TSTP Solution File: GRP318-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP318-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:49 EDT 2022
% Result : Unsatisfiable 0.39s 0.61s
% Output : Refutation 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP318-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 11:43:27 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.39/0.61
% 0.39/0.61 SPASS V 3.9
% 0.39/0.61 SPASS beiseite: Proof found.
% 0.39/0.61 % SZS status Theorem
% 0.39/0.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.61 SPASS derived 1980 clauses, backtracked 712 clauses, performed 16 splits and kept 1354 clauses.
% 0.39/0.61 SPASS allocated 64560 KBytes.
% 0.39/0.61 SPASS spent 0:00:00.24 on the problem.
% 0.39/0.61 0:00:00.04 for the input.
% 0.39/0.61 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.61 0:00:00.01 for inferences.
% 0.39/0.61 0:00:00.00 for the backtracking.
% 0.39/0.61 0:00:00.16 for the reduction.
% 0.39/0.61
% 0.39/0.61
% 0.39/0.61 Here is a proof with depth 5, length 450 :
% 0.39/0.61 % SZS output start Refutation
% 0.39/0.61 1[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.39/0.61 2[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 3[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.39/0.61 4[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 5[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c11,sk_c12),sk_c10).
% 0.39/0.61 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 9[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 11[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 12[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 15[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 16[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 17[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 19[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 21[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 22[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 23[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.39/0.61 24[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 25[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 26[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 29[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 31[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c12,sk_c3),sk_c11).
% 0.39/0.61 32[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 35[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c12,sk_c3),sk_c11).
% 0.39/0.61 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 37[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12)** equal(multiply(sk_c12,sk_c3),sk_c11).
% 0.39/0.61 38[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 39[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 40[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(multiply(sk_c12,sk_c3),sk_c11).
% 0.39/0.61 41[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 42[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 45[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 51[0:Inp] || -> equal(inverse(sk_c2),sk_c12) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 52[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c2),sk_c12)**.
% 0.39/0.61 55[0:Inp] || -> equal(inverse(sk_c2),sk_c12) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 56[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c12)**.
% 0.39/0.61 59[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c12)**.
% 0.39/0.61 61[0:Inp] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c11) equal(inverse(z),sk_c12) equal(inverse(x1),sk_c12) equal(inverse(x2),sk_c11) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c12)** equal(multiply(x1,sk_c12),x3)* equal(multiply(v,sk_c11),sk_c12)** equal(multiply(y,sk_c11),sk_c10)** equal(multiply(z,sk_c12),sk_c11)** equal(multiply(x2,sk_c11),sk_c12)** equal(multiply(sk_c12,x3),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10) -> .
% 0.39/0.61 62[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.39/0.61 63[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.39/0.61 64[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.39/0.61 65[1:Spt:61.0,61.1,61.2,61.7,61.8,61.10] || 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)** -> .
% 0.39/0.61 67[2:Spt:9.1] || -> equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 69[2:SpL:67.0,65.3] || 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)** -> .
% 0.39/0.61 70[3:Spt:59.1] || -> equal(inverse(sk_c2),sk_c12)**.
% 0.39/0.61 72[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 74[5:Spt:49.1] || -> equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 78[6:Spt:39.1] || -> equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 83[7:Spt:19.1] || -> equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 85[7:SpL:83.0,65.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.39/0.61 86[7:Rew:72.0,85.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.39/0.61 88[3:SpR:70.0,63.0] || -> equal(multiply(sk_c12,sk_c2),identity)**.
% 0.39/0.61 89[4:SpR:72.0,63.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.39/0.61 103[3:SpR:88.0,64.0] || -> equal(multiply(sk_c12,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.39/0.61 105[0:SpR:63.0,64.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.39/0.61 106[4:SpR:89.0,64.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.39/0.61 108[3:Rew:62.0,103.0] || -> equal(multiply(sk_c12,multiply(sk_c2,u)),u)**.
