TSTP Solution File: GRP312-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP312-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:48 EDT 2022
% Result : Unsatisfiable 0.43s 0.60s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP312-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 07:14:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.60
% 0.43/0.60 SPASS V 3.9
% 0.43/0.60 SPASS beiseite: Proof found.
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.60 SPASS derived 2185 clauses, backtracked 920 clauses, performed 15 splits and kept 1526 clauses.
% 0.43/0.60 SPASS allocated 64646 KBytes.
% 0.43/0.60 SPASS spent 0:00:00.25 on the problem.
% 0.43/0.60 0:00:00.04 for the input.
% 0.43/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.43/0.60 0:00:00.01 for inferences.
% 0.43/0.60 0:00:00.00 for the backtracking.
% 0.43/0.60 0:00:00.17 for the reduction.
% 0.43/0.60
% 0.43/0.60
% 0.43/0.60 Here is a proof with depth 5, length 514 :
% 0.43/0.60 % SZS output start Refutation
% 0.43/0.60 1[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.43/0.60 2[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 3[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.43/0.60 4[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 5[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.43/0.60 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 9[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 11[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 12[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 15[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 16[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 19[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 21[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 22[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 23[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 24[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 25[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 26[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 29[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 31[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 32[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 34[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 35[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 39[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 41[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 42[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 43[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 44[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 45[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 51[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 52[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 53[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 54[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 55[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 56[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 57[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 58[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 59[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 60[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 61[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 62[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 63[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 64[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 65[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 66[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 69[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 71[0:Inp] || equal(multiply(sk_c11,sk_c12),sk_c10)** 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(w,sk_c11),sk_c12)** equal(inverse(w),sk_c11) 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)* -> .
% 0.43/0.60 72[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.43/0.60 73[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.43/0.60 74[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.43/0.60 75[0:Con:71.7] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c11) 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_c11),sk_c12)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(x1,sk_c12),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.43/0.60 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)** -> .
% 0.43/0.60 78[2:Spt:9.1] || -> equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 80[2:SpL:78.0,76.3] || equal(inverse(u),sk_c12)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.43/0.60 81[3:Spt:69.1] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 83[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 85[5:Spt:29.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 87[6:Spt:59.1] || -> equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 91[7:Spt:39.1] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 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)** -> .
% 0.43/0.60 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)** -> .
% 0.43/0.60 102[3:SpR:81.0,73.0] || -> equal(multiply(sk_c11,sk_c3),identity)**.
% 0.43/0.60 103[4:SpR:83.0,73.0] || -> equal(multiply(sk_c11,sk_c2),identity)**.
% 0.43/0.60 104[5:SpR:85.0,73.0] || -> equal(multiply(sk_c12,sk_c1),identity)**.
% 0.43/0.60 120[0:SpR:73.0,74.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.43/0.60 121[3:SpR:102.0,74.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.43/0.60 122[4:SpR:103.0,74.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.43/0.60 124[3:Rew:72.0,121.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.43/0.60 125[4:Rew:72.0,122.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.43/0.60 126[0:Rew:72.0,120.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.43/0.60 134[6:SpR:87.0,124.0] || -> equal(multiply(sk_c11,sk_c12),sk_c11)**.
% 0.43/0.60 136[6:Rew:78.0,134.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 137[6:Rew:136.0,78.0] || -> equal(multiply(sk_c11,sk_c12),sk_c11)**.
% 0.43/0.60 138[7:Rew:136.0,91.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.43/0.60 139[7:Rew:136.0,94.3] || 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)** -> .
% 0.43/0.60 145[7:Obv:139.1] || 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)** -> .
% 0.43/0.60 156[7:SpR:138.0,125.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 158[7:Rew:156.0,145.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c12)** equal(sk_c12,sk_c11) -> .
% 0.43/0.60 180[0:SpR:126.0,126.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.43/0.60 186[0:SpR:73.0,126.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.43/0.60 187[3:SpR:102.0,126.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c3)**.
% 0.43/0.60 188[4:SpR:103.0,126.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.43/0.60 189[3:SpR:124.0,126.0] || -> equal(multiply(inverse(sk_c11),u),multiply(sk_c3,u))**.
