TSTP Solution File: GRP258-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP258-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:33 EDT 2022
% Result : Unsatisfiable 0.48s 0.66s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP258-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 19:41:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.48/0.66
% 0.48/0.66 SPASS V 3.9
% 0.48/0.66 SPASS beiseite: Proof found.
% 0.48/0.66 % SZS status Theorem
% 0.48/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.66 SPASS derived 2623 clauses, backtracked 985 clauses, performed 15 splits and kept 1629 clauses.
% 0.48/0.66 SPASS allocated 65322 KBytes.
% 0.48/0.66 SPASS spent 0:00:00.31 on the problem.
% 0.48/0.66 0:00:00.04 for the input.
% 0.48/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.66 0:00:00.02 for inferences.
% 0.48/0.66 0:00:00.01 for the backtracking.
% 0.48/0.66 0:00:00.21 for the reduction.
% 0.48/0.66
% 0.48/0.66
% 0.48/0.66 Here is a proof with depth 4, length 513 :
% 0.48/0.66 % SZS output start Refutation
% 0.48/0.66 1[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c1,sk_c12),sk_c11).
% 0.48/0.66 2[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.48/0.66 5[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c1,sk_c12),sk_c11).
% 0.48/0.66 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.48/0.66 9[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.48/0.66 11[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 12[0:Inp] || -> equal(inverse(sk_c4),sk_c12)** equal(inverse(sk_c1),sk_c12).
% 0.48/0.66 13[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 14[0:Inp] || -> equal(inverse(sk_c5),sk_c11)** equal(inverse(sk_c1),sk_c12).
% 0.48/0.66 15[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 16[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c12).
% 0.48/0.66 19[0:Inp] || -> equal(inverse(sk_c7),sk_c9)** equal(inverse(sk_c1),sk_c12).
% 0.48/0.66 21[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 22[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 23[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 24[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 29[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 31[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 32[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c2),sk_c11)**.
% 0.48/0.66 35[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.48/0.66 39[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.48/0.66 41[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 42[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 43[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 44[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 45[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c10,sk_c12),sk_c11).
% 0.48/0.66 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 48[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 51[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 52[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 55[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 56[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 59[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 61[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 62[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 63[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 64[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 65[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 66[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 69[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 71[0:Inp] || equal(multiply(u,sk_c12),sk_c11)** equal(inverse(u),sk_c12) equal(multiply(v,sk_c11),sk_c10)** equal(inverse(v),sk_c11) equal(multiply(sk_c10,sk_c12),sk_c11)** equal(multiply(w,sk_c10),sk_c12)** equal(inverse(w),sk_c10) equal(multiply(x,sk_c12),sk_c11)** equal(inverse(x),sk_c12) equal(multiply(y,sk_c11),sk_c10)** equal(inverse(y),sk_c11) equal(multiply(z,x1),sk_c12)** equal(inverse(z),x1) equal(multiply(x1,sk_c11),sk_c12)** equal(inverse(x2),x3) equal(inverse(x3),x1)* equal(multiply(x2,x1),x3)* -> .
% 0.48/0.66 72[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.48/0.66 73[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.48/0.66 74[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.48/0.66 75[0:Con:71.7] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(x1),sk_c12) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(y,sk_c10),sk_c12)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(x1,sk_c12),sk_c11)** equal(multiply(sk_c10,sk_c12),sk_c11)** -> .
% 0.48/0.66 76[1:Spt:75.0,75.1,75.2,75.6,75.7,75.8] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)* equal(multiply(x,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12)** -> .
% 0.48/0.66 77[1:EqR:76.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12) -> .
% 0.48/0.66 78[2:Spt:49.1] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 80[2:SpL:78.0,76.3] || equal(inverse(u),sk_c12)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.48/0.66 81[3:Spt:69.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 83[4:Spt:39.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.48/0.66 85[5:Spt:19.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.48/0.66 87[6:Spt:59.1] || -> equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 91[7:Spt:29.1] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 93[7:SpL:91.0,76.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c2),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.48/0.66 94[7:Rew:83.0,93.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.48/0.66 97[8:Spt:9.1] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.48/0.66 102[3:SpR:81.0,73.0] || -> equal(multiply(sk_c10,sk_c3),identity)**.
% 0.48/0.66 103[4:SpR:83.0,73.0] || -> equal(multiply(sk_c11,sk_c2),identity)**.
% 0.48/0.66 104[5:SpR:85.0,73.0] || -> equal(multiply(sk_c12,sk_c1),identity)**.
% 0.48/0.66 118[0:SpR:73.0,74.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.48/0.66 119[3:SpR:102.0,74.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.48/0.66 120[4:SpR:103.0,74.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.48/0.66 122[3:Rew:72.0,119.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.48/0.66 123[4:Rew:72.0,120.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.48/0.66 124[0:Rew:72.0,118.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.48/0.66 126[5:SpR:104.0,74.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.48/0.66 129[5:Rew:72.0,126.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.48/0.66 132[6:SpR:87.0,122.0] || -> equal(multiply(sk_c10,sk_c12),sk_c10)**.
