TSTP Solution File: GRP317-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP317-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:46:49 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP317-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 03:12:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 843 clauses, backtracked 576 clauses, performed 12 splits and kept 869 clauses.
% 0.21/0.49 SPASS allocated 63673 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.49 0:00:00.04 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.00 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.07 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 6, length 359 :
% 0.21/0.49 % SZS output start Refutation
% 0.21/0.49 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.21/0.49 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.21/0.49 7[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 11[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 12[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 13[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.21/0.49 14[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 17[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.21/0.49 18[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 20[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 21[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8).
% 0.21/0.49 22[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 23[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c7),sk_c8).
% 0.21/0.49 24[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 25[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.49 26[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.49 31[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.21/0.49 32[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 38[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.49 42[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.49 44[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 48[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 50[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.21/0.49 54[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.21/0.49 55[0:Inp] || equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(inverse(v),sk_c8) equal(inverse(w),x) equal(inverse(x),sk_c9)** equal(multiply(w,sk_c9),x)* equal(multiply(sk_c8,sk_c7),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(z,sk_c9),sk_c7)** equal(inverse(z),sk_c9) -> .
% 0.21/0.49 56[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.49 57[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.49 58[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.49 59[0:Con:55.11] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(x),sk_c8) equal(inverse(y),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),v)*+ equal(multiply(w,sk_c9),sk_c7)** equal(multiply(x,sk_c8),sk_c9)** equal(multiply(y,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 60[1:Spt:59.0,59.2,59.6] || equal(inverse(u),v) equal(inverse(v),sk_c9)** equal(multiply(u,sk_c9),v)* -> .
% 0.21/0.49 62[2:Spt:20.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.49 64[3:Spt:19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.21/0.49 66[4:Spt:24.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.21/0.49 68[5:Spt:22.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.49 70[6:Spt:23.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.21/0.49 75[1:SpL:56.0,60.2] || equal(inverse(identity),u)* equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.21/0.49 76[7:Spt:21.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.49 79[2:SpR:62.0,57.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.21/0.49 80[4:SpR:66.0,57.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.21/0.49 81[5:SpR:68.0,57.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.49 88[3:SpR:64.0,58.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.21/0.49 90[0:SpR:57.0,58.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.49 92[2:SpR:79.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.21/0.49 93[4:SpR:80.0,58.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.21/0.49 95[2:Rew:56.0,92.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.21/0.49 96[4:Rew:56.0,93.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.21/0.49 97[0:Rew:56.0,90.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.49 100[5:SpR:81.0,58.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.49 101[5:Rew:56.0,100.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.21/0.49 104[3:SpR:64.0,95.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.21/0.49 105[5:SpR:81.0,95.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.21/0.49 109[3:SpL:104.0,60.2] || equal(inverse(sk_c7),u)* equal(inverse(u),sk_c9)** equal(sk_c7,u) -> .
% 0.21/0.49 110[5:SpR:105.0,58.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c5,u))**.
% 0.21/0.49 112[5:Rew:56.0,110.0] || -> equal(multiply(sk_c5,u),multiply(sk_c7,u))**.
% 0.21/0.49 113[7:Rew:112.0,76.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.21/0.49 115[5:Rew:112.0,101.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.21/0.49 116[7:Rew:79.0,113.0] || -> equal(identity,sk_c9)**.
% 0.21/0.49 117[7:Rew:116.0,56.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.49 120[7:Rew:116.0,80.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.21/0.49 122[7:Rew:116.0,105.0] || -> equal(multiply(sk_c7,sk_c9),sk_c5)**.
% 0.21/0.49 129[7:Rew:117.0,120.0] || -> equal(sk_c6,sk_c9)**.
% 0.21/0.49 130[7:Rew:129.0,66.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.49 131[7:Rew:129.0,70.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.49 132[7:Rew:104.0,122.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.49 133[7:Rew:132.0,68.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.49 136[7:Rew:133.0,109.0] || equal(sk_c8,u) equal(inverse(u),sk_c9)** equal(sk_c7,u) -> .