% 0.43/0.60 191[6:SpR:137.0,126.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c12)**.
% 0.43/0.60 204[4:Rew:187.0,188.0] || -> equal(sk_c3,sk_c2)**.
% 0.43/0.60 206[6:Rew:204.0,87.0] || -> equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 212[4:Rew:204.0,187.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.43/0.60 213[7:Rew:138.0,206.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 225[7:Rew:213.0,158.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c12,sk_c11) -> .
% 0.43/0.60 236[6:Rew:73.0,191.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 237[7:Rew:213.0,236.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 238[7:Rew:237.0,72.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 240[7:Rew:237.0,103.0] || -> equal(multiply(sk_c11,sk_c2),sk_c11)**.
% 0.43/0.60 245[7:Rew:238.0,240.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 246[7:Rew:245.0,83.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 259[7:Rew:237.0,186.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.43/0.60 268[7:Rew:180.0,259.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 272[7:Rew:213.0,225.4,268.0,225.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.43/0.60 273[7:Obv:272.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 580[7:SpL:246.0,273.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 583[7:Obv:580.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 585[7:SpL:246.0,583.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 588[7:Obv:585.1] || -> .
% 0.43/0.60 589[7:Spt:588.0,39.1,91.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.43/0.60 590[7:Spt:588.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 591[6:Rew:236.0,104.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.43/0.60 592[6:Rew:236.0,103.0] || -> equal(multiply(sk_c11,sk_c2),sk_c12)**.
% 0.43/0.60 593[6:Rew:236.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 594[6:Rew:593.0,591.0] || -> equal(sk_c1,sk_c12)**.
% 0.43/0.60 595[6:Rew:594.0,85.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.43/0.60 600[7:Rew:136.0,589.0] || equal(multiply(sk_c2,sk_c11),sk_c11)** -> .
% 0.43/0.60 601[7:Rew:206.0,600.0] || equal(sk_c12,sk_c11)** -> .
% 0.43/0.60 603[6:Rew:236.0,186.0] || -> equal(multiply(inverse(inverse(u)),sk_c12),u)**.
% 0.43/0.60 606[4:Rew:204.0,189.0] || -> equal(multiply(inverse(sk_c11),u),multiply(sk_c2,u))**.
% 0.43/0.60 615[6:Rew:593.0,12.1,594.0,12.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c12,sk_c11).
% 0.43/0.60 616[7:MRR:615.1,601.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 619[6:Rew:180.0,603.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 630[6:Rew:594.0,11.1,619.0,11.1,619.0,11.0] || -> equal(sk_c4,sk_c11)** equal(sk_c12,sk_c11).
% 0.43/0.60 631[7:MRR:630.1,601.0] || -> equal(sk_c4,sk_c11)**.
% 0.43/0.60 632[7:Rew:631.0,616.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.43/0.60 633[7:Rew:632.0,606.0] || -> equal(multiply(sk_c2,u),multiply(sk_c12,u))**.
% 0.43/0.60 634[7:Rew:593.0,633.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.43/0.60 635[7:Rew:634.0,125.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 639[7:Rew:635.0,592.0] || -> equal(sk_c2,sk_c12)**.
% 0.43/0.60 641[7:Rew:639.0,83.0] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.43/0.60 643[7:Rew:595.0,641.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 644[7:MRR:643.0,601.0] || -> .
% 0.43/0.60 670[6:Spt:644.0,59.1,87.0] || equal(multiply(sk_c3,sk_c11),sk_c12)** -> .
% 0.43/0.60 671[6:Spt:644.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 672[6:Rew:204.0,670.0] || equal(multiply(sk_c2,sk_c11),sk_c12)** -> .
% 0.43/0.60 673[0:Rew:180.0,186.0] || -> equal(multiply(u,identity),u)**.
% 0.43/0.60 674[4:Rew:673.0,212.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.43/0.60 680[4:Rew:36.1,56.1,204.0,56.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c10,sk_c12).
% 0.43/0.60 681[4:Rew:680.1,36.1] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 682[4:Rew:34.1,54.1,204.0,54.1] || -> equal(inverse(sk_c5),sk_c11)** equal(sk_c10,sk_c12).
