TSTP Solution File: GRP384-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP384-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:47:07 EDT 2022
% Result : Unsatisfiable 0.42s 0.58s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP384-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n006.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 : Mon Jun 13 08:17:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/0.58
% 0.42/0.58 SPASS V 3.9
% 0.42/0.58 SPASS beiseite: Proof found.
% 0.42/0.58 % SZS status Theorem
% 0.42/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.58 SPASS derived 1906 clauses, backtracked 724 clauses, performed 13 splits and kept 1374 clauses.
% 0.42/0.58 SPASS allocated 64572 KBytes.
% 0.42/0.58 SPASS spent 0:00:00.24 on the problem.
% 0.42/0.58 0:00:00.03 for the input.
% 0.42/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.42/0.58 0:00:00.01 for inferences.
% 0.42/0.58 0:00:00.00 for the backtracking.
% 0.42/0.58 0:00:00.16 for the reduction.
% 0.42/0.58
% 0.42/0.58
% 0.42/0.58 Here is a proof with depth 5, length 426 :
% 0.42/0.58 % SZS output start Refutation
% 0.42/0.58 1[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c11),sk_c10).
% 0.42/0.58 5[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.42/0.58 7[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c11),sk_c10).
% 0.42/0.58 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.42/0.58 11[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 13[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 17[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 18[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 20[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.42/0.58 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.42/0.58 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.42/0.58 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 27[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.42/0.58 28[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 33[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 37[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 43[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c2)**.
% 0.42/0.58 45[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.42/0.58 47[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.42/0.58 53[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 54[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 55[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 56[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 57[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 59[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 61[0:Inp] || equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10) equal(multiply(u,v),sk_c10)** equal(inverse(u),v) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c11),sk_c10)** equal(inverse(w),sk_c11) equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(y,z),sk_c11)** equal(inverse(y),z) equal(multiply(z,sk_c10),sk_c11)** equal(inverse(x1),x2) equal(inverse(x2),z)* equal(multiply(x1,z),x2)* -> .
% 0.42/0.58 62[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.42/0.58 63[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.42/0.58 64[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.42/0.58 65[0:Con:61.3] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(sk_c11),sk_c10) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 66[1:Spt:65.0,65.1,65.2,65.6,65.7,65.8] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** -> .
% 0.42/0.58 68[2:Spt:9.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.42/0.58 70[3:Spt:29.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 72[3:SpL:70.0,66.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 73[3:Rew:68.0,72.1] || equal(inverse(u),sk_c9)** equal(sk_c10,u) equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 74[3:Obv:73.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 75[4:Spt:19.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 78[5:Spt:49.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.42/0.58 80[6:Spt:59.1] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.42/0.58 85[7:Spt:39.1] || -> equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 90[2:SpR:68.0,63.0] || -> equal(multiply(sk_c10,sk_c11),identity)**.
% 0.42/0.58 91[5:SpR:78.0,63.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.42/0.58 103[0:SpR:63.0,64.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.42/0.58 105[2:SpR:90.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),multiply(identity,u))**.
% 0.42/0.58 106[5:SpR:91.0,64.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.42/0.58 108[2:Rew:62.0,105.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.42/0.58 109[5:Rew:62.0,106.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.42/0.58 110[0:Rew:62.0,103.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.42/0.58 124[7:SpR:85.0,109.0] || -> equal(multiply(sk_c2,sk_c10),sk_c2)**.
% 0.42/0.58 134[0:SpR:110.0,110.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.42/0.58 137[4:SpR:75.0,110.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c9)**.
% 0.42/0.58 140[0:SpR:63.0,110.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.42/0.58 145[7:SpR:124.0,110.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c10)**.
% 0.42/0.58 146[2:SpR:108.0,110.0] || -> equal(multiply(inverse(sk_c10),u),multiply(sk_c11,u))**.
% 0.42/0.58 154[7:Rew:63.0,145.0] || -> equal(sk_c10,identity)**.
