TSTP Solution File: GRP368-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP368-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:47:03 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
% 0.03/0.12 % Problem : GRP368-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 02:50:52 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/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 870 clauses, backtracked 372 clauses, performed 11 splits and kept 721 clauses.
% 0.18/0.47 SPASS allocated 63639 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 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 0:00:00.06 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 409 :
% 0.18/0.47 % SZS output start Refutation
% 0.18/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.18/0.47 2[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 3[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.18/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.18/0.47 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c2),sk_c6).
% 0.18/0.47 7[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 8[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 10[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c2),sk_c6).
% 0.18/0.47 11[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 12[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 13[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 15[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 16[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 17[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 18[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 20[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 22[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 23[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 25[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 26[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 27[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 28[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 29[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 30[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.47 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(inverse(sk_c6),sk_c5) equal(multiply(w,sk_c7),x)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.47 35[1:Spt:31.2,31.4,31.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),v)*+ equal(multiply(sk_c7,v),sk_c6)** -> .
% 0.18/0.47 37[2:Spt:2.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.18/0.47 39[3:Spt:3.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 41[4:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 47[5:Spt:4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.47 49[6:Spt:5.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.47 52[2:SpR:37.0,33.0] || -> equal(multiply(sk_c5,sk_c6),identity)**.
% 0.18/0.47 53[5:SpR:47.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.18/0.47 54[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c6)** -> .
% 0.18/0.47 61[5:SpR:53.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.47 63[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.47 65[2:SpR:52.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.18/0.47 67[5:Rew:32.0,61.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.18/0.47 68[2:Rew:32.0,65.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.18/0.47 69[0:Rew:32.0,63.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.47 73[6:SpR:49.0,67.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 80[4:SpR:41.0,68.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.18/0.47 85[0:SpR:69.0,69.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.47 88[3:SpR:39.0,69.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.18/0.47 89[5:SpR:53.0,69.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.18/0.47 91[6:SpR:73.0,69.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 93[0:SpR:33.0,69.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.47 95[2:SpR:52.0,69.0] || -> equal(multiply(inverse(sk_c5),identity),sk_c6)**.
% 0.18/0.47 102[6:Rew:88.0,91.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 104[6:Rew:102.0,39.0] || -> equal(multiply(sk_c5,sk_c5),sk_c6)**.
% 0.18/0.47 111[6:Rew:102.0,80.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.18/0.47 115[6:Rew:102.0,54.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c5,u),sk_c6)** -> .
% 0.18/0.47 125[6:Rew:104.0,111.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 126[6:Rew:125.0,37.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 127[6:Rew:125.0,52.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.18/0.47 129[6:Rew:125.0,104.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.18/0.47 132[6:Rew:127.0,129.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 133[6:Rew:132.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 170[6:Rew:133.0,115.2,125.0,115.2,132.0,115.1,126.0,115.0,126.0,115.0,102.0,115.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.18/0.47 171[6:Obv:170.1] || equal(u,sk_c5)* -> .
% 0.18/0.47 172[6:UnC:171.0,69.0] || -> .
% 0.18/0.47 175[6:Spt:172.0,5.0,49.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.18/0.47 176[6:Spt:172.0,5.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 177[0:Rew:85.0,93.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.47 178[2:Rew:177.0,95.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.47 179[5:Rew:177.0,89.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.47 181[5:Rew:179.0,88.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.18/0.47 182[6:Rew:181.0,175.0] || equal(sk_c7,sk_c5)** -> .
% 0.18/0.47 185[5:Rew:181.0,30.1] || -> equal(inverse(sk_c3),sk_c5)** equal(sk_c7,sk_c5).
% 0.18/0.47 186[6:MRR:185.1,182.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 187[5:Rew:181.0,20.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c5).