% 0.43/0.60 683[4:Rew:682.1,34.1] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 684[4:Rew:32.1,52.1,204.0,52.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c10,sk_c12).
% 0.43/0.60 685[4:Rew:684.1,32.1] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 688[6:MRR:681.1,672.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 689[6:MRR:683.1,672.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 690[6:MRR:685.1,672.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 695[4:Rew:35.1,55.1,204.0,55.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(sk_c10,sk_c12).
% 0.43/0.60 696[4:Rew:695.1,35.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 697[4:Rew:204.0,53.1] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 698[6:MRR:697.1,672.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 699[4:Rew:31.1,51.1,204.0,51.1] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(sk_c10,sk_c12).
% 0.43/0.60 700[4:Rew:699.1,31.1] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 703[6:MRR:696.1,672.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 704[6:MRR:700.1,672.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 706[4:Rew:674.0,80.1] || equal(inverse(u),sk_c12)** equal(sk_c2,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.43/0.60 745[6:SpR:698.0,126.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.43/0.60 747[6:Rew:689.0,745.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.43/0.60 756[6:SpR:703.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 758[6:Rew:688.0,756.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 760[6:SpR:704.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 762[6:Rew:690.0,760.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 773[6:SpR:747.0,126.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.43/0.60 775[6:Rew:674.0,773.0] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 776[6:Rew:775.0,672.0] || equal(sk_c10,sk_c12)** -> .
% 0.43/0.60 782[6:SpR:758.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 784[6:Rew:73.0,782.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 785[6:Rew:784.0,104.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.43/0.60 787[6:Rew:784.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 791[6:Rew:784.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 794[6:Rew:787.0,762.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 795[6:Rew:787.0,785.0] || -> equal(sk_c1,sk_c12)**.
% 0.43/0.60 804[6:Rew:794.0,85.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.43/0.60 812[6:Rew:794.0,776.0] || equal(sk_c10,sk_c11)** -> .
% 0.43/0.60 825[6:Rew:794.0,795.0] || -> equal(sk_c1,sk_c11)**.
% 0.43/0.60 826[6:Rew:825.0,804.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 827[6:Rew:674.0,826.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 833[6:Rew:827.0,775.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.43/0.60 835[6:Rew:794.0,791.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 862[6:Rew:835.0,833.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 863[6:MRR:862.0,812.0] || -> .
% 0.43/0.60 903[5:Spt:863.0,29.1,85.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.43/0.60 904[5:Spt:863.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 906[5:MRR:26.1,903.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 907[5:MRR:24.1,903.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 908[5:MRR:22.1,903.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 911[5:MRR:25.0,903.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 912[5:MRR:23.0,903.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 913[5:MRR:21.0,903.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 951[5:SpR:911.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 953[5:Rew:906.0,951.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 959[5:SpR:913.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 961[5:Rew:908.0,959.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 962[5:Rew:961.0,706.5] || equal(inverse(u),sk_c12)** equal(sk_c2,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.43/0.60 963[5:Obv:962.5] || equal(inverse(u),sk_c12)** equal(sk_c2,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.43/0.60 969[5:SpR:953.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 971[5:Rew:73.0,969.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 973[5:Rew:971.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 974[5:Rew:971.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 981[5:Rew:973.0,961.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 989[5:Rew:981.0,78.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.43/0.60 1001[5:Rew:981.0,963.0] || equal(inverse(u),sk_c11)** equal(sk_c2,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.43/0.60 1005[5:Rew:981.0,974.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1006[5:Rew:1005.0,912.0] || -> equal(sk_c5,sk_c10)**.
% 0.43/0.60 1007[5:Rew:1006.0,907.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 1010[5:Rew:1005.0,989.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1013[5:Rew:1010.0,1007.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1015[5:Rew:674.0,1013.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 1017[5:Rew:1015.0,674.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1062[5:Rew:1005.0,1001.4,981.0,1001.4,1010.0,1001.3,981.0,1001.2,1015.0,1001.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1063[5:Obv:1062.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1319[5:SpL:1017.0,1063.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 1322[5:Obv:1319.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 1324[5:SpL:1017.0,1322.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 1327[5:Obv:1324.1] || -> .