% 0.42/0.58 156[7:Rew:154.0,68.0] || -> equal(inverse(sk_c11),identity)**.
% 0.42/0.58 158[7:Rew:154.0,75.0] || -> equal(multiply(identity,sk_c9),sk_c11)**.
% 0.42/0.58 161[7:Rew:154.0,90.0] || -> equal(multiply(identity,sk_c11),identity)**.
% 0.42/0.58 174[7:Rew:154.0,74.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(identity,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 188[7:Rew:62.0,158.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 191[7:Rew:62.0,161.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 197[7:Rew:191.0,154.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 198[7:Rew:191.0,156.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 219[7:Rew:191.0,140.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.42/0.58 226[7:Rew:134.0,219.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 234[7:Rew:188.0,174.4,226.0,174.4,197.0,174.4,226.0,174.3,188.0,174.3,191.0,174.2,188.0,174.1,188.0,174.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.42/0.58 235[7:Obv:234.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.42/0.58 541[7:SpL:198.0,235.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.42/0.58 544[7:Obv:541.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 546[7:SpL:198.0,544.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 549[7:Obv:546.1] || -> .
% 0.42/0.58 550[7:Spt:549.0,39.1,85.0] || equal(multiply(sk_c1,sk_c2),sk_c10)** -> .
% 0.42/0.58 551[7:Spt:549.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 552[4:Rew:146.0,137.0] || -> equal(multiply(sk_c11,sk_c11),sk_c9)**.
% 0.42/0.58 558[7:MRR:36.1,550.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 559[7:MRR:34.1,550.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 561[0:Rew:134.0,140.0] || -> equal(multiply(u,identity),u)**.
% 0.42/0.58 564[7:MRR:37.1,550.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 565[7:MRR:35.1,550.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 566[7:MRR:33.1,550.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 597[2:SpR:90.0,110.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c11)**.
% 0.42/0.58 599[2:Rew:561.0,597.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.42/0.58 629[5:SpR:91.0,110.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.42/0.58 631[5:Rew:561.0,629.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.42/0.58 647[7:SpR:565.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 649[7:Rew:558.0,647.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 651[7:SpR:566.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 653[7:Rew:75.0,651.0,559.0,651.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 654[7:Rew:653.0,68.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 657[7:Rew:653.0,90.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.42/0.58 659[7:Rew:653.0,80.0] || -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.42/0.58 662[7:Rew:653.0,564.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 665[7:Rew:653.0,550.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.42/0.58 689[7:Rew:552.0,657.0] || -> equal(identity,sk_c9)**.
% 0.42/0.58 694[7:Rew:689.0,561.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.42/0.58 696[7:Rew:649.0,662.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 706[7:Rew:696.0,649.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 708[7:Rew:694.0,659.0] || -> equal(sk_c2,sk_c11)**.
% 0.42/0.58 710[7:Rew:708.0,631.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.42/0.58 714[7:Rew:654.0,710.0] || -> equal(sk_c1,sk_c11)**.
% 0.42/0.58 717[7:Rew:552.0,706.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 722[7:Rew:717.0,694.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 742[7:Rew:722.0,665.0,714.0,665.0,708.0,665.0] || equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 743[7:Obv:742.0] || -> .
% 0.42/0.58 783[6:Spt:743.0,59.1,80.0] || equal(multiply(sk_c2,sk_c9),sk_c10)** -> .
% 0.42/0.58 784[6:Spt:743.0,59.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 786[6:MRR:56.1,783.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 787[6:MRR:54.1,783.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 790[6:MRR:57.1,783.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 791[6:MRR:55.1,783.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 792[6:MRR:53.1,783.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 847[6:SpR:791.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 849[6:Rew:786.0,847.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 851[6:SpR:792.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 853[6:Rew:75.0,851.0,787.0,851.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 854[6:Rew:853.0,599.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 859[6:Rew:853.0,90.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.42/0.58 861[6:Rew:853.0,790.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 871[6:Rew:853.0,74.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 886[6:Rew:552.0,859.0] || -> equal(identity,sk_c9)**.