% 0.18/0.47 188[6:MRR:187.1,182.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 189[5:Rew:181.0,25.0] || -> equal(sk_c7,sk_c5) equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 190[6:MRR:189.0,182.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 191[5:Rew:181.0,15.0] || -> equal(sk_c7,sk_c5) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 192[6:MRR:191.0,182.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 193[5:Rew:181.0,10.0] || -> equal(sk_c7,sk_c5) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 194[6:MRR:193.0,182.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 211[6:SpR:188.0,69.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.47 223[6:SpR:190.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.47 225[6:Rew:176.0,223.0,186.0,223.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 231[6:Rew:225.0,52.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.18/0.47 237[6:Rew:225.0,194.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.47 245[6:Rew:80.0,231.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 247[6:Rew:245.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 254[6:Rew:247.0,237.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 255[6:Rew:247.0,211.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 260[6:Rew:254.0,192.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.18/0.47 263[6:Rew:255.0,260.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 264[6:MRR:263.0,182.0] || -> .
% 0.18/0.47 275[5:Spt:264.0,4.0,47.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.18/0.47 276[5:Spt:264.0,4.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 277[5:MRR:29.0,275.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 278[5:MRR:19.0,275.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 279[5:MRR:24.0,275.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 280[5:MRR:14.0,275.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 281[5:MRR:9.0,275.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 307[5:SpR:279.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.47 309[5:Rew:276.0,307.0,277.0,307.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 311[5:Rew:309.0,178.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 313[5:Rew:309.0,52.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.18/0.47 322[5:Rew:309.0,281.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.47 324[5:Rew:309.0,54.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c5)** -> .
% 0.18/0.47 330[5:Rew:80.0,313.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 331[5:Rew:330.0,177.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 332[5:Rew:330.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 335[5:Rew:331.0,280.0] || -> equal(sk_c1,sk_c2)**.
% 0.18/0.47 336[5:Rew:335.0,278.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.47 338[5:Rew:332.0,322.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 341[5:Rew:338.0,336.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 342[5:Rew:311.0,341.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 346[5:Rew:342.0,330.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 348[5:Rew:342.0,332.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 371[5:Rew:348.0,324.2,342.0,324.2,346.0,324.1,311.0,324.0,311.0,324.0,342.0,324.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.18/0.47 372[5:Obv:371.1] || equal(u,sk_c5)* -> .
% 0.18/0.47 373[5:UnC:372.0,69.0] || -> .
% 0.18/0.47 376[4:Spt:373.0,1.0,41.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.18/0.47 377[4:Spt:373.0,1.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 378[4:MRR:26.1,376.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 379[4:MRR:16.1,376.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 380[4:MRR:21.0,376.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 381[4:MRR:11.0,376.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 382[4:MRR:6.0,376.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 384[4:SpR:377.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.47 386[4:Rew:178.0,384.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.47 393[4:SpR:379.0,69.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.47 399[4:SpR:380.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.47 401[4:Rew:377.0,399.0,378.0,399.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 403[4:Rew:401.0,37.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 406[4:Rew:401.0,52.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.18/0.47 413[4:Rew:401.0,382.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.47 415[4:Rew:401.0,54.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c5)** -> .
% 0.18/0.47 419[4:Rew:401.0,386.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.18/0.47 420[4:Rew:406.0,419.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 421[4:Rew:420.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 426[4:Rew:421.0,413.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 427[4:Rew:421.0,393.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 428[4:Rew:426.0,381.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.18/0.47 429[4:Rew:427.0,428.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 432[4:Rew:429.0,420.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 433[4:Rew:429.0,421.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 454[4:Rew:433.0,415.2,429.0,415.2,432.0,415.1,403.0,415.0,403.0,415.0,429.0,415.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.18/0.47 455[4:Obv:454.1] || equal(u,sk_c5)* -> .
% 0.18/0.47 456[4:UnC:455.0,69.0] || -> .
% 0.18/0.47 459[3:Spt:456.0,3.0,39.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.18/0.47 460[3:Spt:456.0,3.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 461[3:MRR:28.1,459.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 462[3:MRR:18.1,459.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 463[3:MRR:23.0,459.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 464[3:MRR:13.0,459.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 465[3:MRR:8.0,459.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 467[3:SpR:460.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.47 469[3:Rew:178.0,467.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.47 479[3:SpR:463.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.47 481[3:Rew:460.0,479.0,461.0,479.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 483[3:Rew:481.0,178.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 485[3:Rew:481.0,52.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.18/0.47 490[3:Rew:481.0,465.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.47 492[3:Rew:481.0,54.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c5)** -> .