% 0.43/0.60 1328[4:Spt:1327.0,49.1,83.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.43/0.60 1329[4:Spt:1327.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 1330[3:Rew:673.0,187.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.43/0.60 1334[4:MRR:46.1,1328.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 1336[4:MRR:42.1,1328.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 1340[4:MRR:45.0,1328.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 1342[4:MRR:41.0,1328.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 1344[3:Rew:1330.0,80.1] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.43/0.60 1381[4:SpR:1340.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 1383[4:Rew:1334.0,1381.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 1389[4:SpR:1342.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 1391[4:Rew:1336.0,1389.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 1392[4:Rew:1391.0,1344.5] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.43/0.60 1393[4:Obv:1392.5] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.43/0.60 1399[4:SpR:1383.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 1401[4:Rew:73.0,1399.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 1403[4:Rew:1401.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 1404[4:Rew:1401.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 1410[4:Rew:1403.0,1342.0] || -> equal(sk_c4,sk_c11)**.
% 0.43/0.60 1411[4:Rew:1403.0,78.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1412[4:Rew:1403.0,1393.4] || equal(inverse(u),sk_c12)** equal(sk_c3,u) equal(inverse(v),sk_c12)** equal(sk_c10,u) equal(v,sk_c12) -> .
% 0.43/0.60 1414[4:Rew:1410.0,1336.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.43/0.60 1423[4:Rew:1330.0,1414.0] || -> equal(sk_c3,sk_c12)**.
% 0.43/0.60 1424[4:Rew:1423.0,81.0] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.43/0.60 1430[4:Rew:1404.0,1391.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 1441[4:Rew:1430.0,1423.0] || -> equal(sk_c3,sk_c11)**.
% 0.43/0.60 1442[4:Rew:1430.0,1424.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1491[4:Rew:1430.0,1412.4,1411.0,1412.3,1430.0,1412.2,1441.0,1412.1,1430.0,1412.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1492[4:Obv:1491.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1677[4:SpL:1442.0,1492.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 1679[4:Obv:1677.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 1681[4:SpL:1442.0,1679.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 1683[4:Obv:1681.1] || -> .
% 0.43/0.60 1684[3:Spt:1683.0,69.1,81.0] || equal(inverse(sk_c3),sk_c11)** -> .
% 0.43/0.60 1685[3:Spt:1683.0,69.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 1687[3:MRR:66.1,1684.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 1688[3:MRR:64.1,1684.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 1689[3:MRR:62.1,1684.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 1692[3:MRR:65.0,1684.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 1693[3:MRR:63.0,1684.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 1694[3:MRR:61.0,1684.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 1716[3:SpR:1692.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 1718[3:Rew:1687.0,1716.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 1724[3:SpR:1694.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 1726[3:Rew:1689.0,1724.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 1727[3:Rew:1726.0,80.5] || equal(inverse(u),sk_c12)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.43/0.60 1728[3:Obv:1727.5] || equal(inverse(u),sk_c12)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.43/0.60 1734[3:SpR:1718.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 1736[3:Rew:73.0,1734.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 1737[3:Rew:1736.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 1738[3:Rew:1736.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 1743[3:Rew:1737.0,1726.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 1750[3:Rew:1743.0,78.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.43/0.60 1761[3:Rew:1743.0,1728.0] || equal(inverse(u),sk_c11)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.43/0.60 1764[3:Rew:1743.0,1738.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1765[3:Rew:1764.0,1693.0] || -> equal(sk_c5,sk_c10)**.
% 0.43/0.60 1766[3:Rew:1765.0,1688.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 1769[3:Rew:1764.0,1750.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1772[3:Rew:1769.0,1766.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1810[3:Rew:1764.0,1761.4,1743.0,1761.4,1769.0,1761.3,1743.0,1761.2,1772.0,1761.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1811[3:Obv:1810.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 2122[3:SpL:1772.0,1811.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2125[3:Obv:2122.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 2127[3:SpL:1772.0,2125.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2130[3:Obv:2127.1] || -> .