% 0.42/0.58 888[6:Rew:886.0,561.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.42/0.58 892[6:Rew:849.0,861.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 902[6:Rew:892.0,849.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 904[6:Rew:552.0,902.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 909[6:Rew:904.0,888.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 946[6:Rew:904.0,871.4,909.0,871.4,853.0,871.4,909.0,871.3,904.0,871.3,904.0,871.1,904.0,871.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.42/0.58 947[6:Obv:946.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.42/0.58 1223[6:SpL:854.0,947.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.42/0.58 1225[6:Obv:1223.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 1338[6:SpL:854.0,1225.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 1342[6:Obv:1338.1] || -> .
% 0.42/0.58 1343[5:Spt:1342.0,49.1,78.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.42/0.58 1344[5:Spt:1342.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 1346[5:MRR:46.1,1343.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 1347[5:MRR:44.1,1343.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 1351[5:MRR:47.0,1343.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 1352[5:MRR:45.0,1343.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 1353[5:MRR:43.0,1343.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 1399[5:SpR:1352.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 1401[5:Rew:1346.0,1399.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 1403[5:SpR:1353.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 1405[5:Rew:75.0,1403.0,1347.0,1403.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 1406[5:Rew:1405.0,68.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 1410[5:Rew:1405.0,90.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.42/0.58 1413[5:Rew:1405.0,1351.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 1422[5:Rew:1405.0,74.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.42/0.58 1435[5:Rew:552.0,1410.0] || -> equal(identity,sk_c9)**.
% 0.42/0.58 1437[5:Rew:1435.0,561.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.42/0.58 1440[5:Rew:1401.0,1413.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 1450[5:Rew:1440.0,1401.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 1452[5:Rew:552.0,1450.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 1457[5:Rew:1452.0,1437.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 1492[5:Rew:1452.0,1422.4,1457.0,1422.4,1405.0,1422.4,1457.0,1422.3,1452.0,1422.3,1452.0,1422.1,1452.0,1422.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.42/0.58 1493[5:Obv:1492.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.42/0.58 1739[5:SpL:1406.0,1493.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.42/0.58 1742[5:Obv:1739.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 1744[5:SpL:1406.0,1742.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 1747[5:Obv:1744.1] || -> .
% 0.42/0.58 1748[4:Spt:1747.0,19.1,75.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 1749[4:Spt:1747.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 1751[4:MRR:16.1,1748.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 1752[4:MRR:14.1,1748.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 1756[4:MRR:15.1,1748.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 1757[4:MRR:13.1,1748.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 1758[4:MRR:11.1,1748.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 1794[4:SpR:1756.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 1796[4:Rew:1751.0,1794.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 1798[4:SpR:1757.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 1800[4:Rew:1752.0,1798.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.42/0.58 1801[4:Rew:1800.0,1748.0] || equal(sk_c10,sk_c11)** -> .
% 0.42/0.58 1813[4:SpR:1796.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.42/0.58 1815[4:Rew:63.0,1813.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 1816[4:Rew:1815.0,90.0] || -> equal(multiply(sk_c10,sk_c11),sk_c11)**.
% 0.42/0.58 1817[4:Rew:1815.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 1824[4:Rew:1817.0,1758.0] || -> equal(sk_c10,sk_c3)**.
% 0.42/0.58 1826[4:Rew:1817.0,1816.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 1834[4:Rew:1824.0,1801.0] || equal(sk_c3,sk_c11)** -> .
% 0.42/0.58 1852[4:Rew:1824.0,1826.0] || -> equal(sk_c3,sk_c11)**.
% 0.42/0.58 1860[4:Rew:1852.0,1834.0] || equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 1861[4:Obv:1860.0] || -> .