% 0.48/0.66 134[6:Rew:78.0,132.0] || -> equal(sk_c10,sk_c11)**.
% 0.48/0.66 135[6:Rew:134.0,78.0] || -> equal(multiply(sk_c11,sk_c12),sk_c11)**.
% 0.48/0.66 137[6:Rew:134.0,87.0] || -> equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.48/0.66 138[7:Rew:134.0,91.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.48/0.66 139[6:Rew:134.0,102.0] || -> equal(multiply(sk_c11,sk_c3),identity)**.
% 0.48/0.66 144[7:Rew:134.0,94.3] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.48/0.66 152[7:Obv:144.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.48/0.66 176[7:SpR:138.0,123.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.48/0.66 178[7:Rew:176.0,152.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c12)** equal(sk_c11,sk_c12) -> .
% 0.48/0.66 182[0:SpR:124.0,124.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.48/0.66 186[8:SpR:97.0,124.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c12)**.
% 0.48/0.66 188[0:SpR:73.0,124.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.48/0.66 189[4:SpR:103.0,124.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.48/0.66 190[6:SpR:135.0,124.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c12)**.
% 0.48/0.66 191[6:SpR:139.0,124.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c3)**.
% 0.48/0.66 201[8:Rew:85.0,186.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 204[6:Rew:73.0,190.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 205[6:Rew:204.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 207[6:Rew:204.0,103.0] || -> equal(multiply(sk_c11,sk_c2),sk_c12)**.
% 0.48/0.66 208[6:Rew:204.0,104.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.48/0.66 216[6:Rew:204.0,189.0] || -> equal(multiply(inverse(sk_c11),sk_c12),sk_c2)**.
% 0.48/0.66 217[6:Rew:205.0,129.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.48/0.66 221[8:Rew:205.0,201.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 231[8:Rew:221.0,178.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c11,sk_c12) -> .
% 0.48/0.66 241[6:Rew:205.0,208.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 242[6:Rew:241.0,85.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.48/0.66 243[6:Rew:241.0,204.0] || -> equal(identity,sk_c1)**.
% 0.48/0.66 245[8:Rew:241.0,221.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 262[6:Rew:243.0,188.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.48/0.66 271[6:Rew:182.0,262.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.48/0.66 274[8:Rew:245.0,231.4,241.0,231.4,271.0,231.3,241.0,231.3,245.0,231.2,245.0,231.1,245.0,231.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) equal(sk_c1,sk_c1) -> .
% 0.48/0.66 275[8:Obv:274.4] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.48/0.66 546[8:SpL:242.0,275.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.48/0.66 549[8:Obv:546.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.48/0.66 551[8:SpL:242.0,549.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 554[8:Obv:551.1] || -> .
% 0.48/0.66 555[8:Spt:554.0,9.1,97.0] || equal(multiply(sk_c1,sk_c12),sk_c11)** -> .
% 0.48/0.66 556[8:Spt:554.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 557[6:Rew:241.0,137.0] || -> equal(multiply(sk_c3,sk_c11),sk_c1)**.
% 0.48/0.66 559[6:Rew:241.0,207.0] || -> equal(multiply(sk_c11,sk_c2),sk_c1)**.
% 0.48/0.66 561[6:Rew:271.0,191.0,243.0,191.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.48/0.66 562[6:Rew:271.0,216.0,241.0,216.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.48/0.66 563[6:Rew:561.0,562.0] || -> equal(sk_c3,sk_c2)**.
% 0.48/0.66 565[6:Rew:563.0,557.0] || -> equal(multiply(sk_c2,sk_c11),sk_c1)**.
% 0.48/0.66 567[6:Rew:563.0,561.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.48/0.66 568[7:Rew:138.0,565.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 581[8:Rew:271.0,555.0,241.0,555.0] || equal(sk_c11,sk_c1)** -> .
% 0.48/0.66 582[8:Rew:568.0,581.0] || equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 583[8:Obv:582.0] || -> .
% 0.48/0.66 599[6:Rew:241.0,2.1,217.0,2.1,241.0,2.0] || -> equal(inverse(sk_c4),sk_c1)** equal(sk_c11,sk_c1).
% 0.48/0.66 605[6:Rew:241.0,1.1,217.0,1.1,271.0,1.0,241.0,1.0] || -> equal(sk_c4,sk_c11)** equal(sk_c11,sk_c1).
% 0.48/0.66 651[7:Spt:583.0,29.1,91.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.48/0.66 652[7:Spt:583.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 653[7:Rew:565.0,651.0,134.0,651.0] || equal(sk_c11,sk_c1)** -> .
