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 559[2:Rew:558.0,220.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.46 560[2:Rew:558.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 564[2:Rew:558.0,73.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.19/0.46 565[2:Rew:559.0,543.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 568[2:Rew:565.0,532.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 575[2:Rew:565.0,559.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 576[2:Rew:565.0,560.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 577[2:Rew:576.0,551.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 580[2:Rew:577.0,529.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 586[2:Rew:577.0,568.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.46 587[2:Rew:575.0,586.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 589[2:Rew:587.0,580.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 603[2:Rew:565.0,564.1,589.0,564.0,589.0,564.0,577.0,564.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 604[2:Obv:603.1] || -> .
% 0.19/0.46 607[1:Spt:604.0,31.0,31.1,31.2,31.4,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c7),sk_c5)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 609[2:Spt:4.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 610[2:Rew:609.0,607.3] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 612[2:Obv:610.3] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 614[2:SpR:609.0,87.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.46 616[3:Spt:11.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.19/0.46 618[3:Rew:616.0,612.7] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 619[3:Obv:618.7] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.46 622[3:SpR:616.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.19/0.46 624[4:Spt:16.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.46 626[4:Rew:624.0,619.6] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 627[4:Obv:626.6] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 630[4:SpR:624.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.46 632[4:Rew:609.0,630.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 633[5:Spt:23.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 636[4:SpR:632.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.46 637[4:SpR:632.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.46 639[6:Spt:29.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 641[6:SpR:639.0,87.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 643[6:Rew:633.0,641.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.46 644[6:SpR:643.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 645[6:SpR:643.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.46 647[6:Rew:632.0,645.0,609.0,645.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 651[6:Rew:647.0,622.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.19/0.46 655[6:Rew:647.0,627.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 657[6:Rew:647.0,637.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c6)**.
% 0.19/0.46 658[6:Rew:651.0,657.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 659[6:Rew:658.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 662[6:Rew:658.0,614.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.46 668[6:Rew:662.0,644.0,658.0,644.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 674[6:Rew:658.0,655.5,658.0,655.4,647.0,655.4,647.0,655.3,658.0,655.1] || 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)** -> .
% 0.19/0.46 675[6:Con:674.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 694[0:SpR:33.0,87.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 695[0:SpR:33.0,220.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.46 697[5:SpR:633.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.46 700[6:Rew:668.0,697.0] || -> equal(identity,sk_c1)**.
% 0.19/0.46 702[6:Rew:700.0,220.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.46 704[6:Rew:700.0,695.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.46 705[6:Rew:633.0,704.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.46 712[6:Rew:705.0,702.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 713[6:Rew:712.0,675.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 769[6:SpL:659.0,713.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 771[6:Obv:769.1] || -> .
% 0.19/0.46 772[6:Spt:771.0,29.1,639.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.19/0.46 773[6:Spt:771.0,29.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 774[0:Rew:220.0,694.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.46 775[6:MRR:28.1,772.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 778[6:MRR:30.1,772.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 779[6:MRR:27.1,772.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 782[6:SpR:773.0,87.0] || -> equal(multiply(sk_c5,multiply(sk_c4,u)),u)**.
% 0.19/0.46 784[6:SpR:775.0,87.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.19/0.46 795[6:SpR:778.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.46 810[5:SpR:697.0,87.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.19/0.46 812[5:Rew:609.0,810.0] || -> equal(multiply(sk_c6,identity),sk_c1)**.
% 0.19/0.46 813[5:Rew:220.0,812.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.46 814[5:Rew:813.0,633.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 815[5:Rew:813.0,697.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.19/0.46 816[6:Rew:813.0,772.0] || equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.19/0.46 819[5:Rew:814.0,622.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 820[6:Rew:632.0,816.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.46 826[6:SpR:779.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 828[6:Rew:616.0,826.0,775.0,826.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 836[6:Rew:828.0,779.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.46 845[6:Rew:828.0,784.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.46 846[6:Rew:828.0,815.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.46 847[6:Rew:819.0,846.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 850[6:Rew:847.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 854[6:Rew:850.0,782.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 855[6:Rew:850.0,795.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.19/0.46 858[6:Rew:854.0,855.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 859[6:Rew:858.0,845.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.46 864[6:Rew:859.0,836.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 865[6:MRR:864.0,820.0] || -> .
% 0.19/0.46 872[5:Spt:865.0,23.1,633.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 873[5:Spt:865.0,23.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 874[5:MRR:22.1,872.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 876[5:MRR:24.0,872.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 877[5:MRR:21.0,872.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 901[5:SpR:876.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.19/0.46 903[5:Rew:873.0,901.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 905[5:SpR:877.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c6)**.
% 0.19/0.46 907[5:Rew:616.0,905.0,874.0,905.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 908[5:Rew:907.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 916[5:Rew:907.0,614.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.46 919[5:Rew:907.0,636.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.46 921[5:Rew:907.0,627.1] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 927[5:Rew:916.0,919.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 932[5:Rew:927.0,903.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 938[5:Rew:932.0,927.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 944[5:Rew:907.0,921.5,907.0,921.4,932.0,921.4,932.0,921.3,932.0,921.0] || 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)** -> .