% 0.39/0.61 109[4:Rew:62.0,106.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.39/0.61 110[0:Rew:62.0,105.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.39/0.61 114[5:SpR:74.0,108.0] || -> equal(multiply(sk_c12,sk_c3),sk_c12)**.
% 0.39/0.61 116[6:Rew:78.0,114.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 118[6:Rew:116.0,67.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.39/0.61 120[6:Rew:116.0,74.0] || -> equal(multiply(sk_c2,sk_c11),sk_c3)**.
% 0.39/0.61 121[6:Rew:116.0,78.0] || -> equal(multiply(sk_c11,sk_c3),sk_c11)**.
% 0.39/0.61 122[7:Rew:116.0,83.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.39/0.61 123[6:Rew:116.0,88.0] || -> equal(multiply(sk_c11,sk_c2),identity)**.
% 0.39/0.61 129[7:Rew:116.0,86.4] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.39/0.61 141[7:Rew:118.0,129.5,116.0,129.5,116.0,129.3] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c10,sk_c11) -> .
% 0.39/0.61 142[7:Obv:141.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c10,sk_c11) -> .
% 0.39/0.61 170[7:SpR:122.0,109.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.39/0.61 171[7:Rew:118.0,170.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 172[7:Rew:171.0,118.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.39/0.61 175[7:Rew:171.0,142.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.39/0.61 177[7:Obv:175.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.39/0.61 188[0:SpR:110.0,110.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.39/0.61 191[0:SpR:63.0,110.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.39/0.61 192[4:SpR:89.0,110.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.39/0.61 193[6:SpR:121.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c3)**.
% 0.39/0.61 194[6:SpR:123.0,110.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.39/0.61 200[7:SpR:172.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.39/0.61 203[6:Rew:63.0,193.0] || -> equal(identity,sk_c3)**.
% 0.39/0.61 204[6:Rew:203.0,62.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.39/0.61 205[6:Rew:203.0,63.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.39/0.61 206[6:Rew:203.0,89.0] || -> equal(multiply(sk_c11,sk_c1),sk_c3)**.
% 0.39/0.61 213[6:Rew:203.0,192.0] || -> equal(multiply(inverse(sk_c11),sk_c3),sk_c1)**.
% 0.39/0.61 217[6:Rew:203.0,194.0] || -> equal(multiply(inverse(sk_c11),sk_c3),sk_c2)**.
% 0.39/0.61 220[7:Rew:205.0,200.0] || -> equal(sk_c3,sk_c11)**.
% 0.39/0.61 223[7:Rew:220.0,203.0] || -> equal(identity,sk_c11)**.
% 0.39/0.61 224[7:Rew:220.0,204.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.61 225[7:Rew:220.0,206.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.39/0.61 232[7:Rew:224.0,225.0] || -> equal(sk_c1,sk_c11)**.
% 0.39/0.61 233[7:Rew:232.0,72.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 245[7:Rew:223.0,191.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.39/0.61 251[7:Rew:188.0,245.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.61 252[7:Rew:251.0,177.3] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 454[7:SpL:233.0,252.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.39/0.61 456[7:Obv:454.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.61 458[7:SpL:233.0,456.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 460[7:Obv:458.1] || -> .
% 0.39/0.61 461[7:Spt:460.0,19.1,83.0] || equal(multiply(sk_c1,sk_c11),sk_c12)** -> .
% 0.39/0.61 462[7:Spt:460.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 463[6:Rew:217.0,213.0] || -> equal(sk_c2,sk_c1)**.
% 0.39/0.61 465[6:Rew:463.0,120.0] || -> equal(multiply(sk_c1,sk_c11),sk_c3)**.
% 0.39/0.61 468[7:Rew:116.0,461.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.39/0.61 469[7:Rew:465.0,468.0] || equal(sk_c3,sk_c11)** -> .
% 0.39/0.61 471[6:Rew:203.0,191.0] || -> equal(multiply(inverse(inverse(u)),sk_c3),u)**.