% 0.48/0.66 654[7:MRR:605.1,653.0] || -> equal(sk_c4,sk_c11)**.
% 0.48/0.66 661[7:Rew:567.0,599.0,654.0,599.0] || -> equal(sk_c2,sk_c1)** equal(sk_c11,sk_c1).
% 0.48/0.66 662[7:MRR:661.1,653.0] || -> equal(sk_c2,sk_c1)**.
% 0.48/0.66 667[7:Rew:662.0,559.0] || -> equal(multiply(sk_c11,sk_c1),sk_c1)**.
% 0.48/0.66 674[7:Rew:271.0,667.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 675[7:MRR:674.0,653.0] || -> .
% 0.48/0.66 717[6:Spt:675.0,59.1,87.0] || equal(multiply(sk_c3,sk_c10),sk_c12)** -> .
% 0.48/0.66 718[6:Spt:675.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 721[6:MRR:56.1,717.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 723[6:MRR:52.1,717.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 724[0:Rew:182.0,188.0] || -> equal(multiply(u,identity),u)**.
% 0.48/0.66 729[6:MRR:55.1,717.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 731[6:MRR:51.1,717.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 767[3:SpR:102.0,124.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c3)**.
% 0.48/0.66 769[3:Rew:724.0,767.0] || -> equal(inverse(sk_c10),sk_c3)**.
% 0.48/0.66 771[3:Rew:769.0,80.1] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.48/0.66 777[2:SpR:78.0,124.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.48/0.66 779[3:Rew:769.0,777.0] || -> equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.48/0.66 791[4:SpR:103.0,124.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.48/0.66 793[4:Rew:724.0,791.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.48/0.66 801[6:SpR:729.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 803[6:Rew:721.0,801.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 809[6:SpR:731.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 811[6:Rew:723.0,809.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 823[6:SpR:803.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 825[6:Rew:73.0,823.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 827[6:Rew:825.0,104.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.48/0.66 829[6:Rew:825.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 833[6:Rew:825.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 839[6:Rew:829.0,827.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 840[6:Rew:829.0,811.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 848[6:Rew:839.0,85.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.48/0.66 851[6:Rew:839.0,78.0] || -> equal(multiply(sk_c10,sk_c1),sk_c11)**.
% 0.48/0.66 857[6:Rew:839.0,717.0] || equal(multiply(sk_c3,sk_c10),sk_c1)** -> .
% 0.48/0.66 870[6:Rew:839.0,840.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 882[6:Rew:839.0,833.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.48/0.66 883[6:Rew:882.0,851.0,870.0,851.0] || -> equal(sk_c10,sk_c1)**.
% 0.48/0.66 885[6:Rew:883.0,769.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.48/0.66 888[6:Rew:848.0,885.0] || -> equal(sk_c3,sk_c1)**.
% 0.48/0.66 922[6:Rew:882.0,857.0,888.0,857.0,883.0,857.0] || equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 923[6:Obv:922.0] || -> .
% 0.48/0.66 958[5:Spt:923.0,19.1,85.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.48/0.66 959[5:Spt:923.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 961[5:MRR:16.1,958.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 963[5:MRR:12.1,958.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 966[5:MRR:15.0,958.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 968[5:MRR:11.0,958.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 1013[5:SpR:966.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 1015[5:Rew:961.0,1013.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 1021[5:SpR:968.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 1023[5:Rew:963.0,1021.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 1024[5:Rew:1023.0,771.5] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.48/0.66 1025[5:Obv:1024.5] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.48/0.66 1031[5:SpR:1015.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 1033[5:Rew:73.0,1031.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 1036[5:Rew:1033.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 1037[5:Rew:1033.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 1044[5:Rew:1036.0,968.0] || -> equal(sk_c4,sk_c11)**.
% 0.48/0.66 1045[5:Rew:1036.0,78.0] || -> equal(sk_c10,sk_c11)**.
% 0.48/0.66 1046[5:Rew:1036.0,1025.4] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12)** equal(sk_c11,u) equal(v,sk_c12) -> .
% 0.48/0.66 1048[5:Rew:1044.0,963.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.48/0.66 1051[5:Rew:1045.0,769.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.48/0.66 1060[5:Rew:793.0,1048.0] || -> equal(sk_c2,sk_c12)**.
% 0.48/0.66 1061[5:Rew:1060.0,793.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.48/0.66 1062[5:Rew:1060.0,83.0] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.48/0.66 1067[5:Rew:1051.0,1061.0] || -> equal(sk_c3,sk_c12)**.
% 0.48/0.66 1073[5:Rew:1037.0,1023.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 1086[5:Rew:1073.0,1062.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.48/0.66 1136[5:Rew:1073.0,1046.3,1067.0,1046.1] || equal(inverse(u),sk_c12)** equal(sk_c12,u) equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.48/0.66 1137[5:Obv:1136.1] || equal(inverse(u),sk_c12)**+ equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.48/0.66 1498[5:SpL:1086.0,1137.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c12)** equal(sk_c12,sk_c12) equal(u,sk_c12) -> .
