TSTP Solution File: GRP354-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP354-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:46:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP354-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 07:56:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 480 clauses, backtracked 262 clauses, performed 13 splits and kept 449 clauses.
% 0.19/0.44 SPASS allocated 63438 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.03 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 5, length 167 :
% 0.19/0.44 % SZS output start Refutation
% 0.19/0.44 3[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9).
% 0.19/0.44 4[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.44 5[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c7),sk_c9).
% 0.19/0.44 9[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.44 10[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.44 11[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.44 17[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.44 18[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.44 19[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 27[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 28[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c9),sk_c7).
% 0.19/0.44 29[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.44 30[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.44 31[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c9),sk_c7).
% 0.19/0.44 32[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.44 49[0:Inp] || equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(inverse(sk_c9),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(inverse(v),sk_c7) equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(x,sk_c8),sk_c9)** equal(multiply(y,z),sk_c8)** equal(inverse(y),z) equal(multiply(z,sk_c7),sk_c8)** -> .
% 0.19/0.44 50[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.44 51[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.44 52[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.44 53[0:Con:49.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(sk_c9),sk_c7) equal(multiply(u,sk_c8),sk_c9)**+ equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) -> .
% 0.19/0.44 54[1:Spt:53.1,53.4] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.19/0.44 61[2:Spt:19.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.44 67[3:Spt:11.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.44 69[3:SpL:67.0,54.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.44 70[3:Obv:69.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.44 71[3:Rew:61.0,70.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.44 72[3:Obv:71.0] || -> .
% 0.19/0.44 73[3:Spt:72.0,11.1,67.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.19/0.44 74[3:Spt:72.0,11.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 77[3:MRR:10.1,73.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.44 81[3:MRR:9.1,73.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.44 90[3:SpL:81.0,54.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.44 91[3:Obv:90.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.19/0.44 92[3:Rew:77.0,91.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.44 93[3:Obv:92.0] || -> .
% 0.19/0.44 94[2:Spt:93.0,19.0,61.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.44 95[2:Spt:93.0,19.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 98[2:MRR:18.1,94.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.44 102[2:MRR:17.0,94.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.44 111[2:SpL:102.0,54.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.44 112[2:Obv:111.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.19/0.44 113[2:Rew:98.0,112.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.44 114[2:Obv:113.0] || -> .
% 0.19/0.44 115[1:Spt:114.0,53.0,53.2,53.3,53.5,53.6] || equal(inverse(u),sk_c9) equal(inverse(sk_c9),sk_c7) equal(multiply(u,sk_c8),sk_c9)**+ equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) -> .
% 0.19/0.44 117[2:Spt:27.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.44 118[2:Rew:117.0,115.1] || equal(inverse(u),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) -> .
% 0.19/0.44 121[2:Obv:118.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) -> .
% 0.19/0.44 123[3:Spt:3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.44 124[3:Rew:123.0,121.3] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(sk_c9,sk_c9) -> .
% 0.19/0.44 127[3:Obv:124.3] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.44 129[4:Spt:19.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.44 133[5:Spt:11.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.44 138[2:SpR:117.0,51.0] || -> equal(multiply(sk_c7,sk_c9),identity)**.
% 0.19/0.44 139[4:SpR:129.0,51.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.44 146[0:SpR:51.0,52.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.44 150[2:SpR:138.0,52.0] || -> equal(multiply(sk_c7,multiply(sk_c9,u)),multiply(identity,u))**.
% 0.19/0.44 151[4:SpR:139.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.44 152[2:Rew:50.0,150.0] || -> equal(multiply(sk_c7,multiply(sk_c9,u)),u)**.
% 0.19/0.44 153[4:Rew:50.0,151.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.19/0.44 154[0:Rew:50.0,146.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.44 161[4:SpR:139.0,152.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.19/0.44 163[4:SpR:161.0,52.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.19/0.44 165[4:Rew:50.0,163.0] || -> equal(multiply(sk_c1,u),multiply(sk_c7,u))**.
% 0.19/0.44 166[5:Rew:165.0,133.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.44 167[4:Rew:165.0,153.0] || -> equal(multiply(sk_c9,multiply(sk_c7,u)),u)**.
% 0.19/0.44 169[5:Rew:138.0,166.0] || -> equal(identity,sk_c8)**.
% 0.19/0.44 170[5:Rew:169.0,50.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.44 171[5:Rew:169.0,51.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.44 172[5:Rew:169.0,138.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.44 177[5:Rew:170.0,123.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.44 180[5:Rew:177.0,117.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.44 183[5:Rew:177.0,127.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.44 184[5:Rew:177.0,172.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.44 191[5:Rew:184.0,183.2,177.0,183.1,177.0,183.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.19/0.44 192[5:Obv:191.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.44 228[0:SpR:154.0,154.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.44 234[5:SpR:171.0,154.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.19/0.44 251[5:Rew:228.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.44 252[5:Rew:251.0,192.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.44 269[5:SpL:180.0,252.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.44 271[5:Obv:269.1] || -> .
% 0.19/0.44 273[5:Spt:271.0,11.1,133.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.19/0.44 274[5:Spt:271.0,11.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 275[5:Rew:165.0,273.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.44 276[5:Rew:138.0,275.0] || equal(identity,sk_c8)** -> .