% 0.42/0.58 1922[3:Spt:1861.0,29.1,70.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.42/0.58 1923[3:Spt:1861.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 1925[3:MRR:26.1,1922.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 1926[3:MRR:24.1,1922.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 1927[3:MRR:22.1,1922.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.42/0.58 1930[3:MRR:25.1,1922.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 1931[3:MRR:23.1,1922.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 1932[3:MRR:21.1,1922.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 1960[3:SpR:1930.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 1962[3:Rew:1925.0,1960.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 1964[3:SpR:1931.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 1966[3:Rew:1926.0,1964.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.42/0.58 1968[3:SpR:1932.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.42/0.58 1970[3:Rew:1927.0,1968.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.42/0.58 1978[3:SpR:1962.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.42/0.58 1980[3:Rew:63.0,1978.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 1982[3:Rew:1980.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.58 1983[3:Rew:1980.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 1991[3:Rew:1982.0,1970.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 1997[3:Rew:1982.0,1922.0] || equal(sk_c10,sk_c9)** -> .
% 0.42/0.58 2002[3:Rew:1991.0,1931.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.42/0.58 2011[3:Rew:1991.0,1966.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.42/0.58 2013[3:Rew:1991.0,1997.0] || equal(sk_c9,sk_c11)** -> .
% 0.42/0.58 2027[3:Rew:1983.0,2002.0] || -> equal(sk_c9,sk_c4)**.
% 0.42/0.58 2028[3:Rew:2027.0,2013.0] || equal(sk_c4,sk_c11)** -> .
% 0.42/0.58 2029[3:Rew:1982.0,2011.0,2027.0,2011.0] || -> equal(sk_c4,sk_c11)**.
% 0.42/0.58 2030[3:MRR:2029.0,2028.0] || -> .
% 0.42/0.58 2064[2:Spt:2030.0,9.1,68.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.42/0.58 2065[2:Spt:2030.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 2067[2:MRR:6.1,2064.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2069[2:MRR:2.1,2064.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.42/0.58 2072[2:MRR:5.0,2064.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2074[2:MRR:1.0,2064.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 2093[2:SpR:2072.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 2095[2:Rew:2067.0,2093.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 2101[2:SpR:2074.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.42/0.58 2103[2:Rew:2069.0,2101.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.42/0.58 2109[2:SpR:2095.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.42/0.58 2111[2:Rew:63.0,2109.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 2112[2:Rew:2111.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 2113[2:Rew:2111.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.58 2118[2:Rew:2112.0,2074.0] || -> equal(sk_c10,sk_c3)**.
% 0.42/0.58 2121[2:Rew:2118.0,2064.0] || equal(inverse(sk_c11),sk_c3)** -> .
% 0.42/0.58 2133[2:Rew:2118.0,2103.0] || -> equal(multiply(sk_c11,sk_c3),sk_c11)**.
% 0.42/0.58 2137[2:Rew:2113.0,2133.0] || -> equal(sk_c3,sk_c11)**.
% 0.42/0.58 2138[2:Rew:2137.0,2069.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 2142[2:Rew:2137.0,2121.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.42/0.58 2147[2:Rew:2138.0,2142.0] || equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 2148[2:Obv:2147.0] || -> .
% 0.42/0.58 2194[1:Spt:2148.0,65.3,65.4,65.5,65.9,65.10,65.11,65.12] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(sk_c11),sk_c10) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 2196[2:Spt:8.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.42/0.58 2197[2:Rew:2196.0,2194.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 2199[2:Obv:2197.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 2201[2:SpR:2196.0,110.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.42/0.58 2203[3:Spt:19.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.42/0.58 2205[3:Rew:2203.0,2199.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** equal(sk_c11,sk_c11) -> .
% 0.42/0.58 2206[3:Obv:2205.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.42/0.58 2208[3:SpR:2203.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.42/0.58 2209[3:SpR:2203.0,110.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c9)**.
% 0.42/0.58 2211[4:Spt:28.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.42/0.58 2213[4:Rew:2211.0,2206.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.42/0.58 2214[4:Obv:2213.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.42/0.58 2216[4:SpR:2211.0,64.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.42/0.58 2217[4:SpR:2211.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.42/0.58 2219[4:Rew:2196.0,2217.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.42/0.58 2220[5:Spt:49.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.42/0.58 2223[6:Spt:39.1] || -> equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.42/0.58 2225[6:SpR:2223.0,110.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c2)**.