% 0.48/0.66 1502[5:Obv:1498.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 1504[5:SpL:1086.0,1502.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 1508[5:Obv:1504.1] || -> .
% 0.48/0.66 1509[4:Spt:1508.0,39.1,83.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.48/0.66 1510[4:Spt:1508.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 1512[4:MRR:36.1,1509.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 1514[4:MRR:32.1,1509.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 1518[4:MRR:35.0,1509.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 1520[4:MRR:31.0,1509.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 1564[4:SpR:1518.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 1566[4:Rew:1512.0,1564.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 1572[4:SpR:1520.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 1574[4:Rew:1514.0,1572.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 1582[4:SpR:1566.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 1584[4:Rew:73.0,1582.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 1586[4:Rew:1584.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 1587[4:Rew:1584.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 1588[4:Rew:1584.0,73.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.48/0.66 1593[4:Rew:1586.0,1574.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 1601[4:Rew:1593.0,78.0] || -> equal(multiply(sk_c10,sk_c12),sk_c12)**.
% 0.48/0.66 1603[4:Rew:1593.0,779.0] || -> equal(multiply(sk_c3,sk_c12),sk_c12)**.
% 0.48/0.66 1610[4:Rew:1593.0,77.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c12),sk_c12) -> .
% 0.48/0.66 1617[4:Rew:1587.0,1601.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 1618[4:Rew:1617.0,81.0] || -> equal(inverse(sk_c3),sk_c12)**.
% 0.48/0.66 1623[4:Rew:1587.0,1603.0] || -> equal(sk_c3,sk_c12)**.
% 0.48/0.66 1624[4:Rew:1623.0,1618.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.48/0.66 1674[4:Rew:1587.0,1610.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(v,sk_c12) -> .
% 0.48/0.66 1714[4:SpR:1588.0,124.0] || -> equal(multiply(inverse(inverse(u)),sk_c12),u)**.
% 0.48/0.66 1718[4:Rew:1587.0,1714.0] || -> equal(inverse(inverse(u)),u)**.
% 0.48/0.66 1735[4:SpR:1718.0,1588.0] || -> equal(multiply(u,inverse(u)),sk_c12)**.
% 0.48/0.66 2252[4:SpL:1588.0,1674.0] || equal(inverse(sk_c12),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 2262[4:Rew:1588.0,2252.1,1718.0,2252.1,1624.0,2252.0] || equal(sk_c12,u) equal(sk_c12,u) equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 2263[4:Obv:2262.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c12)** equal(v,sk_c12) -> .
% 0.48/0.66 2424[4:SpL:1735.0,2263.1] || equal(inverse(u),inverse(u))* equal(sk_c12,sk_c12) equal(inverse(u),sk_c12) -> .
% 0.48/0.66 2446[4:Obv:2424.1] || equal(inverse(u),sk_c12)** -> .
% 0.48/0.66 2447[4:UnC:2446.0,1718.0] || -> .
% 0.48/0.66 2453[3:Spt:2447.0,69.1,81.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.48/0.66 2454[3:Spt:2447.0,69.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 2456[3:MRR:66.1,2453.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 2457[3:MRR:64.1,2453.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.66 2458[3:MRR:62.1,2453.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 2462[3:MRR:65.0,2453.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 2463[3:MRR:63.0,2453.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 2464[3:MRR:61.0,2453.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 2494[3:SpR:2462.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 2496[3:Rew:2456.0,2494.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 2502[3:SpR:2464.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 2504[3:Rew:2458.0,2502.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 2505[3:Rew:2504.0,80.5] || equal(inverse(u),sk_c12)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.48/0.66 2506[3:Obv:2505.5] || equal(inverse(u),sk_c12)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.48/0.66 2515[3:SpR:2496.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 2517[3:Rew:73.0,2515.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 2518[3:Rew:2517.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 2519[3:Rew:2517.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 2525[3:Rew:2518.0,2504.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 2530[3:Rew:2525.0,2457.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.48/0.66 2531[3:Rew:2525.0,78.0] || -> equal(multiply(sk_c10,sk_c12),sk_c12)**.
% 0.48/0.66 2533[3:Rew:2525.0,2463.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.48/0.66 2544[3:Rew:2525.0,2506.3] || equal(inverse(u),sk_c12)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c12) equal(sk_c12,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.48/0.66 2545[3:Rew:2519.0,2531.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 2558[3:Rew:2519.0,2533.0,2545.0,2533.0] || -> equal(sk_c5,sk_c12)**.
