TSTP Solution File: GRP390-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP390-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:47:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP390-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 03:12:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 1314 clauses, backtracked 402 clauses, performed 13 splits and kept 803 clauses.
% 0.19/0.50 SPASS allocated 64012 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.08 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 5, length 378 :
% 0.19/0.50 % SZS output start Refutation
% 0.19/0.50 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 2[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c8),sk_c7).
% 0.19/0.50 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c8),sk_c7).
% 0.19/0.50 7[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 8[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 9[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 11[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 12[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.19/0.50 14[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.50 17[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.50 18[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.50 19[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 20[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 21[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 22[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 25[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 26[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 27[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 28[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 29[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 30[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.19/0.50 31[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 32[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 33[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 34[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 35[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 36[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 37[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,w),sk_c8)** equal(inverse(v),w) equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c9),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(y,sk_c8),sk_c7)** equal(inverse(y),sk_c8) equal(inverse(z),sk_c9) equal(multiply(z,sk_c8),sk_c9)** -> .
% 0.19/0.50 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.50 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.50 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.50 41[0:Con:37.10] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(y,sk_c8),sk_c9)** -> .
% 0.19/0.50 42[1:Spt:41.0,41.5,41.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.50 45[2:Spt:2.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.50 47[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 55[1:SpL:38.0,42.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 56[4:Spt:1.1] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 62[5:Spt:3.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 64[5:SpL:62.0,42.1] || equal(inverse(sk_c5),sk_c8) equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.50 65[5:Rew:47.0,64.0] || equal(sk_c8,sk_c8) equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.50 66[5:Obv:65.0] || equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.50 70[3:SpR:47.0,39.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.50 79[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.50 84[0:Rew:38.0,79.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.50 105[0:SpR:84.0,84.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.50 108[5:SpR:62.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.50 110[0:SpR:39.0,84.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.50 111[4:SpR:56.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.50 117[3:SpR:70.0,84.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.50 123[5:Rew:47.0,108.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 124[5:Rew:123.0,66.1] || equal(sk_c7,sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.50 126[4:Rew:45.0,111.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.50 140[5:Obv:124.1] || equal(sk_c7,sk_c8)** -> .
% 0.19/0.50 142[0:Rew:105.0,110.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.50 143[3:Rew:142.0,117.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.50 151[3:SpR:143.0,39.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.19/0.50 154[5:Rew:62.0,151.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 156[5:Rew:154.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.50 178[4:SpR:126.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.50 180[5:Rew:156.0,178.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 181[5:MRR:180.0,140.0] || -> .
% 0.19/0.50 182[5:Spt:181.0,3.1,62.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.19/0.50 183[5:Spt:181.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 184[5:Rew:143.0,183.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.50 185[5:Rew:184.0,47.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.50 190[5:Rew:184.0,70.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.50 191[4:Rew:39.0,178.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 193[5:Rew:191.0,190.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 195[4:Rew:191.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 196[4:Rew:191.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 199[5:Rew:195.0,193.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 205[5:Rew:199.0,185.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 237[5:Rew:196.0,55.2,199.0,55.2,205.0,55.0,191.0,55.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.19/0.50 238[5:Obv:237.1] || equal(u,sk_c8)* -> .
% 0.19/0.50 239[5:UnC:238.0,84.0] || -> .
% 0.19/0.50 246[4:Spt:239.0,1.1,56.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.19/0.50 247[4:Spt:239.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 248[4:Rew:143.0,247.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.50 249[4:Rew:248.0,143.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 251[4:Rew:248.0,151.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.50 257[4:MRR:25.1,246.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 265[4:MRR:19.0,246.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 305[4:SpR:265.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.19/0.50 307[4:Rew:257.0,305.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.19/0.50 313[4:SpR:307.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.19/0.50 315[4:Rew:39.0,313.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 316[4:Rew:315.0,251.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.19/0.50 319[4:Rew:315.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 322[4:Rew:315.0,55.0] || equal(inverse(sk_c8),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 330[4:Rew:319.0,316.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 347[4:Rew:330.0,249.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 388[4:Rew:319.0,322.2,330.0,322.2,347.0,322.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.19/0.50 389[4:Obv:388.1] || equal(u,sk_c8)* -> .
% 0.19/0.50 390[4:UnC:389.0,84.0] || -> .