% 0.21/0.49 138[7:Rew:117.0,131.0] || -> equal(sk_c7,sk_c9)**.
% 0.21/0.49 146[7:Rew:138.0,133.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.21/0.49 147[7:Rew:130.0,146.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 154[7:Rew:147.0,130.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 155[7:Rew:147.0,138.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 168[7:Rew:155.0,136.2,147.0,136.1] || equal(sk_c8,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.21/0.49 169[7:Obv:168.0] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.21/0.49 192[0:SpR:97.0,97.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.49 217[7:SpL:154.0,169.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 218[7:Obv:217.1] || -> .
% 0.21/0.49 219[7:Spt:218.0,21.0,76.0] || equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.21/0.49 220[7:Spt:218.0,21.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 221[7:Rew:112.0,219.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.21/0.49 222[7:Rew:79.0,221.0] || equal(identity,sk_c9)** -> .
% 0.21/0.49 231[5:Rew:115.0,88.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.49 233[5:Rew:231.0,96.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 234[7:Rew:231.0,220.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 235[5:Rew:231.0,80.0] || -> equal(identity,sk_c6)**.
% 0.21/0.49 238[7:Rew:234.0,79.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.21/0.49 239[7:Rew:234.0,70.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.21/0.49 245[5:Rew:235.0,81.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.21/0.49 248[7:Rew:235.0,222.0] || equal(sk_c6,sk_c9)** -> .
% 0.21/0.49 250[7:Rew:235.0,238.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.21/0.49 251[7:Rew:233.0,239.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 255[7:Rew:251.0,231.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 256[7:Rew:251.0,248.0] || equal(sk_c6,sk_c8)** -> .
% 0.21/0.49 261[7:Rew:255.0,245.0] || -> equal(sk_c6,sk_c5)**.
% 0.21/0.49 262[7:Rew:255.0,250.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 267[7:Rew:261.0,256.0] || equal(sk_c5,sk_c8)** -> .
% 0.21/0.49 268[7:Rew:261.0,262.0] || -> equal(sk_c5,sk_c8)**.
% 0.21/0.49 274[7:Rew:268.0,267.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 275[7:Obv:274.0] || -> .
% 0.21/0.49 297[6:Spt:275.0,23.0,70.0] || equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.21/0.49 298[6:Spt:275.0,23.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 299[5:Rew:235.0,79.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.49 301[6:Rew:231.0,298.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 303[6:Rew:301.0,64.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.49 305[6:Rew:301.0,299.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.21/0.49 307[6:Rew:303.0,305.0] || -> equal(sk_c6,sk_c9)**.
% 0.21/0.49 316[6:Rew:231.0,297.0,307.0,297.0,301.0,297.0] || equal(sk_c9,sk_c8)** -> .
% 0.21/0.49 330[6:Rew:231.0,17.1,307.0,17.1,301.0,17.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c9,sk_c8).
% 0.21/0.49 331[6:MRR:330.1,316.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 341[6:Rew:231.0,11.0,307.0,11.0,301.0,11.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 342[6:MRR:341.0,316.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 372[6:SpR:331.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.49 374[6:Rew:231.0,372.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 375[6:Rew:374.0,342.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 376[6:MRR:375.0,316.0] || -> .
% 0.21/0.49 377[5:Spt:376.0,22.0,68.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.49 378[5:Spt:376.0,22.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 382[5:MRR:16.0,377.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 385[5:MRR:10.0,377.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 400[5:SpR:382.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.49 403[3:SpR:104.0,97.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.49 405[3:Rew:57.0,403.0] || -> equal(identity,sk_c9)**.