% 0.48/0.66 2559[3:Rew:2558.0,2530.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.48/0.66 2587[3:Rew:2519.0,2544.4,2559.0,2544.1,2545.0,2544.1] || equal(inverse(u),sk_c12)** equal(sk_c12,u) equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.48/0.66 2588[3:Obv:2587.1] || equal(inverse(u),sk_c12)**+ equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.48/0.66 2798[3:SpL:2559.0,2588.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c12)** equal(sk_c12,sk_c12) equal(u,sk_c12) -> .
% 0.48/0.66 2800[3:Obv:2798.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 2802[3:SpL:2559.0,2800.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 2804[3:Obv:2802.1] || -> .
% 0.48/0.66 2805[2:Spt:2804.0,49.1,78.0] || equal(multiply(sk_c10,sk_c12),sk_c11)** -> .
% 0.48/0.66 2806[2:Spt:2804.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 2808[2:MRR:46.1,2805.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 2809[2:MRR:44.1,2805.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.66 2810[2:MRR:42.1,2805.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 2813[2:MRR:45.1,2805.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 2814[2:MRR:43.1,2805.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 2815[2:MRR:41.1,2805.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 2834[2:SpR:2813.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 2836[2:Rew:2808.0,2834.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 2838[2:SpR:2814.0,124.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.48/0.66 2840[2:Rew:2809.0,2838.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.48/0.66 2842[2:SpR:2815.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 2844[2:Rew:2810.0,2842.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 2850[2:SpR:2836.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 2852[2:Rew:73.0,2850.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 2853[2:Rew:2852.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 2854[2:Rew:2852.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 2859[2:Rew:2853.0,2844.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 2866[2:Rew:2859.0,2814.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.48/0.66 2868[2:Rew:2859.0,2805.0] || equal(multiply(sk_c10,sk_c12),sk_c12)** -> .
% 0.48/0.66 2876[2:Rew:2859.0,2840.0] || -> equal(multiply(sk_c12,sk_c10),sk_c12)**.
% 0.48/0.66 2888[2:Rew:2854.0,2866.0] || -> equal(sk_c10,sk_c5)**.
% 0.48/0.66 2889[2:Rew:2853.0,2876.0,2888.0,2876.0] || -> equal(sk_c5,sk_c12)**.
% 0.48/0.66 2891[2:Rew:2889.0,2888.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 2904[2:Rew:2854.0,2868.0,2891.0,2868.0] || equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 2905[2:Obv:2904.0] || -> .
% 0.48/0.66 2924[1:Spt:2905.0,75.3,75.4,75.5,75.9,75.10,75.11,75.12] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** equal(multiply(sk_c10,sk_c12),sk_c11)** -> .
% 0.48/0.66 2926[2:Spt:48.1] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.48/0.66 2927[2:Rew:2926.0,2924.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.48/0.66 2929[2:Obv:2927.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.48/0.66 2932[2:SpR:2926.0,124.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.48/0.66 2934[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.48/0.66 2935[3:SpR:2934.0,124.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.48/0.66 2937[4:Spt:39.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.48/0.66 2940[5:Spt:69.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.48/0.66 2941[5:SpR:2940.0,124.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.48/0.66 2943[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.48/0.66 2945[6:SpR:2943.0,124.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c12)**.
% 0.48/0.66 2947[6:Rew:2934.0,2945.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 2948[7:Spt:29.1] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.48/0.66 2950[7:SpR:2948.0,124.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c11)**.
% 0.48/0.66 2952[7:Rew:2937.0,2950.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.48/0.66 2953[8:Spt:59.1] || -> equal(multiply(sk_c3,sk_c10),sk_c12)**.
% 0.48/0.66 2955[8:SpR:2953.0,124.0] || -> equal(multiply(inverse(sk_c3),sk_c12),sk_c10)**.
% 0.48/0.66 2957[8:Rew:2926.0,2955.0,2940.0,2955.0] || -> equal(sk_c10,sk_c11)**.
% 0.48/0.66 2962[8:Rew:2957.0,2929.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.48/0.66 2964[8:Rew:2957.0,2932.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c12)**.
% 0.48/0.66 2969[8:Rew:73.0,2964.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 2970[8:Rew:2969.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 2971[8:Rew:2969.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 2974[8:Rew:2970.0,2943.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 2978[8:Rew:2974.0,2947.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.48/0.66 2979[8:Rew:2974.0,2957.0] || -> equal(sk_c10,sk_c1)**.
% 0.48/0.66 2985[8:Rew:2971.0,2978.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 2986[8:Rew:2985.0,2934.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.48/0.66 2988[8:Rew:2985.0,2970.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.48/0.66 3003[8:Rew:2988.0,2962.5,2985.0,2962.5,2974.0,2962.5,2988.0,2962.4,2974.0,2962.4,2979.0,2962.4,2988.0,2962.3,2979.0,2962.3,2985.0,2962.3,2985.0,2962.2,2974.0,2962.1,2974.0,2962.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.48/0.66 3004[8:Con:3003.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.48/0.66 3034[8:SpL:2986.0,3004.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 3035[8:Obv:3034.1] || -> .