% 0.42/0.58 2227[6:Rew:2220.0,2225.0] || -> equal(multiply(sk_c2,sk_c10),sk_c2)**.
% 0.42/0.58 2239[6:SpR:2227.0,110.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c10)**.
% 0.42/0.58 2241[6:Rew:63.0,2239.0] || -> equal(sk_c10,identity)**.
% 0.42/0.58 2242[6:Rew:2241.0,2196.0] || -> equal(inverse(sk_c11),identity)**.
% 0.42/0.58 2243[6:Rew:2241.0,2203.0] || -> equal(multiply(identity,sk_c9),sk_c11)**.
% 0.42/0.58 2247[6:Rew:2241.0,2219.0] || -> equal(multiply(identity,identity),sk_c9)**.
% 0.42/0.58 2252[6:Rew:2241.0,2214.0] || equal(inverse(u),identity) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.42/0.58 2260[6:Rew:62.0,2243.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 2263[6:Rew:62.0,2247.0] || -> equal(identity,sk_c9)**.
% 0.42/0.58 2264[6:Rew:2260.0,2263.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 2266[6:Rew:2264.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 2269[6:Rew:2264.0,2241.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 2270[6:Rew:2264.0,2242.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 2293[6:Rew:2266.0,2252.3,2269.0,2252.3,2266.0,2252.2,2269.0,2252.2,2260.0,2252.2,2264.0,2252.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.42/0.58 2294[6:Con:2293.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 2323[6:SpL:2270.0,2294.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 2324[6:Obv:2323.1] || -> .
% 0.42/0.58 2325[6:Spt:2324.0,39.1,2223.0] || equal(multiply(sk_c1,sk_c2),sk_c10)** -> .
% 0.42/0.58 2326[6:Spt:2324.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 2328[6:MRR:36.1,2325.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2329[6:MRR:34.1,2325.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 2332[6:MRR:37.1,2325.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 2333[6:MRR:35.1,2325.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2334[6:MRR:33.1,2325.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 2368[6:SpR:2333.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 2370[6:Rew:2328.0,2368.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 2372[6:SpR:2334.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 2374[6:Rew:2203.0,2372.0,2329.0,2372.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 2375[6:Rew:2374.0,2196.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 2377[6:Rew:2374.0,2219.0] || -> equal(multiply(sk_c11,sk_c11),sk_c9)**.
% 0.42/0.58 2380[6:Rew:2374.0,2332.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 2385[6:Rew:2374.0,2201.0] || -> equal(multiply(sk_c11,multiply(sk_c11,u)),u)**.
% 0.42/0.58 2386[6:Rew:2374.0,2216.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.42/0.58 2391[6:Rew:2374.0,2214.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.42/0.58 2395[6:Rew:2370.0,2380.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 2405[6:Rew:2395.0,2370.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 2406[6:Rew:2377.0,2405.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 2414[6:Rew:2385.0,2386.0,2406.0,2386.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.58 2431[6:Rew:2374.0,2391.3,2374.0,2391.2,2406.0,2391.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.42/0.58 2432[6:Con:2431.1] || equal(inverse(u),sk_c11) equal(multiply(u,sk_c11),sk_c11)** -> .
% 0.42/0.58 2462[6:SpR:2414.0,561.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 2465[6:Rew:2462.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 2468[6:Rew:2465.0,2432.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 2504[6:SpL:2375.0,2468.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 2505[6:Obv:2504.1] || -> .