% 0.39/0.61 479[6:Rew:116.0,16.1] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.39/0.61 480[6:Rew:465.0,479.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c3,sk_c11).
% 0.39/0.61 481[7:MRR:480.1,469.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 488[6:Rew:188.0,471.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.39/0.61 492[6:Rew:116.0,17.1,116.0,17.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.39/0.61 493[6:Rew:465.0,492.1] || -> equal(multiply(sk_c9,sk_c11),sk_c11)** equal(sk_c3,sk_c11).
% 0.39/0.61 494[7:MRR:493.1,469.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.39/0.61 495[6:Rew:116.0,15.1,116.0,15.0] || -> equal(multiply(sk_c6,sk_c9),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.39/0.61 496[6:Rew:465.0,495.1] || -> equal(multiply(sk_c6,sk_c9),sk_c11)** equal(sk_c3,sk_c11).
% 0.39/0.61 497[7:MRR:496.1,469.0] || -> equal(multiply(sk_c6,sk_c9),sk_c11)**.
% 0.39/0.61 533[6:SpR:206.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c3),sk_c1)**.
% 0.39/0.61 535[6:Rew:488.0,533.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.39/0.61 549[7:SpR:494.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c11)**.
% 0.39/0.61 552[7:SpR:497.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c11),sk_c9)**.
% 0.39/0.61 554[7:Rew:494.0,552.0,481.0,552.0] || -> equal(sk_c9,sk_c11)**.
% 0.39/0.61 564[7:Rew:554.0,549.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.39/0.61 575[7:Rew:465.0,564.0,535.0,564.0] || -> equal(sk_c3,sk_c11)**.
% 0.39/0.61 576[7:MRR:575.0,469.0] || -> .
% 0.39/0.61 581[6:Spt:576.0,39.1,78.0] || equal(multiply(sk_c12,sk_c3),sk_c11)** -> .
% 0.39/0.61 582[6:Spt:576.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 583[6:Rew:114.0,581.0] || equal(sk_c12,sk_c11)** -> .
% 0.39/0.61 584[0:Rew:188.0,191.0] || -> equal(multiply(u,identity),u)**.
% 0.39/0.61 585[4:Rew:584.0,192.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.39/0.61 587[5:Rew:114.0,38.1] || -> equal(inverse(sk_c8),sk_c7)** equal(sk_c12,sk_c11).
% 0.39/0.61 588[6:MRR:587.1,583.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.39/0.61 589[5:Rew:114.0,36.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c12,sk_c11).
% 0.39/0.61 590[6:MRR:589.1,583.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 593[5:Rew:114.0,32.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 594[6:MRR:593.1,583.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 595[5:Rew:114.0,40.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(sk_c12,sk_c11).
% 0.39/0.61 596[6:MRR:595.1,583.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.39/0.61 597[5:Rew:114.0,37.1] || -> equal(multiply(sk_c9,sk_c11),sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 598[6:MRR:597.1,583.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.39/0.61 599[5:Rew:114.0,35.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 600[6:MRR:599.1,583.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 603[5:Rew:114.0,31.1] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(sk_c12,sk_c11).
% 0.39/0.61 604[6:MRR:603.1,583.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 607[4:Rew:585.0,69.1] || equal(inverse(u),sk_c12)** equal(sk_c1,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)** -> .
% 0.39/0.61 617[6:SpR:590.0,110.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.39/0.61 621[6:SpR:594.0,110.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.39/0.61 624[5:SpR:114.0,110.0] || -> equal(multiply(inverse(sk_c12),sk_c12),sk_c3)**.
% 0.39/0.61 626[5:Rew:63.0,624.0] || -> equal(identity,sk_c3)**.
% 0.39/0.61 629[5:Rew:626.0,62.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.39/0.61 630[5:Rew:626.0,63.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.39/0.61 633[5:Rew:626.0,584.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.39/0.61 640[6:SpR:596.0,110.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.39/0.61 642[6:Rew:588.0,640.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.39/0.61 653[6:SpR:598.0,64.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),multiply(sk_c12,u))**.