% 0.48/0.66 3036[8:Spt:3035.0,59.1,2953.0] || equal(multiply(sk_c3,sk_c10),sk_c12)** -> .
% 0.48/0.66 3037[8:Spt:3035.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 3071[7:SpR:2952.0,124.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.48/0.66 3073[7:Rew:73.0,3071.0] || -> equal(identity,sk_c10)**.
% 0.48/0.66 3074[7:Rew:3073.0,72.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.48/0.66 3075[7:Rew:3073.0,724.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.48/0.66 3076[7:Rew:3073.0,73.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.48/0.66 3078[7:Rew:3074.0,2926.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 3080[7:Rew:3074.0,2941.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.48/0.66 3086[7:Rew:3078.0,2943.0] || -> equal(multiply(sk_c1,sk_c12),sk_c12)**.
% 0.48/0.66 3087[7:Rew:3078.0,2947.0] || -> equal(multiply(sk_c12,sk_c12),sk_c12)**.
% 0.48/0.66 3097[8:Rew:3075.0,3036.0] || equal(sk_c3,sk_c12)** -> .
% 0.48/0.66 3148[7:SpR:3087.0,124.0] || -> equal(multiply(inverse(sk_c12),sk_c12),sk_c12)**.
% 0.48/0.66 3150[7:Rew:3076.0,3148.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 3156[7:Rew:3150.0,3075.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 3171[7:Rew:3156.0,3086.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 3182[8:Rew:3171.0,3097.0] || equal(sk_c3,sk_c1)** -> .
% 0.48/0.66 3191[7:Rew:3171.0,3156.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.48/0.66 3251[7:SpR:3191.0,3080.0] || -> equal(sk_c3,sk_c1)**.
% 0.48/0.66 3253[8:MRR:3251.0,3182.0] || -> .
% 0.48/0.66 3256[7:Spt:3253.0,29.1,2948.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.48/0.66 3257[7:Spt:3253.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 3260[7:MRR:24.1,3256.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.66 3261[7:MRR:22.1,3256.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 3265[7:MRR:23.1,3256.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 3266[7:MRR:21.1,3256.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 3281[7:SpR:3261.0,124.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.48/0.66 3287[6:SpR:2947.0,124.0] || -> equal(multiply(inverse(sk_c12),sk_c12),sk_c11)**.
% 0.48/0.66 3289[6:Rew:73.0,3287.0] || -> equal(identity,sk_c11)**.
% 0.48/0.66 3290[6:Rew:3289.0,724.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.48/0.66 3291[6:Rew:3289.0,72.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.48/0.66 3293[6:Rew:3289.0,73.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.48/0.66 3296[7:Rew:3290.0,3265.0] || -> equal(sk_c10,sk_c5)**.
% 0.48/0.66 3298[7:Rew:3290.0,3256.0] || equal(sk_c2,sk_c10)** -> .
% 0.48/0.66 3299[6:Rew:3290.0,2932.0] || -> equal(inverse(sk_c10),sk_c12)**.
% 0.48/0.66 3301[7:Rew:3296.0,2926.0] || -> equal(multiply(sk_c5,sk_c12),sk_c11)**.
% 0.48/0.66 3310[7:Rew:3296.0,3298.0] || equal(sk_c2,sk_c5)** -> .
% 0.48/0.66 3311[7:Rew:3296.0,3299.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.48/0.66 3312[7:Rew:3260.0,3311.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 3313[7:Rew:3312.0,2937.0] || -> equal(inverse(sk_c2),sk_c12)**.
% 0.48/0.66 3315[7:Rew:3312.0,2943.0] || -> equal(multiply(sk_c1,sk_c12),sk_c12)**.
% 0.48/0.66 3318[7:Rew:3312.0,3266.0] || -> equal(multiply(sk_c4,sk_c12),sk_c12)**.
% 0.48/0.66 3321[7:Rew:3312.0,3290.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 3322[7:Rew:3312.0,3291.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 3323[7:Rew:3322.0,3281.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.48/0.66 3325[7:Rew:3312.0,3301.0] || -> equal(multiply(sk_c5,sk_c12),sk_c12)**.
% 0.48/0.66 3326[7:Rew:3321.0,3318.0] || -> equal(sk_c4,sk_c12)**.
% 0.48/0.66 3327[7:Rew:3321.0,3315.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 3330[7:Rew:3321.0,3325.0] || -> equal(sk_c5,sk_c12)**.
% 0.48/0.66 3334[7:Rew:3327.0,3312.0] || -> equal(sk_c11,sk_c1)**.
% 0.48/0.66 3338[7:Rew:3327.0,3313.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.48/0.66 3342[7:Rew:3327.0,3326.0] || -> equal(sk_c4,sk_c1)**.
% 0.48/0.66 3346[7:Rew:3327.0,3330.0] || -> equal(sk_c5,sk_c1)**.