% 0.18/0.47 496[3:Rew:481.0,469.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.18/0.47 497[3:Rew:485.0,496.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 498[3:Rew:497.0,177.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 499[3:Rew:497.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 503[3:Rew:498.0,464.0] || -> equal(sk_c1,sk_c2)**.
% 0.18/0.47 504[3:Rew:503.0,462.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.47 506[3:Rew:499.0,490.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 508[3:Rew:506.0,504.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 509[3:Rew:483.0,508.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 511[3:Rew:509.0,497.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 513[3:Rew:509.0,499.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 532[3:Rew:513.0,492.2,509.0,492.2,511.0,492.1,483.0,492.0,483.0,492.0,509.0,492.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.18/0.47 533[3:Obv:532.1] || equal(u,sk_c5)* -> .
% 0.18/0.47 534[3:UnC:533.0,69.0] || -> .
% 0.18/0.47 537[2:Spt:534.0,2.0,37.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.18/0.47 538[2:Spt:534.0,2.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 539[2:MRR:27.0,537.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 540[2:MRR:17.0,537.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 541[2:MRR:22.0,537.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 542[2:MRR:12.0,537.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 543[2:MRR:7.0,537.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 545[2:SpR:538.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.47 549[2:SpR:540.0,69.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.47 552[2:SpR:541.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.47 554[2:Rew:538.0,552.0,539.0,552.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 556[2:Rew:554.0,537.0] || equal(inverse(sk_c5),sk_c5)** -> .
% 0.18/0.47 557[2:Rew:554.0,543.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.47 563[2:Rew:554.0,545.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.18/0.47 565[2:Rew:33.0,563.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 566[2:Rew:565.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 567[2:Rew:565.0,177.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 570[2:Rew:566.0,557.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 571[2:Rew:566.0,549.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 572[2:Rew:570.0,542.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.18/0.47 573[2:Rew:571.0,572.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 575[2:Rew:573.0,541.0] || -> equal(multiply(sk_c3,sk_c5),sk_c5)**.
% 0.18/0.47 578[2:Rew:573.0,567.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.18/0.47 580[2:Rew:578.0,575.0] || -> equal(sk_c3,sk_c5)**.
% 0.18/0.47 581[2:Rew:580.0,539.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 582[2:MRR:581.0,556.0] || -> .
% 0.18/0.47 597[1:Spt:582.0,31.0,31.1,31.3,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 599[2:Spt:2.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.18/0.47 600[2:Rew:599.0,597.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(sk_c5,sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 602[2:Obv:600.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 604[2:SpR:599.0,69.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.18/0.47 606[3:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 608[3:Rew:606.0,602.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 609[3:Obv:608.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.18/0.47 612[3:SpR:606.0,69.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.18/0.47 614[3:Rew:599.0,612.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.18/0.47 615[4:Spt:3.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 617[4:Rew:615.0,609.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(sk_c6,sk_c6) equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.18/0.47 618[4:Obv:617.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.18/0.47 621[4:SpR:615.0,69.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.18/0.47 623[5:Spt:4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.47 624[5:SpR:623.0,69.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.18/0.47 629[6:Spt:5.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.47 631[6:SpR:629.0,69.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c6)**.
% 0.18/0.47 633[6:Rew:623.0,631.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 634[3:SpR:614.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.18/0.47 637[6:SpR:633.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.18/0.47 638[6:SpR:633.0,69.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 640[6:Rew:621.0,638.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 642[6:Rew:640.0,615.0] || -> equal(multiply(sk_c5,sk_c5),sk_c6)**.
% 0.18/0.47 643[6:Rew:640.0,623.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.18/0.47 645[6:Rew:640.0,614.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.18/0.47 648[6:Rew:640.0,618.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(sk_c5,sk_c5),sk_c6)** -> .