% 0.39/0.61 654[6:SpR:598.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.39/0.61 657[6:SpR:600.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 659[6:Rew:590.0,657.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 690[6:SpR:642.0,110.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c7)**.
% 0.39/0.61 692[6:Rew:582.0,690.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.39/0.61 698[6:SpR:659.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 700[6:Rew:630.0,698.0] || -> equal(sk_c3,sk_c12)**.
% 0.39/0.61 704[6:Rew:700.0,629.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 710[6:Rew:700.0,633.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 715[6:Rew:704.0,621.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.39/0.61 719[6:Rew:704.0,653.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),u)**.
% 0.39/0.61 729[6:Rew:710.0,604.0] || -> equal(sk_c4,sk_c11)**.
% 0.39/0.61 732[6:Rew:710.0,654.0] || -> equal(inverse(sk_c9),sk_c11)**.
% 0.39/0.61 746[6:Rew:729.0,715.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.61 754[6:Rew:746.0,719.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.39/0.61 756[6:Rew:754.0,692.0] || -> equal(sk_c7,sk_c9)**.
% 0.39/0.61 757[6:Rew:754.0,617.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.39/0.61 762[6:Rew:756.0,582.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.39/0.61 767[6:Rew:732.0,762.0] || -> equal(sk_c9,sk_c11)**.
% 0.39/0.61 769[6:Rew:767.0,600.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.39/0.61 779[6:Rew:757.0,769.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 780[6:MRR:779.0,583.0] || -> .
% 0.39/0.61 799[5:Spt:780.0,49.1,74.0] || equal(multiply(sk_c2,sk_c12),sk_c3)** -> .
% 0.39/0.61 800[5:Spt:780.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 802[5:MRR:46.1,799.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 804[5:MRR:42.1,799.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 807[5:MRR:45.1,799.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 809[5:MRR:41.1,799.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 844[3:SpR:88.0,110.0] || -> equal(multiply(inverse(sk_c12),identity),sk_c2)**.
% 0.39/0.61 846[3:Rew:584.0,844.0] || -> equal(inverse(sk_c12),sk_c2)**.
% 0.39/0.61 856[5:SpR:807.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 858[5:Rew:802.0,856.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 864[5:SpR:809.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 866[5:Rew:804.0,864.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 867[5:Rew:866.0,607.5] || equal(inverse(u),sk_c12)** equal(sk_c1,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.39/0.61 868[5:Obv:867.5] || equal(inverse(u),sk_c12)** equal(sk_c1,u) equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.39/0.61 874[5:SpR:858.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 876[5:Rew:63.0,874.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 879[5:Rew:876.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 880[5:Rew:876.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 887[5:Rew:879.0,809.0] || -> equal(sk_c4,sk_c11)**.
% 0.39/0.61 888[5:Rew:879.0,67.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 889[5:Rew:879.0,868.4] || equal(inverse(u),sk_c12)** equal(sk_c1,u) equal(inverse(v),sk_c12)** equal(sk_c10,u) equal(v,sk_c12) -> .
% 0.39/0.61 892[5:Rew:887.0,804.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.39/0.61 901[5:Rew:585.0,892.0] || -> equal(sk_c1,sk_c12)**.
% 0.39/0.61 902[5:Rew:901.0,585.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.39/0.61 915[5:Rew:880.0,866.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 925[5:Rew:915.0,901.0] || -> equal(sk_c1,sk_c11)**.
% 0.39/0.61 926[5:Rew:915.0,902.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 978[5:Rew:915.0,889.4,888.0,889.3,915.0,889.2,925.0,889.1,915.0,889.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 979[5:Obv:978.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 1279[5:SpL:926.0,979.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.39/0.61 1282[5:Obv:1279.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.61 1284[5:SpL:926.0,1282.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 1287[5:Obv:1284.1] || -> .