% 0.48/0.66 3348[7:Rew:3346.0,3310.0] || equal(sk_c2,sk_c1)** -> .
% 0.48/0.66 3357[7:Rew:3342.0,3323.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.48/0.66 3359[7:Rew:3334.0,3293.0] || -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.48/0.66 3407[7:SpR:3338.0,3359.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.48/0.66 3409[7:Rew:3357.0,3407.0] || -> equal(sk_c2,sk_c1)**.
% 0.48/0.66 3410[7:MRR:3409.0,3348.0] || -> .
% 0.48/0.66 3417[6:Spt:3410.0,9.1,2943.0] || equal(multiply(sk_c1,sk_c12),sk_c11)** -> .
% 0.48/0.66 3418[6:Spt:3410.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 3420[6:MRR:6.1,3417.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 3422[6:MRR:2.1,3417.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 3425[6:MRR:5.1,3417.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 3427[6:MRR:1.1,3417.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 3455[6:SpR:3425.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 3457[6:Rew:3420.0,3455.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 3463[6:SpR:3427.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 3465[6:Rew:3422.0,3463.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 3474[6:SpR:3457.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 3476[6:Rew:73.0,3474.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 3477[6:Rew:3476.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 3481[6:Rew:3477.0,3465.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 3483[6:Rew:3477.0,2935.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.48/0.66 3495[6:Rew:3481.0,3417.0] || equal(multiply(sk_c1,sk_c12),sk_c12)** -> .
% 0.48/0.66 3533[6:Rew:3483.0,3495.0] || equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 3534[6:Obv:3533.0] || -> .
% 0.48/0.66 3554[5:Spt:3534.0,69.1,2940.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.48/0.66 3555[5:Spt:3534.0,69.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 3557[5:MRR:66.1,3554.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 3559[5:MRR:62.1,3554.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 3562[5:MRR:65.0,3554.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 3564[5:MRR:61.0,3554.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 3588[5:SpR:3562.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 3590[5:Rew:3557.0,3588.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 3596[5:SpR:3564.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 3598[5:Rew:3559.0,3596.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 3607[5:SpR:3590.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 3609[5:Rew:73.0,3607.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 3610[5:Rew:3609.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 3611[5:Rew:3609.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 3613[5:Rew:3609.0,73.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.48/0.66 3614[5:Rew:3610.0,3598.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 3623[5:Rew:3614.0,2926.0] || -> equal(multiply(sk_c10,sk_c12),sk_c12)**.
% 0.48/0.66 3630[5:Rew:3614.0,2929.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.48/0.66 3635[5:Rew:3611.0,3623.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 3678[5:Rew:3611.0,3630.5,3614.0,3630.5,3611.0,3630.4,3614.0,3630.4,3635.0,3630.4,3611.0,3630.3,3635.0,3630.3,3635.0,3630.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(w,sk_c12) -> .
% 0.48/0.66 3679[5:Con:3678.1] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 3711[5:SpR:2934.0,3613.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.48/0.66 3715[5:Rew:3610.0,3711.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 3716[5:Rew:3715.0,2934.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.48/0.66 3732[5:Rew:3715.0,3679.0] || equal(inverse(u),sk_c1)** equal(u,sk_c12) -> .
% 0.48/0.66 3741[5:Rew:3715.0,3732.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.48/0.66 3776[5:SpL:3716.0,3741.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 3777[5:Obv:3776.1] || -> .
% 0.48/0.66 3778[4:Spt:3777.0,39.1,2937.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.48/0.66 3779[4:Spt:3777.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 3781[4:MRR:36.1,3778.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 3783[4:MRR:32.1,3778.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 3786[4:MRR:35.0,3778.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 3788[4:MRR:31.0,3778.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 3812[4:SpR:3786.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 3814[4:Rew:3781.0,3812.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 3820[4:SpR:3788.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 3822[4:Rew:3783.0,3820.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 3831[4:SpR:3814.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 3833[4:Rew:73.0,3831.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 3834[4:Rew:3833.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 3835[4:Rew:3833.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 3836[4:Rew:3833.0,73.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.48/0.66 3838[4:Rew:3834.0,3822.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 3846[4:Rew:3838.0,2926.0] || -> equal(multiply(sk_c10,sk_c12),sk_c12)**.
% 0.48/0.66 3853[4:Rew:3838.0,2929.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.48/0.66 3858[4:Rew:3835.0,3846.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 3899[4:Rew:3835.0,3853.5,3838.0,3853.5,3835.0,3853.4,3838.0,3853.4,3858.0,3853.4,3835.0,3853.3,3858.0,3853.3,3858.0,3853.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(w,sk_c12) -> .
% 0.48/0.66 3900[4:Con:3899.1] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 3929[4:SpR:2934.0,3836.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.48/0.66 3932[4:Rew:3834.0,3929.0] || -> equal(sk_c12,sk_c1)**.