% 0.19/0.44 295[5:SpR:274.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.44 299[5:Rew:167.0,295.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.44 301[5:Rew:299.0,123.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.44 302[5:Rew:301.0,274.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.44 306[5:Rew:301.0,138.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.44 316[5:Rew:302.0,306.0] || -> equal(identity,sk_c8)**.
% 0.19/0.44 317[5:MRR:316.0,276.0] || -> .
% 0.19/0.44 322[4:Spt:317.0,19.0,129.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.44 323[4:Spt:317.0,19.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.44 333[4:Rew:323.0,127.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.44 334[4:Obv:333.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.45 336[4:SpR:323.0,154.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.19/0.45 338[4:Rew:117.0,336.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.45 370[4:SpR:338.0,154.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.45 372[4:Rew:51.0,370.0] || -> equal(identity,sk_c8)**.
% 0.19/0.45 374[4:Rew:372.0,50.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.45 375[4:Rew:372.0,51.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.45 378[4:Rew:374.0,123.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.45 386[4:Rew:378.0,117.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 393[4:Rew:378.0,334.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.45 409[4:Rew:378.0,393.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.45 443[4:SpR:375.0,154.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.19/0.45 449[4:Rew:228.0,443.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.45 450[4:Rew:449.0,409.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 519[4:SpL:386.0,450.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 521[4:Obv:519.1] || -> .
% 0.19/0.45 523[3:Spt:521.0,3.1,123.0] || equal(multiply(sk_c8,sk_c7),sk_c9)** -> .
% 0.19/0.45 524[3:Spt:521.0,3.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.45 526[3:MRR:4.1,523.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.45 530[3:MRR:5.1,523.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.45 533[3:SpR:524.0,154.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.19/0.45 535[3:Rew:117.0,533.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.45 556[3:SpR:530.0,154.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c8)**.
% 0.19/0.45 558[3:Rew:526.0,556.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.45 567[3:SpR:535.0,154.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.45 569[3:Rew:51.0,567.0] || -> equal(identity,sk_c8)**.
% 0.19/0.45 571[3:Rew:569.0,50.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.45 575[3:Rew:571.0,523.0] || equal(sk_c9,sk_c7)** -> .
% 0.19/0.45 593[3:SpR:558.0,154.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.19/0.45 595[3:Rew:535.0,593.0,117.0,593.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.45 596[3:MRR:595.0,575.0] || -> .
% 0.19/0.45 598[2:Spt:596.0,27.0,117.0] || equal(inverse(sk_c9),sk_c7)** -> .
% 0.19/0.45 599[2:Spt:596.0,27.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.45 600[2:MRR:31.1,598.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.45 601[2:MRR:28.1,598.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.45 603[2:MRR:32.0,598.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.45 604[2:MRR:30.0,598.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.45 605[2:MRR:29.0,598.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.45 608[2:SpR:599.0,154.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.19/0.45 617[2:SpR:603.0,154.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.19/0.45 620[2:SpR:604.0,154.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.19/0.45 622[2:Rew:600.0,620.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.19/0.45 624[2:SpR:605.0,154.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c8)**.
% 0.19/0.45 626[2:Rew:601.0,624.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.45 635[2:SpR:622.0,154.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.19/0.45 637[2:Rew:51.0,635.0] || -> equal(identity,sk_c8)**.
% 0.19/0.45 638[2:Rew:637.0,50.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.45 640[2:Rew:637.0,51.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.45 651[2:SpR:626.0,154.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.19/0.45 653[2:Rew:608.0,651.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.45 655[2:Rew:653.0,601.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.45 657[2:Rew:653.0,598.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.45 660[2:Rew:653.0,608.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c7)**.
% 0.19/0.45 690[2:SpR:617.0,52.0] || -> equal(multiply(inverse(sk_c6),multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.45 694[2:Rew:638.0,690.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c7,u))**.
% 0.19/0.45 696[2:SpR:660.0,52.0] || -> equal(multiply(inverse(sk_c7),multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.45 700[2:Rew:638.0,696.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c7,u))**.
% 0.19/0.45 708[2:SpR:640.0,154.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.19/0.45 711[2:SpR:600.0,640.0] || -> equal(multiply(sk_c6,sk_c5),sk_c8)**.
% 0.19/0.45 712[2:SpR:655.0,640.0] || -> equal(multiply(sk_c7,sk_c4),sk_c8)**.
% 0.19/0.45 714[2:Rew:228.0,708.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.45 717[2:SpR:711.0,154.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c5)**.
% 0.19/0.45 719[2:Rew:714.0,717.0,694.0,717.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 720[2:Rew:719.0,600.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 725[2:Rew:720.0,657.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.45 726[2:Rew:720.0,700.0] || -> equal(multiply(sk_c6,u),multiply(sk_c7,u))**.
% 0.19/0.45 745[2:SpR:712.0,154.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c4)**.
% 0.19/0.45 747[2:Rew:720.0,745.0] || -> equal(multiply(sk_c6,sk_c8),sk_c4)**.
% 0.19/0.45 748[2:Rew:714.0,747.0,726.0,747.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.45 749[2:Rew:748.0,655.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 752[2:Rew:720.0,749.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 753[2:MRR:752.0,725.0] || -> .
% 0.19/0.45 % SZS output end Refutation
% 0.19/0.45 Formulae used in the proof : prove_this_3 prove_this_4 prove_this_5 prove_this_9 prove_this_10 prove_this_11 prove_this_17 prove_this_18 prove_this_19 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_49 left_identity left_inverse associativity
% 0.19/0.45
%------------------------------------------------------------------------------