% 0.39/0.61 1288[4:Spt:1287.0,29.1,72.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.39/0.61 1289[4:Spt:1287.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 1291[4:MRR:26.1,1288.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 1292[4:MRR:24.1,1288.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.39/0.61 1293[4:MRR:22.1,1288.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 1297[4:MRR:25.0,1288.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 1298[4:MRR:23.0,1288.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.39/0.61 1299[4:MRR:21.0,1288.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 1338[4:SpR:1297.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 1340[4:Rew:1291.0,1338.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 1342[4:SpR:1298.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.39/0.61 1344[4:Rew:1292.0,1342.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.39/0.61 1346[4:SpR:1299.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 1348[4:Rew:1293.0,1346.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 1349[4:Rew:1348.0,69.5] || 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) -> .
% 0.39/0.61 1350[4:Obv:1349.5] || 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)** -> .
% 0.39/0.61 1356[4:SpR:1340.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 1358[4:Rew:63.0,1356.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 1359[4:Rew:1358.0,88.0] || -> equal(multiply(sk_c12,sk_c2),sk_c12)**.
% 0.39/0.61 1360[4:Rew:1358.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 1361[4:Rew:1358.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 1367[4:Rew:1360.0,1359.0] || -> equal(sk_c2,sk_c12)**.
% 0.39/0.61 1368[4:Rew:1360.0,1348.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 1370[4:Rew:1360.0,108.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.39/0.61 1376[4:Rew:1367.0,846.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.39/0.61 1390[4:Rew:1368.0,1350.0] || 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)** -> .
% 0.39/0.61 1393[4:Rew:1368.0,1367.0] || -> equal(sk_c2,sk_c11)**.
% 0.39/0.61 1394[4:Rew:1368.0,1376.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 1396[4:Rew:1368.0,1361.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.61 1401[4:Rew:1393.0,1370.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.61 1402[4:Rew:1401.0,1344.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 1444[4:Rew:1396.0,1390.4,1368.0,1390.4,1402.0,1390.3,1368.0,1390.2,1394.0,1390.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 1445[4:Obv:1444.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 1635[4:SpL:1394.0,1445.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.39/0.61 1637[4:Obv:1635.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.61 1639[4:SpL:1394.0,1637.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 1641[4:Obv:1639.1] || -> .
% 0.39/0.61 1642[3:Spt:1641.0,59.1,70.0] || equal(inverse(sk_c2),sk_c12)** -> .
% 0.39/0.61 1643[3:Spt:1641.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 1645[3:MRR:56.1,1642.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 1647[3:MRR:52.1,1642.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 1650[3:MRR:55.0,1642.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 1652[3:MRR:51.0,1642.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 1674[3:SpR:1650.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 1676[3:Rew:1645.0,1674.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 1682[3:SpR:1652.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 1684[3:Rew:1647.0,1682.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 1685[3:Rew:1684.0,69.5] || 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) -> .
% 0.39/0.61 1686[3:Obv:1685.5] || 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)** -> .
% 0.39/0.61 1692[3:SpR:1676.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 1694[3:Rew:63.0,1692.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 1695[3:Rew:1694.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 1696[3:Rew:1694.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 1701[3:Rew:1695.0,1652.0] || -> equal(sk_c4,sk_c11)**.
% 0.39/0.61 1702[3:Rew:1695.0,67.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 1703[3:Rew:1695.0,1686.4] || equal(inverse(u),sk_c12)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c12)** equal(sk_c10,u) equal(v,sk_c12) -> .
% 0.39/0.61 1705[3:Rew:1701.0,1647.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.39/0.61 1713[3:Rew:1696.0,1684.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 1724[3:Rew:1713.0,1705.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 1768[3:Rew:1713.0,1703.4,1702.0,1703.3,1713.0,1703.2,1724.0,1703.1,1713.0,1703.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 1769[3:Obv:1768.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.39/0.61 2120[3:SpL:1724.0,1769.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.39/0.61 2124[3:Obv:2120.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.61 2126[3:SpL:1724.0,2124.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 2130[3:Obv:2126.1] || -> .