% 0.19/0.50 400[3:Spt:390.0,4.0,47.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.50 401[3:Spt:390.0,4.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 402[3:MRR:28.0,400.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 404[3:MRR:34.0,400.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 405[3:MRR:22.0,400.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 407[3:SpR:401.0,84.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 420[3:SpR:404.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.50 424[3:SpR:405.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.19/0.50 426[3:Rew:402.0,424.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.19/0.50 432[3:SpR:426.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.19/0.50 434[3:Rew:39.0,432.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 436[3:Rew:434.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 437[3:Rew:434.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 440[3:Rew:434.0,55.0] || equal(inverse(sk_c8),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 443[3:Rew:436.0,407.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 444[3:Rew:436.0,420.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.50 454[3:Rew:443.0,444.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 455[3:Rew:454.0,404.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 457[3:Rew:455.0,401.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 475[3:Rew:437.0,440.2,455.0,440.2,457.0,440.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.19/0.50 476[3:Obv:475.1] || equal(u,sk_c8)* -> .
% 0.19/0.50 477[3:UnC:476.0,84.0] || -> .
% 0.19/0.50 486[2:Spt:477.0,2.0,45.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.50 487[2:Spt:477.0,2.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 489[2:MRR:26.0,486.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 492[2:MRR:32.0,486.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 493[2:MRR:20.0,486.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 498[2:SpR:487.0,84.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 513[2:SpR:492.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.50 517[2:SpR:493.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.19/0.50 519[2:Rew:489.0,517.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.19/0.50 525[2:SpR:519.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.19/0.50 527[2:Rew:39.0,525.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 529[2:Rew:527.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 530[2:Rew:527.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 532[2:Rew:527.0,55.0] || equal(inverse(sk_c8),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 548[2:Rew:530.0,498.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 549[2:Rew:530.0,513.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.50 552[2:Rew:548.0,549.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 553[2:Rew:552.0,492.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 555[2:Rew:553.0,487.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 570[2:Rew:529.0,532.2,553.0,532.2,555.0,532.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.19/0.50 571[2:Obv:570.1] || equal(u,sk_c8)* -> .
% 0.19/0.50 572[2:UnC:571.0,84.0] || -> .
% 0.19/0.50 579[1:Spt:572.0,41.1,41.2,41.3,41.4,41.6,41.7,41.9] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c7)**+ equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.50 581[2:Spt:4.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 582[2:Rew:581.0,579.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.50 584[2:Obv:582.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.50 586[2:SpR:581.0,84.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 588[3:Spt:26.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.50 591[4:Spt:8.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 594[5:Spt:32.1] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 595[5:SpR:594.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.50 596[5:SpR:594.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.50 601[6:Spt:20.1] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.19/0.50 603[6:SpR:601.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.19/0.50 605[6:Rew:588.0,603.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.19/0.50 606[7:Spt:14.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.50 608[7:SpR:606.0,84.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c8)**.
% 0.19/0.50 610[7:Rew:591.0,608.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.50 612[6:SpR:605.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.19/0.50 614[6:Rew:39.0,612.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 615[6:Rew:614.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 616[6:Rew:614.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 619[6:Rew:615.0,586.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 620[6:Rew:615.0,595.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.50 623[7:Rew:616.0,606.0] || -> equal(sk_c1,sk_c9)**.
% 0.19/0.50 626[6:Rew:616.0,584.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 627[7:Rew:623.0,591.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 630[6:Rew:619.0,620.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 631[6:Rew:630.0,594.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 633[6:Rew:631.0,581.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 643[6:Rew:616.0,626.3,631.0,626.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)**+ equal(w,sk_c9) -> .
% 0.19/0.50 682[7:SpL:610.0,643.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c9),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c8) equal(sk_c8,sk_c8) equal(v,sk_c9) -> .
% 0.19/0.50 683[7:Obv:682.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c9),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c8) equal(v,sk_c9) -> .
% 0.19/0.50 684[7:Rew:627.0,683.1] || equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(inverse(v),sk_c9)** equal(u,sk_c8) equal(v,sk_c9) -> .
% 0.19/0.50 685[7:Obv:684.1] || equal(inverse(u),sk_c8)**+ equal(inverse(v),sk_c9)** equal(u,sk_c8) equal(v,sk_c9) -> .
% 0.19/0.50 705[6:SpR:105.0,616.0] || -> equal(multiply(u,sk_c8),inverse(inverse(u)))**.
% 0.19/0.50 706[0:SpR:105.0,84.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.50 711[6:Rew:616.0,705.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.50 864[7:SpL:633.0,685.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c9)** equal(sk_c8,sk_c8) equal(u,sk_c9) -> .