% 0.42/0.58 2506[5:Spt:2505.0,49.1,2220.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.42/0.58 2507[5:Spt:2505.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 2509[5:MRR:46.1,2506.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2510[5:MRR:44.1,2506.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 2513[5:MRR:47.0,2506.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 2514[5:MRR:45.0,2506.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2515[5:MRR:43.0,2506.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 2547[5:SpR:2514.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 2549[5:Rew:2509.0,2547.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 2551[5:SpR:2515.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 2553[5:Rew:2203.0,2551.0,2510.0,2551.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 2554[5:Rew:2553.0,2196.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 2558[5:Rew:2553.0,2219.0] || -> equal(multiply(sk_c11,sk_c11),sk_c9)**.
% 0.42/0.58 2559[5:Rew:2553.0,2513.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 2563[5:Rew:2553.0,2201.0] || -> equal(multiply(sk_c11,multiply(sk_c11,u)),u)**.
% 0.42/0.58 2564[5:Rew:2553.0,2208.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.42/0.58 2569[5:Rew:2553.0,2214.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.42/0.58 2573[5:Rew:2549.0,2559.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 2583[5:Rew:2573.0,2549.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 2584[5:Rew:2558.0,2583.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 2592[5:Rew:2563.0,2564.0,2584.0,2564.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.58 2609[5:Rew:2553.0,2569.3,2553.0,2569.2,2584.0,2569.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.42/0.58 2610[5:Con:2609.1] || equal(inverse(u),sk_c11) equal(multiply(u,sk_c11),sk_c11)** -> .
% 0.42/0.58 2640[5:SpR:2592.0,561.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 2642[5:Rew:2640.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 2646[5:Rew:2642.0,2610.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.42/0.58 2684[5:SpL:2554.0,2646.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 2685[5:Obv:2684.1] || -> .
% 0.42/0.58 2686[4:Spt:2685.0,28.1,2211.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.42/0.58 2687[4:Spt:2685.0,28.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.42/0.58 2688[4:MRR:26.1,2686.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2689[4:MRR:24.1,2686.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 2693[4:MRR:27.1,2686.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 2694[4:MRR:25.1,2686.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2695[4:MRR:23.1,2686.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 2720[4:SpR:2694.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 2722[4:Rew:2688.0,2720.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 2724[4:SpR:2695.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 2726[4:Rew:2203.0,2724.0,2689.0,2724.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.58 2727[4:Rew:2726.0,2196.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.58 2730[4:Rew:2726.0,2693.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.58 2732[4:Rew:2726.0,2209.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c9)**.
% 0.42/0.58 2733[4:Rew:2726.0,2686.0] || equal(multiply(sk_c11,sk_c9),sk_c11)** -> .
% 0.42/0.58 2740[4:Rew:2722.0,2730.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.58 2750[4:Rew:2740.0,2722.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.42/0.58 2751[4:Rew:2750.0,2732.0,2727.0,2732.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.58 2754[4:Rew:2750.0,2733.0,2751.0,2733.0] || equal(sk_c11,sk_c11)* -> .
% 0.42/0.58 2755[4:Obv:2754.0] || -> .
% 0.42/0.58 2773[3:Spt:2755.0,19.1,2203.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.42/0.58 2774[3:Spt:2755.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.42/0.58 2775[3:MRR:18.1,2773.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.42/0.58 2776[3:MRR:16.1,2773.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2777[3:MRR:14.1,2773.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.42/0.58 2778[3:MRR:12.1,2773.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.42/0.58 2779[3:MRR:20.1,2773.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.42/0.58 2780[3:MRR:17.1,2773.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 2781[3:MRR:15.1,2773.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2782[3:MRR:13.1,2773.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.42/0.58 2783[3:MRR:11.1,2773.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 2790[3:SpR:2776.0,110.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.42/0.58 2794[3:SpR:2778.0,110.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.42/0.58 2797[3:SpR:2779.0,110.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.42/0.58 2799[3:Rew:2775.0,2797.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.42/0.58 2800[3:SpR:2780.0,64.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),multiply(sk_c11,u))**.
% 0.42/0.58 2801[3:SpR:2780.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c10)**.