% 0.18/0.47 656[6:Rew:642.0,645.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 657[6:Rew:656.0,599.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 658[6:Rew:656.0,604.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.18/0.47 665[6:Rew:658.0,637.0,640.0,637.0,656.0,637.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 671[6:Rew:665.0,648.4,656.0,648.4,640.0,648.3,656.0,648.2,640.0,648.2,640.0,648.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c5) equal(multiply(u,sk_c5),sk_c5)** equal(multiply(v,sk_c5),sk_c5)** equal(sk_c5,sk_c5) -> .
% 0.18/0.47 672[6:Obv:671.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c5) equal(multiply(u,sk_c5),sk_c5)** equal(multiply(v,sk_c5),sk_c5)** -> .
% 0.18/0.47 673[6:Con:672.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c5),sk_c5)** -> .
% 0.18/0.47 679[0:SpR:33.0,69.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.47 681[0:Rew:177.0,679.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.47 685[6:SpR:643.0,33.0] || -> equal(multiply(sk_c5,sk_c4),identity)**.
% 0.18/0.47 687[6:Rew:665.0,685.0] || -> equal(identity,sk_c4)**.
% 0.18/0.47 689[6:Rew:687.0,33.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.18/0.47 690[6:Rew:687.0,177.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.18/0.47 706[6:SpR:657.0,689.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.18/0.47 707[6:Rew:665.0,706.0] || -> equal(sk_c4,sk_c5)**.
% 0.18/0.47 712[6:Rew:707.0,690.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.18/0.47 713[6:Rew:712.0,673.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.18/0.47 719[0:SpR:681.0,69.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.18/0.47 763[6:SpL:657.0,713.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.18/0.47 765[6:Obv:763.1] || -> .
% 0.18/0.47 766[6:Spt:765.0,5.0,629.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.18/0.47 767[6:Spt:765.0,5.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 768[6:MRR:30.1,766.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 769[6:MRR:20.1,766.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 770[6:MRR:25.0,766.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 771[6:MRR:15.0,766.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 772[6:MRR:10.0,766.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 781[5:SpR:623.0,681.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.47 784[5:Rew:781.0,621.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.18/0.47 785[6:Rew:784.0,766.0] || equal(sk_c7,sk_c5)** -> .
% 0.18/0.47 787[6:SpR:768.0,681.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.18/0.47 793[2:SpR:599.0,681.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.47 794[2:SpR:599.0,719.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.18/0.47 796[6:Rew:787.0,793.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.47 798[6:Rew:796.0,770.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.18/0.47 806[6:SpR:769.0,681.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.47 809[6:Rew:781.0,806.0] || -> equal(sk_c1,sk_c4)**.
% 0.18/0.47 811[6:Rew:809.0,771.0] || -> equal(multiply(sk_c4,sk_c7),sk_c2)**.
% 0.18/0.47 832[6:SpR:772.0,69.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c2)**.
% 0.18/0.47 834[6:Rew:781.0,832.0] || -> equal(multiply(sk_c4,sk_c6),sk_c2)**.
% 0.18/0.47 835[6:Rew:784.0,834.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 837[6:Rew:835.0,811.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.47 849[6:SpR:798.0,69.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.18/0.47 851[6:Rew:767.0,849.0,599.0,849.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.47 860[6:Rew:851.0,604.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.18/0.47 869[6:Rew:634.0,860.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 870[6:Rew:869.0,624.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.18/0.47 873[6:Rew:870.0,837.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 874[6:MRR:873.0,785.0] || -> .
% 0.18/0.47 878[5:Spt:874.0,4.0,623.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.18/0.47 879[5:Spt:874.0,4.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.47 882[5:MRR:29.0,878.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.47 883[5:MRR:19.0,878.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 884[5:MRR:24.0,878.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.47 885[5:MRR:14.0,878.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.47 886[5:MRR:9.0,878.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.47 887[5:Rew:879.0,618.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.18/0.47 888[5:Obv:887.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** -> .
% 0.18/0.47 892[5:SpR:879.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.47 894[5:Rew:793.0,892.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.47 896[5:SpR:882.0,681.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.18/0.47 899[5:Rew:793.0,896.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.47 901[5:Rew:899.0,884.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.18/0.47 914[5:SpR:883.0,681.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.47 930[5:SpR:885.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c2,u))**.