% 0.19/0.46 945[5:Con:944.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 959[0:SpR:774.0,87.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.46 995[5:SpR:908.0,33.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.46 997[5:Rew:938.0,995.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 1000[5:Rew:997.0,220.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 1002[5:Rew:1000.0,945.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 1053[5:SpL:908.0,1002.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 1055[5:Obv:1053.1] || -> .
% 0.19/0.46 1056[4:Spt:1055.0,16.1,624.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.46 1057[4:Spt:1055.0,16.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 1059[4:MRR:14.1,1056.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 1060[4:MRR:17.1,1056.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 1062[4:MRR:18.1,1056.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 1063[4:MRR:15.1,1056.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 1064[4:MRR:13.1,1056.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 1066[4:SpR:1057.0,774.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.19/0.46 1069[4:Rew:1066.0,622.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.46 1071[2:SpR:609.0,774.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 1072[2:SpR:609.0,959.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.46 1074[4:Rew:1066.0,1071.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 1076[4:Rew:1074.0,1063.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 1078[4:Rew:1074.0,1069.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 1083[4:SpR:1059.0,774.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.46 1086[4:Rew:609.0,1083.0] || -> equal(sk_c2,sk_c6)**.
% 0.19/0.46 1088[4:Rew:1086.0,1064.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 1099[4:SpR:1060.0,774.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.46 1119[4:SpR:1076.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.19/0.46 1121[4:Rew:616.0,1119.0,609.0,1119.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 1122[4:Rew:1121.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 1127[4:Rew:1121.0,1056.0] || equal(multiply(sk_c7,sk_c5),sk_c7)** -> .
% 0.19/0.46 1131[4:Rew:1121.0,1088.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.46 1132[4:Rew:1078.0,1131.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 1134[4:Rew:1132.0,1062.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.46 1135[4:Rew:1132.0,1099.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.46 1142[4:Rew:1122.0,1135.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 1144[4:Rew:1142.0,1134.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.46 1145[4:Rew:1144.0,1127.0,1132.0,1127.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 1146[4:Obv:1145.0] || -> .
% 0.19/0.46 1153[3:Spt:1146.0,11.1,616.0] || equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.19/0.46 1154[3:Spt:1146.0,11.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 1155[3:MRR:10.1,1153.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 1157[3:MRR:12.1,1153.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 1158[3:MRR:9.1,1153.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 1169[3:SpR:1155.0,774.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.19/0.46 1172[3:Rew:1071.0,1169.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 1174[3:Rew:1172.0,1158.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 1193[3:SpR:1157.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.19/0.46 1195[3:Rew:1154.0,1193.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 1200[3:SpR:1174.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.46 1201[3:SpR:1174.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.19/0.46 1203[3:Rew:609.0,1201.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 1204[3:Rew:1203.0,1153.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 1205[3:Rew:1072.0,1200.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 1206[3:Rew:1205.0,1195.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 1213[3:Rew:1206.0,1174.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 1215[3:Rew:1206.0,1205.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 1227[3:Rew:1215.0,1213.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 1228[3:MRR:1227.0,1204.0] || -> .
% 0.19/0.46 1230[2:Spt:1228.0,4.1,609.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.46 1231[2:Spt:1228.0,4.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 1232[2:MRR:2.1,1230.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 1233[2:MRR:5.1,1230.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 1234[2:MRR:6.0,1230.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.46 1235[2:MRR:3.0,1230.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.46 1236[2:MRR:1.0,1230.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.46 1239[2:SpR:1231.0,959.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.19/0.46 1242[2:SpR:1232.0,774.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.46 1245[2:Rew:1242.0,1230.0] || equal(sk_c2,sk_c6)** -> .
% 0.19/0.46 1246[2:SpR:1233.0,87.0] || -> equal(multiply(sk_c5,multiply(sk_c4,u)),u)**.
% 0.19/0.46 1247[2:SpR:1233.0,774.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.46 1263[2:SpR:1234.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.19/0.46 1265[2:Rew:1233.0,1263.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 1266[2:SpR:1235.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.46 1270[2:Rew:1239.0,1266.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 1271[2:Rew:1270.0,1265.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 1272[2:Rew:1270.0,1246.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 1276[2:Rew:1271.0,1247.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.46 1281[2:Rew:1242.0,1276.0] || -> equal(sk_c4,sk_c2)**.
% 0.19/0.46 1283[2:Rew:1281.0,1272.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 1285[2:Rew:1283.0,1236.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 1288[2:Rew:1285.0,1245.0] || equal(sk_c2,sk_c7)** -> .
% 0.19/0.46 1322[2:SpR:1283.0,220.0] || -> equal(identity,sk_c2)**.
% 0.19/0.46 1324[2:Rew:1322.0,695.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.46 1329[2:Rew:1232.0,1324.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.46 1330[2:MRR:1329.0,1288.0] || -> .
% 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_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_21 prove_this_22 prove_this_23 prove_this_24 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.46
%------------------------------------------------------------------------------