% 0.39/0.61 2131[2:Spt:2130.0,9.1,67.0] || equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.39/0.61 2132[2:Spt:2130.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 2135[2:MRR:6.1,2131.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 2136[2:MRR:4.1,2131.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.39/0.61 2137[2:MRR:2.1,2131.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 2140[2:MRR:5.1,2131.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 2141[2:MRR:3.1,2131.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.39/0.61 2142[2:MRR:1.1,2131.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 2169[2:SpR:2140.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 2171[2:Rew:2135.0,2169.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 2173[2:SpR:2141.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.39/0.61 2175[2:Rew:2136.0,2173.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.39/0.61 2177[2:SpR:2142.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 2179[2:Rew:2137.0,2177.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 2185[2:SpR:2171.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 2187[2:Rew:63.0,2185.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 2188[2:Rew:2187.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 2189[2:Rew:2187.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 2194[2:Rew:2188.0,2179.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 2204[2:Rew:2194.0,2131.0] || equal(multiply(sk_c11,sk_c11),sk_c10)** -> .
% 0.39/0.61 2210[2:Rew:2194.0,2188.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.61 2211[2:Rew:2194.0,2189.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.61 2228[2:Rew:2210.0,2175.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 2242[2:Rew:2211.0,2204.0,2228.0,2204.0] || equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 2243[2:Obv:2242.0] || -> .
% 0.39/0.61 2261[1:Spt:2243.0,61.3,61.4,61.5,61.6,61.9,61.11,61.12,61.13,61.14,61.15] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(w,sk_c12),y)*+ equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,y),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10) -> .
% 0.39/0.61 2262[1:EqR:2261.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,multiply(w,sk_c12)),sk_c11)** equal(multiply(sk_c11,sk_c12),sk_c10) -> .
% 0.39/0.61 2264[2:Spt:8.1] || -> equal(multiply(sk_c11,sk_c12),sk_c10)**.
% 0.39/0.61 2267[2:Rew:2264.0,2262.8] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,multiply(w,sk_c12)),sk_c11)** equal(sk_c10,sk_c10) -> .
% 0.39/0.61 2268[2:Obv:2267.8] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,multiply(w,sk_c12)),sk_c11)** -> .
% 0.39/0.61 2272[2:SpR:2264.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c12)**.
% 0.39/0.61 2274[3:Spt:29.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.39/0.61 2275[3:SpR:2274.0,110.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.39/0.61 2277[4:Spt:59.1] || -> equal(inverse(sk_c2),sk_c12)**.
% 0.39/0.61 2278[4:SpR:2277.0,110.0] || -> equal(multiply(sk_c12,multiply(sk_c2,u)),u)**.
% 0.39/0.61 2280[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.39/0.61 2282[5:SpR:2280.0,110.0] || -> equal(multiply(inverse(sk_c1),sk_c12),sk_c11)**.
% 0.39/0.61 2284[5:Rew:2264.0,2282.0,2274.0,2282.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 2290[5:Rew:2284.0,2268.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,multiply(w,sk_c12)),sk_c11)** -> .
% 0.39/0.61 2291[5:Rew:2284.0,2272.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c12)**.
% 0.39/0.61 2293[5:Rew:63.0,2291.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 2294[5:Rew:2293.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 2295[5:Rew:2293.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 2297[5:Rew:2293.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.39/0.61 2298[5:Rew:2294.0,31.0] || -> equal(sk_c4,sk_c11) equal(multiply(sk_c12,sk_c3),sk_c11)**.
% 0.39/0.61 2299[5:Rew:2294.0,41.0] || -> equal(sk_c4,sk_c11) equal(multiply(sk_c2,sk_c12),sk_c3)**.
% 0.39/0.61 2303[5:Rew:2294.0,42.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c2,sk_c3).
% 0.39/0.61 2308[5:Rew:2295.0,2278.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.39/0.61 2312[5:Rew:2295.0,32.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c3,sk_c11).