% 0.43/0.60 2131[2:Spt:2130.0,9.1,78.0] || equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.43/0.60 2132[2:Spt:2130.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 2135[2:MRR:6.1,2131.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 2136[2:MRR:4.1,2131.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 2137[2:MRR:2.1,2131.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 2140[2:MRR:5.1,2131.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 2141[2:MRR:3.1,2131.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 2142[2:MRR:1.1,2131.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 2169[2:SpR:2140.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 2171[2:Rew:2135.0,2169.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 2173[2:SpR:2141.0,126.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.43/0.60 2175[2:Rew:2136.0,2173.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.43/0.60 2177[2:SpR:2142.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 2179[2:Rew:2137.0,2177.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 2185[2:SpR:2171.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 2187[2:Rew:73.0,2185.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 2188[2:Rew:2187.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 2189[2:Rew:2187.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 2196[2:Rew:2188.0,2131.0] || equal(sk_c10,sk_c11)** -> .
% 0.43/0.60 2200[2:Rew:2189.0,2179.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2212[2:Rew:2200.0,2189.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2229[2:Rew:2212.0,2175.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2230[2:MRR:2229.0,2196.0] || -> .
% 0.43/0.60 2262[1:Spt:2230.0,75.3,75.4,75.5,75.9,75.10,75.11,75.12] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c11),sk_c12)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.43/0.60 2264[2:Spt:8.1] || -> equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.43/0.60 2265[2:Rew:2264.0,2262.6] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** equal(sk_c10,sk_c10) -> .
% 0.43/0.60 2267[2:Obv:2265.6] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.43/0.60 2270[2:SpR:2264.0,126.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c12)**.
% 0.43/0.60 2272[3:Spt:29.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.43/0.60 2273[3:SpR:2272.0,126.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.43/0.60 2275[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.43/0.60 2276[4:SpR:2275.0,126.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.43/0.60 2278[5:Spt:69.1] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 2279[5:SpR:2278.0,126.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.43/0.60 2281[6:Spt:19.1] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 2283[6:SpR:2281.0,126.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c12)**.
% 0.43/0.60 2285[6:Rew:2272.0,2283.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 2286[7:Spt:39.1] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 2288[7:SpR:2286.0,126.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c11)**.
% 0.43/0.60 2290[7:Rew:2275.0,2288.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.43/0.60 2291[8:Spt:59.1] || -> equal(multiply(sk_c3,sk_c11),sk_c12)**.
% 0.43/0.60 2293[8:SpR:2291.0,126.0] || -> equal(multiply(inverse(sk_c3),sk_c12),sk_c11)**.
% 0.43/0.60 2295[8:Rew:2264.0,2293.0,2278.0,2293.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2297[8:Rew:2295.0,2286.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.43/0.60 2298[8:Rew:2295.0,2267.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c11)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.43/0.60 2300[8:Rew:2295.0,2270.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c12)**.
% 0.43/0.60 2304[8:Rew:73.0,2300.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 2305[8:Rew:2304.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 2306[8:Rew:2304.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 2310[8:Rew:2305.0,2285.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2318[8:Rew:2310.0,2306.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2319[8:Rew:2318.0,2297.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 2320[8:Rew:2319.0,2275.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2333[8:Rew:2318.0,2298.5,2310.0,2298.5,2318.0,2298.4,2318.0,2298.3,2310.0,2298.3,2310.0,2298.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.43/0.60 2334[8:Con:2333.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 2371[8:SpL:2320.0,2334.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2372[8:Obv:2371.1] || -> .
% 0.43/0.60 2373[8:Spt:2372.0,59.1,2291.0] || equal(multiply(sk_c3,sk_c11),sk_c12)** -> .
% 0.43/0.60 2374[8:Spt:2372.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 2377[8:MRR:54.1,2373.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 2382[8:MRR:53.1,2373.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 2408[7:SpR:2290.0,126.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.43/0.60 2410[7:Rew:73.0,2408.0] || -> equal(identity,sk_c10)**.