% 0.19/0.50 867[7:Obv:864.2] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.50 894[7:SpL:627.0,867.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.50 897[7:Obv:894.1] || -> .
% 0.19/0.50 899[7:Spt:897.0,14.1,606.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.19/0.50 900[7:Spt:897.0,14.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.50 901[7:Rew:616.0,899.0] || equal(sk_c1,sk_c9)** -> .
% 0.19/0.50 904[6:Rew:616.0,17.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c1,sk_c9).
% 0.19/0.50 905[7:MRR:904.1,901.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 911[6:Rew:616.0,18.1,616.0,18.0] || -> equal(sk_c6,sk_c9) equal(sk_c1,sk_c9)**.
% 0.19/0.50 912[7:MRR:911.1,901.0] || -> equal(sk_c6,sk_c9)**.
% 0.19/0.50 913[7:Rew:912.0,905.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 918[7:SpR:900.0,711.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.19/0.50 922[7:Rew:913.0,918.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.50 923[7:Rew:922.0,900.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.50 924[7:Rew:922.0,591.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.19/0.50 925[7:Rew:922.0,901.0] || equal(sk_c1,sk_c4)** -> .
% 0.19/0.50 947[7:SpR:924.0,711.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.19/0.50 951[7:Rew:923.0,947.0] || -> equal(sk_c1,sk_c4)**.
% 0.19/0.50 952[7:MRR:951.0,925.0] || -> .
% 0.19/0.50 953[6:Spt:952.0,20.1,601.0] || equal(multiply(sk_c2,sk_c3),sk_c8)** -> .
% 0.19/0.50 954[6:Spt:952.0,20.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.50 955[6:MRR:22.1,953.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 958[6:MRR:21.1,953.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 959[6:MRR:19.1,953.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 971[2:SpR:581.0,706.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.19/0.50 974[6:SpR:955.0,706.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.50 977[3:SpR:588.0,706.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.19/0.50 985[6:SpR:958.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.50 986[6:SpR:958.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.50 988[6:Rew:955.0,986.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 989[6:Rew:974.0,985.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 990[6:Rew:989.0,595.0] || -> equal(multiply(sk_c3,u),multiply(sk_c8,u))**.
% 0.19/0.50 991[6:Rew:989.0,971.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 993[6:Rew:991.0,988.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 999[6:Rew:993.0,596.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.50 1003[6:Rew:991.0,990.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 1004[6:Rew:1003.0,977.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.50 1006[6:Rew:1004.0,953.0] || equal(sk_c3,sk_c8)** -> .
% 0.19/0.50 1014[6:SpR:959.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.50 1016[6:Rew:954.0,1014.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.50 1031[6:SpR:1016.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.50 1033[6:Rew:39.0,1031.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 1035[6:Rew:1033.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 1037[6:Rew:1033.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.50 1040[6:Rew:1035.0,999.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 1066[6:SpR:1040.0,1037.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.50 1075[6:Rew:991.0,1066.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.50 1076[6:MRR:1075.0,1006.0] || -> .
% 0.19/0.50 1079[5:Spt:1076.0,32.1,594.0] || equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.50 1080[5:Spt:1076.0,32.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.50 1081[5:MRR:34.1,1079.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 1082[5:MRR:35.1,1079.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1083[5:MRR:33.1,1079.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 1084[5:MRR:31.1,1079.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 1085[5:MRR:36.1,1079.0] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.19/0.50 1096[5:SpR:1081.0,706.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.50 1101[5:SpR:1083.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.50 1102[5:SpR:1083.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.50 1104[5:Rew:1081.0,1102.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 1105[5:Rew:1096.0,1101.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1106[5:Rew:1105.0,971.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1108[5:Rew:1106.0,1104.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 1111[5:Rew:1108.0,581.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 1114[5:Rew:1108.0,584.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.50 1124[5:SpR:1084.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.50 1126[5:Rew:1080.0,1124.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.50 1129[5:SpR:1085.0,84.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c8)**.
% 0.19/0.50 1131[5:Rew:1082.0,1129.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.50 1141[5:SpR:1126.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.50 1143[5:Rew:39.0,1141.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 1145[5:Rew:1143.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 1146[5:Rew:1143.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.50 1149[5:Rew:1145.0,1114.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1153[5:Rew:1145.0,1149.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1157[5:SpR:1131.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.19/0.50 1159[5:Rew:1145.0,1157.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 1166[5:SpR:1080.0,1146.0] || -> equal(multiply(sk_c9,sk_c4),sk_c8)**.