% 0.48/0.66 3933[4:Rew:3932.0,2934.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.48/0.66 3948[4:Rew:3932.0,3900.0] || equal(inverse(u),sk_c1)** equal(u,sk_c12) -> .
% 0.48/0.66 3954[4:Rew:3932.0,3948.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.48/0.66 4019[4:SpL:3933.0,3954.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.48/0.66 4021[4:Obv:4019.1] || -> .
% 0.48/0.66 4022[3:Spt:4021.0,19.1,2934.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.48/0.66 4023[3:Spt:4021.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.66 4025[3:MRR:16.1,4022.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 4026[3:MRR:14.1,4022.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.66 4027[3:MRR:12.1,4022.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 4030[3:MRR:15.0,4022.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 4031[3:MRR:13.0,4022.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 4032[3:MRR:11.0,4022.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 4054[3:SpR:4030.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 4056[3:Rew:4025.0,4054.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 4062[3:SpR:4032.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 4064[3:Rew:4027.0,4062.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 4070[3:SpR:4056.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 4072[3:Rew:73.0,4070.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 4073[3:Rew:4072.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 4074[3:Rew:4072.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 4078[3:Rew:4073.0,4064.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 4083[3:Rew:4078.0,4026.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.48/0.66 4084[3:Rew:4078.0,2926.0] || -> equal(multiply(sk_c10,sk_c12),sk_c12)**.
% 0.48/0.66 4086[3:Rew:4078.0,4031.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.48/0.66 4090[3:Rew:4078.0,2929.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c10),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.48/0.66 4095[3:Rew:4074.0,4084.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 4107[3:Rew:4074.0,4086.0,4095.0,4086.0] || -> equal(sk_c5,sk_c12)**.
% 0.48/0.66 4108[3:Rew:4107.0,4083.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.48/0.66 4136[3:Rew:4074.0,4090.5,4078.0,4090.5,4074.0,4090.4,4078.0,4090.4,4095.0,4090.4,4074.0,4090.3,4095.0,4090.3,4095.0,4090.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(w,sk_c12) -> .
% 0.48/0.66 4137[3:Con:4136.1] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.66 4210[3:SpL:4108.0,4137.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 4212[3:Obv:4210.1] || -> .
% 0.48/0.66 4213[2:Spt:4212.0,48.1,2926.0] || equal(multiply(sk_c10,sk_c12),sk_c11)** -> .
% 0.48/0.66 4214[2:Spt:4212.0,48.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.48/0.66 4215[2:MRR:46.1,4213.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.66 4216[2:MRR:44.1,4213.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.66 4217[2:MRR:42.1,4213.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.66 4221[2:MRR:45.1,4213.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.66 4222[2:MRR:43.1,4213.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.66 4223[2:MRR:41.1,4213.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.66 4242[2:SpR:4221.0,124.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.66 4244[2:Rew:4215.0,4242.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.66 4246[2:SpR:4222.0,124.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.48/0.66 4248[2:Rew:4216.0,4246.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.48/0.66 4250[2:SpR:4223.0,124.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.48/0.66 4252[2:Rew:4217.0,4250.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.48/0.66 4261[2:SpR:4244.0,124.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.48/0.66 4263[2:Rew:73.0,4261.0] || -> equal(identity,sk_c12)**.
% 0.48/0.66 4264[2:Rew:4263.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.66 4265[2:Rew:4263.0,724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.66 4268[2:Rew:4264.0,4252.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.66 4275[2:Rew:4268.0,4222.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.48/0.66 4277[2:Rew:4268.0,4213.0] || equal(multiply(sk_c10,sk_c12),sk_c12)** -> .
% 0.48/0.66 4281[2:Rew:4268.0,4248.0] || -> equal(multiply(sk_c12,sk_c10),sk_c12)**.
% 0.48/0.66 4293[2:Rew:4265.0,4275.0] || -> equal(sk_c10,sk_c5)**.
% 0.48/0.66 4294[2:Rew:4264.0,4281.0,4293.0,4281.0] || -> equal(sk_c5,sk_c12)**.
% 0.48/0.66 4296[2:Rew:4294.0,4293.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.66 4309[2:Rew:4264.0,4277.0,4296.0,4277.0] || equal(sk_c12,sk_c12)* -> .
% 0.48/0.66 4310[2:Obv:4309.0] || -> .
% 0.48/0.66 % SZS output end Refutation
% 0.48/0.66 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_29 prove_this_31 prove_this_32 prove_this_35 prove_this_36 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_48 prove_this_49 prove_this_51 prove_this_52 prove_this_55 prove_this_56 prove_this_59 prove_this_61 prove_this_62 prove_this_63 prove_this_64 prove_this_65 prove_this_66 prove_this_69 prove_this_71 left_identity left_inverse associativity
% 0.52/0.67
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