% 0.43/0.60 2411[7:Rew:2410.0,673.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.43/0.60 2412[7:Rew:2410.0,72.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.43/0.60 2413[7:Rew:2410.0,73.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.43/0.60 2415[7:Rew:2411.0,2270.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.43/0.60 2427[6:SpR:2285.0,126.0] || -> equal(multiply(inverse(sk_c12),sk_c12),sk_c11)**.
% 0.43/0.60 2429[7:Rew:2413.0,2427.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2433[8:Rew:2429.0,2382.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.43/0.60 2436[7:Rew:2429.0,2411.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2437[7:Rew:2429.0,2412.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2440[8:Rew:2436.0,2433.0] || -> equal(sk_c5,sk_c11)**.
% 0.43/0.60 2443[8:Rew:2436.0,2373.0] || equal(sk_c3,sk_c12)** -> .
% 0.43/0.60 2444[8:Rew:2440.0,2377.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2457[8:Rew:2415.0,2444.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2470[8:Rew:2457.0,2443.0] || equal(sk_c3,sk_c11)** -> .
% 0.43/0.60 2473[7:Rew:2437.0,2279.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.43/0.60 2533[7:SpR:2473.0,2436.0] || -> equal(sk_c3,sk_c11)**.
% 0.43/0.60 2535[8:MRR:2533.0,2470.0] || -> .
% 0.43/0.60 2537[7:Spt:2535.0,39.1,2286.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.43/0.60 2538[7:Spt:2535.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 2539[6:Rew:73.0,2427.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 2540[6:Rew:2539.0,72.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2541[6:Rew:2539.0,673.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2544[6:Rew:2540.0,2264.0] || -> equal(sk_c10,sk_c12)**.
% 0.43/0.60 2546[7:Rew:2541.0,2537.0,2544.0,2537.0] || equal(sk_c2,sk_c12)** -> .
% 0.43/0.60 2547[6:Rew:2540.0,2276.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.43/0.60 2548[6:Rew:2540.0,2279.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.43/0.60 2549[6:Rew:2548.0,58.1] || -> equal(inverse(sk_c8),sk_c7)** equal(sk_c12,sk_c11).
% 0.43/0.60 2551[6:Rew:2548.0,54.1] || -> equal(inverse(sk_c5),sk_c11)** equal(sk_c12,sk_c11).
% 0.43/0.60 2560[6:Rew:2548.0,60.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(sk_c12,sk_c11).
% 0.43/0.60 2561[6:Rew:2548.0,57.1,2541.0,57.0] || -> equal(sk_c9,sk_c12)** equal(sk_c12,sk_c11).
% 0.43/0.60 2563[6:Rew:2561.0,2560.0] || -> equal(multiply(sk_c8,sk_c12),sk_c7)** equal(sk_c12,sk_c11).
% 0.43/0.60 2565[6:Rew:2548.0,53.1,2541.0,53.0,2544.0,53.0] || -> equal(sk_c5,sk_c12)** equal(sk_c12,sk_c11).
% 0.43/0.60 2566[6:Rew:2565.0,2551.0] || -> equal(inverse(sk_c12),sk_c11)** equal(sk_c12,sk_c11).
% 0.43/0.60 2577[7:SpR:2538.0,126.0] || -> equal(multiply(sk_c9,multiply(sk_c7,u)),u)**.
% 0.43/0.60 2603[6:SpR:2547.0,2541.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 2605[7:Rew:2603.0,2546.0] || equal(sk_c12,sk_c11)** -> .
% 0.43/0.60 2608[7:MRR:2549.1,2605.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.43/0.60 2610[7:MRR:2561.1,2605.0] || -> equal(sk_c9,sk_c12)**.
% 0.43/0.60 2612[7:MRR:2563.1,2605.0] || -> equal(multiply(sk_c8,sk_c12),sk_c7)**.
% 0.43/0.60 2615[7:MRR:2566.1,2605.0] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.43/0.60 2618[7:Rew:2610.0,2538.0] || -> equal(inverse(sk_c7),sk_c12)**.
% 0.43/0.60 2619[7:Rew:2610.0,2577.0] || -> equal(multiply(sk_c12,multiply(sk_c7,u)),u)**.