% 0.19/0.50 1203[5:SpR:1166.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c4)**.
% 0.19/0.50 1205[5:Rew:1159.0,1203.0] || -> equal(multiply(sk_c9,sk_c8),sk_c4)**.
% 0.19/0.50 1206[5:Rew:1145.0,1205.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.50 1207[5:Rew:1206.0,1080.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.50 1208[5:Rew:1206.0,1084.0] || -> equal(multiply(sk_c4,sk_c4),sk_c8)**.
% 0.19/0.50 1217[5:Rew:1206.0,1153.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1219[5:Rew:1206.0,1217.5,1206.0,1217.4,1206.0,1217.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c4)** equal(u,sk_c8) equal(multiply(v,sk_c4),sk_c8)**+ equal(w,sk_c4) -> .
% 0.19/0.50 1243[5:SpL:1208.0,1219.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(sk_c8,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.50 1244[5:Obv:1243.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.50 1245[5:Rew:1207.0,1244.1] || equal(inverse(u),sk_c8)** equal(sk_c4,sk_c4) equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.50 1246[5:Obv:1245.1] || equal(inverse(u),sk_c8)**+ equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.50 1394[5:SpL:1111.0,1246.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c4)** equal(sk_c8,sk_c8) equal(u,sk_c4) -> .
% 0.19/0.50 1398[5:Obv:1394.2] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.19/0.50 1402[5:SpL:1207.0,1398.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.19/0.50 1406[5:Obv:1402.1] || -> .
% 0.19/0.50 1407[4:Spt:1406.0,8.1,591.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.50 1408[4:Spt:1406.0,8.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.50 1409[4:MRR:10.1,1407.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 1410[4:MRR:11.1,1407.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1411[4:MRR:9.0,1407.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.50 1412[4:MRR:7.0,1407.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.50 1413[4:MRR:12.0,1407.0] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.19/0.50 1421[4:SpR:1409.0,706.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.50 1426[4:SpR:1411.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.50 1427[4:SpR:1411.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.50 1429[4:Rew:1409.0,1427.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 1430[4:Rew:1421.0,1426.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1431[4:Rew:1430.0,971.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1433[4:Rew:1431.0,1429.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.50 1436[4:Rew:1433.0,581.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.50 1438[4:Rew:1433.0,584.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.50 1448[4:SpR:1412.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.50 1450[4:Rew:1408.0,1448.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.50 1453[4:SpR:1413.0,84.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c8)**.
% 0.19/0.50 1455[4:Rew:1410.0,1453.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.50 1461[4:SpR:1450.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.50 1463[4:Rew:39.0,1461.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 1465[4:Rew:1463.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 1467[4:Rew:1463.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.50 1469[4:Rew:1465.0,1438.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1472[4:Rew:1465.0,1469.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1476[4:SpR:1455.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.19/0.50 1478[4:Rew:1465.0,1476.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 1488[4:SpR:1408.0,1467.0] || -> equal(multiply(sk_c9,sk_c4),sk_c8)**.
% 0.19/0.50 1506[4:SpR:1488.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c4)**.
% 0.19/0.50 1508[4:Rew:1478.0,1506.0] || -> equal(multiply(sk_c9,sk_c8),sk_c4)**.
% 0.19/0.50 1509[4:Rew:1465.0,1508.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.50 1510[4:Rew:1509.0,1408.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.50 1513[4:Rew:1509.0,1412.0] || -> equal(multiply(sk_c4,sk_c4),sk_c8)**.
% 0.19/0.50 1521[4:Rew:1509.0,1472.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.50 1524[4:Rew:1509.0,1521.5,1509.0,1521.4,1509.0,1521.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c4)** equal(u,sk_c8) equal(multiply(v,sk_c4),sk_c8)**+ equal(w,sk_c4) -> .
% 0.19/0.50 1552[4:SpL:1513.0,1524.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(sk_c8,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.50 1553[4:Obv:1552.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1554[4:Rew:1510.0,1553.1] || equal(inverse(u),sk_c8)** equal(sk_c4,sk_c4) equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1555[4:Obv:1554.1] || equal(inverse(u),sk_c8)**+ equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1692[4:SpL:1436.0,1555.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c4)** equal(sk_c8,sk_c8) equal(u,sk_c4) -> .
% 0.19/0.51 1696[4:Obv:1692.2] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.19/0.51 1700[4:SpL:1510.0,1696.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.19/0.51 1704[4:Obv:1700.1] || -> .