% 0.21/0.49 407[3:Rew:405.0,56.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.49 410[3:Rew:405.0,75.0] || equal(inverse(sk_c9),u)* equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.21/0.49 412[5:Rew:407.0,378.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 416[5:Rew:407.0,400.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 420[5:Rew:412.0,62.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 429[5:Rew:416.0,385.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 458[5:Rew:429.0,410.2,429.0,410.1,420.0,410.0,429.0,410.0] || equal(sk_c8,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.21/0.49 459[5:Obv:458.0] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.21/0.49 521[5:SpL:420.0,459.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 522[5:Obv:521.1] || -> .
% 0.21/0.49 523[4:Spt:522.0,24.0,66.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.21/0.49 524[4:Spt:522.0,24.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 525[4:Rew:407.0,524.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 526[4:Rew:525.0,62.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 532[4:MRR:48.0,523.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 533[4:MRR:42.0,523.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.49 535[4:MRR:18.0,523.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 539[4:MRR:54.0,523.0] || -> equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.21/0.49 541[4:MRR:12.0,523.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 551[4:SpR:532.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.21/0.49 553[4:Rew:407.0,551.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 556[4:SpR:533.0,97.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),u)**.
% 0.21/0.49 558[4:Rew:553.0,556.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.21/0.49 559[4:Rew:558.0,539.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.49 560[4:Rew:559.0,532.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.49 563[4:Rew:560.0,410.0] || equal(sk_c9,u) equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.21/0.49 565[4:Obv:563.0] || equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.21/0.49 569[4:SpR:535.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.49 571[4:Rew:407.0,569.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 572[4:Rew:571.0,541.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 582[4:Rew:572.0,565.0] || equal(inverse(u),sk_c8)** equal(sk_c9,u) -> .
% 0.21/0.49 591[4:Rew:572.0,582.1] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.21/0.49 652[4:SpL:526.0,591.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 653[4:Obv:652.1] || -> .
% 0.21/0.49 654[3:Spt:653.0,19.0,64.0] || equal(multiply(sk_c8,sk_c7),sk_c9)** -> .
% 0.21/0.49 655[3:Spt:653.0,19.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 658[3:MRR:31.1,654.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 659[3:MRR:13.1,654.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 661[3:MRR:25.0,654.0] || -> equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.49 662[3:MRR:7.0,654.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 663[3:MRR:1.0,654.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.21/0.49 664[3:SpR:655.0,58.0] || -> equal(multiply(sk_c9,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.21/0.49 686[3:SpR:661.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c8)**.
% 0.21/0.49 688[3:Rew:658.0,686.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.21/0.49 689[3:Rew:663.0,688.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 690[3:Rew:689.0,655.0] || -> equal(multiply(sk_c9,sk_c8),sk_c8)**.
% 0.21/0.49 692[3:Rew:689.0,79.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.21/0.49 693[3:Rew:689.0,654.0] || equal(multiply(sk_c8,sk_c8),sk_c9)** -> .
% 0.21/0.49 694[3:Rew:689.0,95.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.21/0.49 697[3:Rew:689.0,664.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.21/0.49 699[3:Rew:692.0,693.0] || equal(identity,sk_c9)** -> .
% 0.21/0.49 705[3:SpR:662.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.49 707[3:Rew:659.0,705.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.49 708[3:Rew:690.0,707.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 713[3:Rew:708.0,699.0] || equal(identity,sk_c8)** -> .
% 0.21/0.49 728[3:Rew:708.0,697.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.21/0.49 737[3:Rew:694.0,728.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 739[3:Rew:737.0,692.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 748[3:MRR:739.0,713.0] || -> .
% 0.21/0.49 762[2:Spt:748.0,20.0,62.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.21/0.49 763[2:Spt:748.0,20.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 764[2:MRR:44.0,762.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 765[2:MRR:38.0,762.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.49 766[2:MRR:32.0,762.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 767[2:MRR:14.0,762.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 768[2:MRR:50.0,762.0] || -> equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.21/0.49 769[2:MRR:26.0,762.0] || -> equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.49 770[2:MRR:8.0,762.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 771[2:MRR:2.0,762.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.21/0.49 773[2:SpR:763.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.21/0.49 775[2:SpR:764.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.21/0.49 784[2:SpR:768.0,97.0] || -> equal(multiply(inverse(sk_c4),sk_c3),sk_c9)**.