% 0.43/0.60 2631[7:SpR:2608.0,126.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.43/0.60 2637[7:SpR:2615.0,126.0] || -> equal(multiply(sk_c11,multiply(sk_c12,u)),u)**.
% 0.43/0.60 2639[7:Rew:2540.0,2637.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 2642[7:Rew:2639.0,2619.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.43/0.60 2647[7:Rew:2642.0,2631.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.43/0.60 2650[7:Rew:2647.0,2612.0] || -> equal(sk_c7,sk_c12)**.
% 0.43/0.60 2652[7:Rew:2650.0,2618.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.43/0.60 2654[7:Rew:2615.0,2652.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2655[7:MRR:2654.0,2605.0] || -> .
% 0.43/0.60 2656[6:Spt:2655.0,19.1,2281.0] || equal(multiply(sk_c1,sk_c12),sk_c11)** -> .
% 0.43/0.60 2657[6:Spt:2655.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 2659[6:MRR:16.1,2656.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 2661[6:MRR:12.1,2656.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 2664[6:MRR:15.1,2656.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 2666[6:MRR:11.1,2656.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 2690[6:SpR:2664.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 2692[6:Rew:2659.0,2690.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 2698[6:SpR:2666.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 2700[6:Rew:2661.0,2698.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 2709[6:SpR:2692.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 2711[6:Rew:73.0,2709.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 2712[6:Rew:2711.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 2716[6:Rew:2712.0,2700.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2718[6:Rew:2712.0,2273.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.43/0.60 2731[6:Rew:2716.0,2656.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.43/0.60 2772[6:Rew:2718.0,2731.0] || equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2773[6:Obv:2772.0] || -> .
% 0.43/0.60 2791[5:Spt:2773.0,69.1,2278.0] || equal(inverse(sk_c3),sk_c11)** -> .
% 0.43/0.60 2792[5:Spt:2773.0,69.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 2794[5:MRR:66.1,2791.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 2795[5:MRR:64.1,2791.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 2796[5:MRR:62.1,2791.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 2799[5:MRR:65.0,2791.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 2800[5:MRR:63.0,2791.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 2801[5:MRR:61.0,2791.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 2825[5:SpR:2799.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 2827[5:Rew:2794.0,2825.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 2833[5:SpR:2801.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 2835[5:Rew:2796.0,2833.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 2844[5:SpR:2827.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 2846[5:Rew:73.0,2844.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 2847[5:Rew:2846.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 2848[5:Rew:2846.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 2851[5:Rew:2847.0,2835.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2860[5:Rew:2851.0,2264.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.43/0.60 2866[5:Rew:2851.0,2267.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.43/0.60 2871[5:Rew:2851.0,2848.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2872[5:Rew:2871.0,2800.0] || -> equal(sk_c5,sk_c10)**.
% 0.43/0.60 2873[5:Rew:2872.0,2795.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 2876[5:Rew:2871.0,2860.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2879[5:Rew:2876.0,2873.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2918[5:Rew:2871.0,2866.5,2851.0,2866.5,2871.0,2866.4,2876.0,2866.4,2871.0,2866.3,2851.0,2866.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.43/0.60 2919[5:Con:2918.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 3018[5:SpL:2879.0,2919.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 3020[5:Obv:3018.1] || -> .
% 0.43/0.60 3021[4:Spt:3020.0,49.1,2275.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.43/0.60 3022[4:Spt:3020.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 3024[4:MRR:46.1,3021.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 3025[4:MRR:44.1,3021.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 3026[4:MRR:42.1,3021.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 3029[4:MRR:45.0,3021.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 3030[4:MRR:43.0,3021.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 3031[4:MRR:41.0,3021.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 3055[4:SpR:3029.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 3057[4:Rew:3024.0,3055.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 3063[4:SpR:3031.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 3065[4:Rew:3026.0,3063.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 3071[4:SpR:3057.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 3073[4:Rew:73.0,3071.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 3074[4:Rew:3073.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 3075[4:Rew:3073.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 3078[4:Rew:3074.0,3065.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 3087[4:Rew:3078.0,2264.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.43/0.60 3093[4:Rew:3078.0,2267.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.43/0.60 3098[4:Rew:3078.0,3075.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 3099[4:Rew:3098.0,3030.0] || -> equal(sk_c5,sk_c10)**.