% 0.19/0.51 1705[3:Spt:1704.0,26.1,588.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.19/0.51 1706[3:Spt:1704.0,26.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.51 1707[3:MRR:28.1,1705.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.51 1708[3:MRR:29.1,1705.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.51 1709[3:MRR:27.0,1705.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.51 1710[3:MRR:25.0,1705.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.51 1711[3:MRR:30.0,1705.0] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.19/0.51 1719[3:SpR:1707.0,706.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.51 1724[3:SpR:1709.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.51 1725[3:SpR:1709.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.51 1727[3:Rew:1707.0,1725.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.51 1728[3:Rew:1719.0,1724.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.51 1729[3:Rew:1728.0,971.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1731[3:Rew:1729.0,1727.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 1734[3:Rew:1731.0,581.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 1736[3:Rew:1731.0,584.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.51 1746[3:SpR:1710.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.51 1748[3:Rew:1706.0,1746.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.51 1751[3:SpR:1711.0,84.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c8)**.
% 0.19/0.51 1753[3:Rew:1708.0,1751.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1759[3:SpR:1748.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.51 1761[3:Rew:39.0,1759.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1762[3:Rew:1761.0,142.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1764[3:Rew:1761.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.51 1767[3:Rew:1762.0,1736.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.51 1770[3:Rew:1762.0,1767.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.51 1774[3:SpR:1753.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.19/0.51 1776[3:Rew:1762.0,1774.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.51 1785[3:SpR:1706.0,1764.0] || -> equal(multiply(sk_c9,sk_c4),sk_c8)**.
% 0.19/0.51 1797[3:SpR:1785.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c4)**.
% 0.19/0.51 1799[3:Rew:1776.0,1797.0] || -> equal(multiply(sk_c9,sk_c8),sk_c4)**.
% 0.19/0.51 1800[3:Rew:1762.0,1799.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.51 1801[3:Rew:1800.0,1706.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.51 1803[3:Rew:1800.0,1710.0] || -> equal(multiply(sk_c4,sk_c4),sk_c8)**.
% 0.19/0.51 1811[3:Rew:1800.0,1770.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** equal(w,sk_c9) -> .
% 0.19/0.51 1814[3:Rew:1800.0,1811.5,1800.0,1811.4,1800.0,1811.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c4)** equal(u,sk_c8) equal(multiply(v,sk_c4),sk_c8)**+ equal(w,sk_c4) -> .
% 0.19/0.51 1849[3:SpL:1803.0,1814.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(sk_c8,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1853[3:Obv:1849.4] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1854[3:Rew:1801.0,1853.1] || equal(inverse(u),sk_c8)** equal(sk_c4,sk_c4) equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1855[3:Obv:1854.1] || equal(inverse(u),sk_c8)**+ equal(inverse(v),sk_c4)** equal(u,sk_c8) equal(v,sk_c4) -> .
% 0.19/0.51 1899[3:SpL:1734.0,1855.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c4)** equal(sk_c8,sk_c8) equal(u,sk_c4) -> .
% 0.19/0.51 1902[3:Obv:1899.2] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.19/0.51 1905[3:SpL:1801.0,1902.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.19/0.51 1908[3:Obv:1905.1] || -> .
% 0.19/0.51 1909[2:Spt:1908.0,4.1,581.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.51 1910[2:Spt:1908.0,4.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.51 1911[2:MRR:2.1,1909.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.51 1913[2:MRR:3.0,1909.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.51 1914[2:MRR:1.0,1909.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.51 1920[2:SpR:1911.0,706.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),u)**.
% 0.19/0.51 1926[2:SpR:1913.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.19/0.51 1928[2:Rew:1910.0,1926.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.51 1930[2:SpR:1914.0,40.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.19/0.51 1931[2:SpR:1914.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.51 1933[2:Rew:1911.0,1931.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.51 1934[2:Rew:1920.0,1930.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1935[2:Rew:1934.0,1928.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 1938[2:Rew:1935.0,1909.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.19/0.51 1951[2:SpR:1933.0,84.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.51 1953[2:Rew:39.0,1951.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1957[2:Rew:1953.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.51 1976[2:SpR:1910.0,1957.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.51 1980[2:Rew:1934.0,1976.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.51 1981[2:Rew:1980.0,1910.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 1983[2:MRR:1981.0,1938.0] || -> .
% 0.19/0.51 % SZS output end Refutation
% 0.19/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_14 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.19/0.51
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