% 0.21/0.49 786[2:Rew:765.0,784.0] || -> equal(multiply(sk_c3,sk_c3),sk_c9)**.
% 0.21/0.49 788[2:SpR:769.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c8)**.
% 0.21/0.49 790[2:Rew:766.0,788.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.21/0.49 791[2:Rew:771.0,790.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 792[2:Rew:791.0,763.0] || -> equal(multiply(sk_c9,sk_c8),sk_c8)**.
% 0.21/0.49 793[2:Rew:791.0,762.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.21/0.49 795[2:Rew:791.0,773.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c8)**.
% 0.21/0.49 799[2:SpR:770.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.49 801[2:Rew:767.0,799.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.49 802[2:Rew:792.0,801.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 803[2:Rew:802.0,764.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 812[2:Rew:802.0,795.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.21/0.49 814[2:Rew:802.0,775.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 816[2:Rew:802.0,786.0] || -> equal(multiply(sk_c3,sk_c3),sk_c8)**.
% 0.21/0.49 822[2:Rew:57.0,812.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 823[2:Rew:822.0,56.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 826[2:Rew:823.0,814.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 827[2:Rew:826.0,816.0] || -> equal(sk_c3,sk_c8)**.
% 0.21/0.49 830[2:Rew:827.0,803.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 833[2:MRR:830.0,793.0] || -> .
% 0.21/0.49 842[1:Spt:833.0,59.1,59.3,59.4,59.5,59.7,59.8,59.9,59.10,59.11,59.12] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 844[2:Spt:2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.49 845[2:Rew:844.0,842.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 847[2:Obv:845.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 849[2:SpR:844.0,97.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.21/0.49 851[3:Spt:1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.21/0.49 853[3:Rew:851.0,847.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(sk_c9,sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 854[3:Obv:853.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.21/0.49 857[3:SpR:851.0,97.0] || -> equal(multiply(inverse(sk_c8),sk_c9),sk_c7)**.
% 0.21/0.49 859[3:Rew:844.0,857.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.21/0.49 860[4:Spt:24.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.21/0.49 861[4:SpR:860.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.21/0.49 863[5:Spt:46.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.49 864[5:SpR:863.0,97.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.21/0.49 867[3:SpR:859.0,97.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.49 869[3:Rew:57.0,867.0] || -> equal(identity,sk_c9)**.
% 0.21/0.49 870[3:Rew:869.0,56.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.49 871[3:Rew:869.0,57.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.21/0.49 872[4:Rew:870.0,861.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 874[3:Rew:870.0,854.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.21/0.49 875[3:Rew:870.0,23.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(sk_c7,sk_c8).
% 0.21/0.49 876[3:Rew:870.0,21.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c7,sk_c8).
% 0.21/0.49 879[4:Rew:872.0,11.0] || -> equal(sk_c7,sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 882[4:Rew:872.0,17.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c7,sk_c9).
% 0.21/0.49 886[4:Rew:872.0,875.0] || -> equal(sk_c7,sk_c9)** equal(sk_c7,sk_c8).
% 0.21/0.49 898[6:Spt:886.0] || -> equal(sk_c7,sk_c9)**.
% 0.21/0.49 899[6:Rew:898.0,844.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.21/0.49 902[6:Rew:898.0,849.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),u)**.
% 0.21/0.49 905[6:Rew:898.0,874.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(sk_c9,sk_c8) equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.21/0.49 906[6:Rew:898.0,876.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c9,sk_c8).