% 0.43/0.60 3100[4:Rew:3099.0,3025.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 3103[4:Rew:3098.0,3087.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 3106[4:Rew:3103.0,3100.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 3144[4:Rew:3098.0,3093.5,3078.0,3093.5,3098.0,3093.4,3103.0,3093.4,3098.0,3093.3,3078.0,3093.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.43/0.60 3145[4:Con:3144.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 3217[4:SpL:3106.0,3145.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 3219[4:Obv:3217.1] || -> .
% 0.43/0.60 3220[3:Spt:3219.0,29.1,2272.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.43/0.60 3221[3:Spt:3219.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.43/0.60 3223[3:MRR:26.1,3220.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 3225[3:MRR:22.1,3220.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 3228[3:MRR:25.0,3220.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 3230[3:MRR:21.0,3220.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 3252[3:SpR:3228.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 3254[3:Rew:3223.0,3252.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 3260[3:SpR:3230.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 3262[3:Rew:3225.0,3260.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 3268[3:SpR:3254.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 3270[3:Rew:73.0,3268.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 3271[3:Rew:3270.0,673.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.43/0.60 3272[3:Rew:3270.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 3275[3:Rew:3271.0,3230.0] || -> equal(sk_c4,sk_c11)**.
% 0.43/0.60 3276[3:Rew:3271.0,2264.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 3279[3:Rew:3271.0,2267.5] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12)** equal(multiply(u,sk_c11),sk_c12)** equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.43/0.60 3280[3:Rew:3275.0,3225.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.43/0.60 3288[3:Rew:3272.0,3262.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 3295[3:Rew:3288.0,3271.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 3296[3:Rew:3288.0,3280.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 3340[3:Rew:3295.0,3279.4,3276.0,3279.4,3295.0,3279.3,3288.0,3279.3,3288.0,3279.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.43/0.60 3341[3:Con:3340.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 3388[3:SpL:3296.0,3341.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 3390[3:Obv:3388.1] || -> .
% 0.43/0.60 3391[2:Spt:3390.0,8.1,2264.0] || equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.43/0.60 3392[2:Spt:3390.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.43/0.60 3393[2:MRR:6.1,3391.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.43/0.60 3394[2:MRR:4.1,3391.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 3395[2:MRR:2.1,3391.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.43/0.60 3399[2:MRR:5.1,3391.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.43/0.60 3400[2:MRR:3.1,3391.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.43/0.60 3401[2:MRR:1.1,3391.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.43/0.60 3420[2:SpR:3399.0,126.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.43/0.60 3422[2:Rew:3393.0,3420.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.43/0.60 3424[2:SpR:3400.0,126.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.43/0.60 3426[2:Rew:3394.0,3424.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.43/0.60 3428[2:SpR:3401.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.43/0.60 3430[2:Rew:3395.0,3428.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.43/0.60 3439[2:SpR:3422.0,126.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.43/0.60 3441[2:Rew:73.0,3439.0] || -> equal(identity,sk_c12)**.
% 0.43/0.60 3442[2:Rew:3441.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.43/0.60 3446[2:Rew:3442.0,3430.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 3456[2:Rew:3446.0,3391.0] || equal(multiply(sk_c11,sk_c11),sk_c10)** -> .
% 0.43/0.61 3459[2:Rew:3446.0,3442.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.61 3477[2:Rew:3459.0,3426.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.61 3491[2:Rew:3459.0,3456.0,3477.0,3456.0] || equal(sk_c11,sk_c11)* -> .
% 0.43/0.61 3492[2:Obv:3491.0] || -> .
% 0.43/0.61 % SZS output end Refutation
% 0.43/0.61 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_11 prove_this_12 prove_this_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_29 prove_this_31 prove_this_32 prove_this_34 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_49 prove_this_51 prove_this_52 prove_this_53 prove_this_54 prove_this_55 prove_this_56 prove_this_57 prove_this_58 prove_this_59 prove_this_60 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
% 0.43/0.61
%------------------------------------------------------------------------------