% 0.18/0.47 931[5:SpR:885.0,69.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.18/0.47 933[5:Rew:883.0,931.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.18/0.47 934[5:Rew:886.0,933.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 937[5:Rew:934.0,793.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 938[5:Rew:934.0,599.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.47 939[5:Rew:934.0,606.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.18/0.47 941[5:Rew:934.0,794.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 947[5:Rew:934.0,888.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** -> .
% 0.18/0.47 949[5:Rew:934.0,894.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.18/0.47 950[5:Rew:934.0,901.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.47 952[5:Rew:914.0,938.0] || -> equal(sk_c1,sk_c5)**.
% 0.18/0.47 955[5:Rew:952.0,885.0] || -> equal(multiply(sk_c5,sk_c7),sk_c2)**.
% 0.18/0.47 958[5:Rew:939.0,949.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.47 964[5:Rew:958.0,937.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.18/0.47 970[5:Rew:958.0,950.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.18/0.47 972[5:Rew:970.0,955.0,958.0,955.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.47 974[5:Rew:958.0,941.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.18/0.47 978[5:Rew:974.0,930.0,952.0,930.0,958.0,930.0,972.0,930.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 982[5:Rew:958.0,947.3,958.0,947.2,958.0,947.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c5) equal(multiply(u,sk_c5),sk_c5)** equal(multiply(v,sk_c5),sk_c5)** -> .
% 0.18/0.47 983[5:Con:982.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c5),sk_c5)** -> .
% 0.18/0.47 1011[5:SpR:978.0,177.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 1014[5:Rew:1011.0,177.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.18/0.48 1018[5:Rew:1014.0,983.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.18/0.48 1051[5:SpL:964.0,1018.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.18/0.48 1052[5:Obv:1051.1] || -> .
% 0.18/0.48 1053[4:Spt:1052.0,3.0,615.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.18/0.48 1054[4:Spt:1052.0,3.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.48 1055[4:MRR:28.1,1053.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.48 1056[4:MRR:18.1,1053.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.48 1057[4:MRR:23.0,1053.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.48 1058[4:MRR:13.0,1053.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.48 1059[4:MRR:8.0,1053.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.48 1061[4:SpR:1054.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.48 1063[4:Rew:793.0,1061.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.48 1065[4:SpR:1055.0,681.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.18/0.48 1068[4:Rew:793.0,1065.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.48 1070[4:Rew:1068.0,1057.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.18/0.48 1087[4:SpR:1058.0,69.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.18/0.48 1089[4:Rew:1056.0,1087.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.18/0.48 1090[4:Rew:1059.0,1089.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.48 1095[4:Rew:1090.0,606.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.18/0.48 1096[4:Rew:1090.0,1053.0] || equal(multiply(sk_c7,sk_c5),sk_c7)** -> .
% 0.18/0.48 1102[4:Rew:1090.0,1063.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.18/0.48 1103[4:Rew:1090.0,1070.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.48 1110[4:Rew:1095.0,1102.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.48 1120[4:Rew:1110.0,1103.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.18/0.48 1123[4:Rew:1120.0,1096.0,1110.0,1096.0] || equal(sk_c5,sk_c5)* -> .
% 0.18/0.48 1124[4:Obv:1123.0] || -> .
% 0.18/0.48 1132[3:Spt:1124.0,1.0,606.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.18/0.48 1133[3:Spt:1124.0,1.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.48 1134[3:MRR:26.1,1132.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.48 1135[3:MRR:16.1,1132.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.48 1136[3:MRR:21.0,1132.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.48 1137[3:MRR:11.0,1132.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.48 1138[3:MRR:6.0,1132.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.48 1140[3:SpR:1133.0,69.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.18/0.48 1142[3:Rew:793.0,1140.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.48 1152[3:SpR:1134.0,681.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.18/0.48 1155[3:Rew:793.0,1152.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.48 1157[3:Rew:1155.0,1136.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.18/0.48 1162[3:SpR:1135.0,681.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.48 1169[3:SpR:1137.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c2,u))**.