% 0.21/0.49 908[6:Rew:870.0,902.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 909[6:Rew:908.0,864.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 918[6:Rew:909.0,906.0] || -> equal(sk_c9,sk_c8)** equal(sk_c9,sk_c8)**.
% 0.21/0.49 919[6:Obv:918.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 923[6:Rew:919.0,871.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.49 925[6:Rew:919.0,898.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 926[6:Rew:919.0,899.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 928[6:Rew:919.0,905.7,908.0,905.7,925.0,905.7,919.0,905.6,919.0,905.5,919.0,905.4,919.0,905.3,925.0,905.3,919.0,905.2,919.0,905.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(sk_c8,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.49 929[6:Obv:928.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.21/0.49 930[6:Con:929.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.21/0.49 937[6:SpR:923.0,97.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.49 943[6:Rew:192.0,937.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 944[6:Rew:943.0,930.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 972[6:SpL:926.0,944.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 973[6:Obv:972.1] || -> .
% 0.21/0.49 974[6:Spt:973.0,886.0,898.0] || equal(sk_c7,sk_c9)** -> .
% 0.21/0.49 975[6:Spt:973.0,886.1] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 977[6:Rew:975.0,974.0] || equal(sk_c9,sk_c8)** -> .
% 0.21/0.49 980[6:Rew:975.0,882.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c9,sk_c8).
% 0.21/0.49 981[6:MRR:980.1,977.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 990[6:Rew:975.0,879.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 991[6:MRR:990.0,977.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 1008[6:SpR:981.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.49 1010[6:Rew:870.0,1008.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 1011[6:Rew:1010.0,991.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 1012[6:MRR:1011.0,977.0] || -> .
% 0.21/0.49 1013[5:Spt:1012.0,46.0,863.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.49 1014[5:Spt:1012.0,46.1] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 1017[5:MRR:16.0,1013.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 1018[3:Rew:870.0,22.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c7,sk_c8).
% 0.21/0.49 1019[5:MRR:1018.0,1013.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 1020[5:Rew:1019.0,844.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 1021[5:Rew:1019.0,859.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.21/0.49 1031[5:MRR:10.0,1013.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 1033[5:Rew:1021.0,874.7,1019.0,874.7,1019.0,874.6,1019.0,874.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(sk_c8,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.49 1034[5:Obv:1033.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** -> .
% 0.21/0.49 1035[5:Con:1034.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.21/0.49 1051[5:SpR:1017.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.49 1053[5:Rew:870.0,1051.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 1054[5:Rew:1053.0,1031.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.49 1060[5:Rew:1054.0,871.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.49 1064[5:Rew:1054.0,1035.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.21/0.49 1069[5:Rew:1054.0,1064.3,1054.0,1064.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.21/0.49 1070[5:Con:1069.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.21/0.49 1107[5:SpR:1060.0,97.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.49 1126[5:Rew:192.0,1107.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 1127[5:Rew:1126.0,1070.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 1141[5:SpL:1020.0,1127.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 1142[5:Obv:1141.1] || -> .
% 0.21/0.49 1143[4:Spt:1142.0,24.0,860.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.21/0.49 1144[4:Spt:1142.0,24.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.21/0.49 1145[4:Rew:870.0,1144.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 1146[4:Rew:1145.0,844.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 1148[4:Rew:1145.0,859.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.21/0.49 1154[4:MRR:18.0,1143.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 1159[4:MRR:12.0,1143.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 1162[4:Rew:1148.0,874.7,1145.0,874.7,1145.0,874.6,1145.0,874.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(sk_c8,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.50 1163[4:Obv:1162.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** -> .
% 0.21/0.50 1164[4:Con:1163.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.21/0.50 1183[4:SpR:1154.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.50 1185[4:Rew:870.0,1183.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.50 1186[4:Rew:1185.0,1159.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.50 1194[4:Rew:1186.0,871.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.50 1196[4:Rew:1186.0,1164.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.21/0.50 1201[4:Rew:1186.0,1196.3,1186.0,1196.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.21/0.50 1202[4:Con:1201.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.21/0.50 1229[4:SpR:1194.0,97.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.50 1244[4:Rew:192.0,1229.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.50 1245[4:Rew:1244.0,1202.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.50 1258[4:SpL:1146.0,1245.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 1259[4:Obv:1258.1] || -> .