% 0.42/0.58 2804[3:SpR:2781.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.58 2806[3:Rew:2776.0,2804.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.58 2808[3:SpR:2782.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.42/0.58 2810[3:Rew:2777.0,2808.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.42/0.58 2811[3:Rew:2810.0,2773.0] || equal(sk_c10,sk_c11)** -> .
% 0.42/0.58 2817[3:SpR:2799.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.42/0.58 2819[3:Rew:2774.0,2817.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.42/0.58 2824[3:SpR:2806.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.42/0.58 2826[3:Rew:63.0,2824.0] || -> equal(identity,sk_c11)**.
% 0.42/0.58 2827[3:Rew:2826.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.58 2828[3:Rew:2826.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.58 2832[3:Rew:2827.0,2794.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.42/0.58 2834[3:Rew:2827.0,2800.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),u)**.
% 0.42/0.58 2838[3:Rew:2828.0,2783.0] || -> equal(sk_c10,sk_c3)**.
% 0.42/0.58 2839[3:Rew:2828.0,2801.0] || -> equal(inverse(sk_c8),sk_c10)**.
% 0.42/0.58 2844[3:Rew:2838.0,2811.0] || equal(sk_c3,sk_c11)** -> .
% 0.42/0.58 2848[3:Rew:2838.0,2839.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.42/0.58 2853[3:Rew:2832.0,2834.0,2838.0,2834.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.42/0.58 2854[3:Rew:2853.0,2790.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.42/0.58 2857[3:Rew:2853.0,2819.0] || -> equal(sk_c6,sk_c8)**.
% 0.42/0.58 2861[3:Rew:2857.0,2774.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.42/0.58 2866[3:Rew:2848.0,2861.0] || -> equal(sk_c8,sk_c3)**.
% 0.42/0.58 2868[3:Rew:2866.0,2781.0] || -> equal(multiply(sk_c5,sk_c3),sk_c11)**.
% 0.42/0.58 2878[3:Rew:2854.0,2868.0] || -> equal(sk_c3,sk_c11)**.
% 0.42/0.58 2879[3:MRR:2878.0,2844.0] || -> .
% 0.42/0.58 2888[2:Spt:2879.0,8.1,2196.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.42/0.58 2889[2:Spt:2879.0,8.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.42/0.58 2890[2:MRR:6.1,2888.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.42/0.58 2892[2:MRR:2.1,2888.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.42/0.58 2895[2:MRR:7.0,2888.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.42/0.58 2896[2:MRR:5.0,2888.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.42/0.58 2898[2:MRR:1.0,2888.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.42/0.58 2917[2:SpR:2896.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.42/0.59 2919[2:Rew:2890.0,2917.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.42/0.59 2925[2:SpR:2898.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.42/0.59 2927[2:Rew:2892.0,2925.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.42/0.59 2933[2:SpR:2919.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.42/0.59 2935[2:Rew:63.0,2933.0] || -> equal(identity,sk_c11)**.
% 0.42/0.59 2936[2:Rew:2935.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.59 2937[2:Rew:2935.0,561.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.59 2940[2:Rew:2936.0,2927.0] || -> equal(sk_c10,sk_c11)**.
% 0.42/0.59 2946[2:Rew:2940.0,2888.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.42/0.59 2947[2:Rew:2940.0,2895.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.42/0.59 2954[2:Rew:2937.0,2947.0] || -> equal(sk_c8,sk_c11)**.
% 0.42/0.59 2955[2:Rew:2954.0,2890.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.42/0.59 2958[2:Rew:2954.0,2896.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.42/0.59 2978[2:Rew:2937.0,2958.0] || -> equal(sk_c5,sk_c11)**.
% 0.42/0.59 2979[2:Rew:2978.0,2955.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.42/0.59 2980[2:MRR:2979.0,2946.0] || -> .
% 0.42/0.59 % SZS output end Refutation
% 0.42/0.59 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 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_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_39 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_49 prove_this_53 prove_this_54 prove_this_55 prove_this_56 prove_this_57 prove_this_59 prove_this_61 left_identity left_inverse associativity
% 0.42/0.59
%------------------------------------------------------------------------------