% 0.18/0.48 1170[3:SpR:1137.0,69.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.18/0.48 1172[3:Rew:1135.0,1170.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.18/0.48 1173[3:Rew:1138.0,1172.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.48 1174[3:Rew:1173.0,1133.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.18/0.48 1176[3:Rew:1173.0,599.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.48 1178[3:Rew:1173.0,1132.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.18/0.48 1180[3:Rew:1173.0,604.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.18/0.48 1183[3:Rew:1173.0,1142.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.18/0.48 1184[3:Rew:1173.0,1157.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.48 1185[3:Rew:1162.0,1176.0] || -> equal(sk_c1,sk_c5)**.
% 0.18/0.48 1188[3:Rew:1185.0,1137.0] || -> equal(multiply(sk_c5,sk_c7),sk_c2)**.
% 0.18/0.48 1191[3:Rew:1174.0,1188.0] || -> equal(sk_c2,sk_c7)**.
% 0.18/0.48 1193[3:Rew:1183.0,1178.0] || equal(sk_c7,sk_c5)** -> .
% 0.18/0.48 1194[3:Rew:1180.0,1169.0,1185.0,1169.0,1191.0,1169.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.48 1197[3:Rew:1194.0,1184.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.48 1198[3:MRR:1197.0,1193.0] || -> .
% 0.18/0.48 1199[2:Spt:1198.0,2.0,599.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.18/0.48 1200[2:Spt:1198.0,2.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.18/0.48 1201[2:MRR:27.0,1199.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.18/0.48 1202[2:MRR:17.0,1199.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.48 1203[2:MRR:22.0,1199.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.18/0.48 1204[2:MRR:12.0,1199.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.18/0.48 1205[2:MRR:7.0,1199.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.18/0.48 1210[2:SpR:1201.0,681.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.18/0.48 1211[2:SpR:1201.0,719.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),u)**.
% 0.18/0.48 1214[2:SpR:1202.0,69.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.48 1215[2:SpR:1202.0,681.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.48 1226[2:SpR:1203.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.18/0.48 1227[2:SpR:1203.0,69.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c5)**.
% 0.18/0.48 1229[2:Rew:1200.0,1227.0,1201.0,1227.0] || -> equal(sk_c6,sk_c5)**.
% 0.18/0.48 1231[2:Rew:1229.0,1199.0] || equal(inverse(sk_c5),sk_c5)** -> .
% 0.18/0.48 1232[2:Rew:1229.0,1205.0] || -> equal(multiply(sk_c7,sk_c2),sk_c5)**.
% 0.18/0.48 1235[2:Rew:1210.0,1231.0] || equal(sk_c3,sk_c5)** -> .
% 0.18/0.48 1236[2:Rew:1211.0,1226.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.48 1237[2:Rew:1236.0,1232.0] || -> equal(sk_c2,sk_c5)**.
% 0.18/0.48 1238[2:Rew:1236.0,1214.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.48 1240[2:Rew:1237.0,1204.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.18/0.48 1241[2:Rew:1238.0,1240.0] || -> equal(sk_c7,sk_c5)**.
% 0.18/0.48 1243[2:Rew:1241.0,1215.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.18/0.48 1247[2:Rew:1210.0,1243.0] || -> equal(sk_c3,sk_c1)**.
% 0.18/0.48 1249[2:Rew:1247.0,1210.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.18/0.48 1252[2:Rew:1247.0,1235.0] || equal(sk_c1,sk_c5)** -> .
% 0.18/0.48 1288[2:SpR:1238.0,177.0] || -> equal(identity,sk_c1)**.
% 0.18/0.48 1294[2:Rew:1288.0,33.0] || -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.18/0.48 1305[2:SpR:1249.0,1294.0] || -> equal(multiply(sk_c1,sk_c5),sk_c1)**.
% 0.18/0.48 1306[2:Rew:1238.0,1305.0] || -> equal(sk_c1,sk_c5)**.
% 0.18/0.48 1307[2:MRR:1306.0,1252.0] || -> .
% 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_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_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.18/0.48
%------------------------------------------------------------------------------