% 0.21/0.50 1260[3:Spt:1259.0,1.0,851.0] || equal(multiply(sk_c8,sk_c7),sk_c9)** -> .
% 0.21/0.50 1261[3:Spt:1259.0,1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.21/0.50 1264[3:MRR:31.1,1260.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 1267[3:MRR:25.0,1260.0] || -> equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.50 1271[3:SpR:1261.0,97.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.21/0.50 1273[3:Rew:844.0,1271.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.21/0.50 1289[3:SpR:1267.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c8)**.
% 0.21/0.50 1291[3:Rew:1261.0,1289.0,1264.0,1289.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 1294[3:Rew:1291.0,1260.0] || equal(multiply(sk_c8,sk_c8),sk_c9)** -> .
% 0.21/0.50 1297[3:Rew:1291.0,1273.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.50 1299[3:Rew:1297.0,1294.0] || equal(sk_c9,sk_c9)* -> .
% 0.21/0.50 1300[3:Obv:1299.0] || -> .
% 0.21/0.50 1301[2:Spt:1300.0,2.0,844.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.21/0.50 1302[2:Spt:1300.0,2.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.21/0.50 1303[2:MRR:44.0,1301.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.50 1304[2:MRR:38.0,1301.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.50 1305[2:MRR:32.0,1301.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 1306[2:MRR:14.0,1301.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 1307[2:MRR:50.0,1301.0] || -> equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.21/0.50 1308[2:MRR:26.0,1301.0] || -> equal(multiply(sk_c2,sk_c8),sk_c9)**.
% 0.21/0.50 1309[2:MRR:8.0,1301.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 1312[2:SpR:1302.0,97.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.21/0.50 1314[2:SpR:1303.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.21/0.50 1320[2:SpR:1306.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.50 1323[2:SpR:1307.0,97.0] || -> equal(multiply(inverse(sk_c4),sk_c3),sk_c9)**.
% 0.21/0.50 1325[2:Rew:1304.0,1323.0] || -> equal(multiply(sk_c3,sk_c3),sk_c9)**.
% 0.21/0.50 1327[2:SpR:1308.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c8)**.
% 0.21/0.50 1329[2:Rew:1302.0,1327.0,1305.0,1327.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 1331[2:Rew:1329.0,1301.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.21/0.50 1333[2:Rew:1329.0,1312.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.21/0.50 1335[2:Rew:57.0,1333.0] || -> equal(identity,sk_c9)**.
% 0.21/0.50 1336[2:Rew:1335.0,56.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.50 1338[2:Rew:1336.0,1320.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.50 1339[2:Rew:1336.0,1314.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.50 1341[2:Rew:1338.0,1309.0] || -> equal(sk_c9,sk_c8)**.
% 0.21/0.50 1342[2:Rew:1341.0,1303.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 1346[2:Rew:1341.0,1325.0] || -> equal(multiply(sk_c3,sk_c3),sk_c8)**.
% 0.21/0.50 1351[2:Rew:1339.0,1346.0] || -> equal(sk_c3,sk_c8)**.
% 0.21/0.50 1353[2:Rew:1351.0,1342.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 1356[2:MRR:1353.0,1331.0] || -> .
% 0.21/0.50 % SZS output end Refutation
% 0.21/0.50 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_7 prove_this_8 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_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_31 prove_this_32 prove_this_38 prove_this_42 prove_this_44 prove_this_46 prove_this_48 prove_this_50 prove_this_54 prove_this_55 left_identity left_inverse associativity
% 0.21/0.50
%------------------------------------------------------------------------------