% 0.39/0.61 2317[5:Rew:2312.1,2303.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c2,sk_c11).
% 0.39/0.61 2322[5:Rew:2295.0,2298.1] || -> equal(sk_c4,sk_c11) equal(sk_c3,sk_c11)**.
% 0.39/0.61 2324[5:Rew:2308.0,2299.1,2322.1,2299.1] || -> equal(sk_c4,sk_c11)** equal(sk_c12,sk_c11).
% 0.39/0.61 2332[5:Rew:2294.0,2290.7,2295.0,2290.7,2294.0,2290.5] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(v,sk_c11) equal(multiply(x,sk_c11),sk_c12)** equal(w,sk_c11) -> .
% 0.39/0.61 2333[5:Con:2332.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12)** equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(v,sk_c11) equal(multiply(w,sk_c11),sk_c12)** -> .
% 0.39/0.61 2350[5:SpR:2308.0,2294.0] || -> equal(sk_c2,sk_c12)**.
% 0.39/0.61 2352[5:Rew:2350.0,2277.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.39/0.61 2361[5:Rew:2350.0,2317.1] || -> equal(inverse(sk_c4),sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 2364[5:Rew:2324.0,2361.0] || -> equal(inverse(sk_c11),sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 2376[5:SpR:2274.0,2297.0] || -> equal(multiply(sk_c11,sk_c1),sk_c12)**.
% 0.39/0.61 2382[5:SpR:2376.0,110.0] || -> equal(multiply(inverse(sk_c11),sk_c12),sk_c1)**.
% 0.39/0.61 2384[5:Rew:2294.0,2382.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.39/0.61 2385[5:Rew:2384.0,2364.0] || -> equal(sk_c1,sk_c12)** equal(sk_c12,sk_c11).
% 0.39/0.61 2398[6:Spt:2385.1] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 2402[6:Rew:2398.0,2294.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.61 2404[6:Rew:2398.0,2352.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 2409[6:Rew:2398.0,2333.1] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(v,sk_c11) equal(multiply(w,sk_c11),sk_c12)** -> .
% 0.39/0.61 2412[6:Rew:2384.0,2404.0] || -> equal(sk_c1,sk_c11)**.
% 0.39/0.61 2413[6:Rew:2412.0,2274.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.61 2436[6:Rew:2402.0,2409.5,2398.0,2409.5,2402.0,2409.3] || 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) -> .
% 0.39/0.61 2437[6:Con:2436.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.61 2500[6:SpL:2413.0,2437.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 2501[6:Obv:2500.1] || -> .
% 0.39/0.61 2502[6:Spt:2501.0,2385.1,2398.0] || equal(sk_c12,sk_c11)** -> .
% 0.39/0.61 2503[6:Spt:2501.0,2385.0] || -> equal(sk_c1,sk_c12)**.
% 0.39/0.61 2505[6:Rew:2352.0,2274.0,2503.0,2274.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 2511[6:Rew:2505.0,2502.0] || equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 2512[6:Obv:2511.0] || -> .
% 0.39/0.61 2537[5:Spt:2512.0,19.1,2280.0] || equal(multiply(sk_c1,sk_c11),sk_c12)** -> .
% 0.39/0.61 2538[5:Spt:2512.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 2540[5:MRR:16.1,2537.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 2542[5:MRR:12.1,2537.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 2545[5:MRR:15.1,2537.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 2547[5:MRR:11.1,2537.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 2573[5:SpR:2545.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 2575[5:Rew:2540.0,2573.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 2581[5:SpR:2547.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 2583[5:Rew:2542.0,2581.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 2589[5:SpR:2575.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 2591[5:Rew:63.0,2589.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 2592[5:Rew:2591.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 2597[5:Rew:2592.0,2583.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.61 2614[5:Rew:2597.0,2537.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.39/0.61 2617[5:Rew:2597.0,2592.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.61 2639[5:Rew:2617.0,2275.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.39/0.61 2652[5:Rew:2639.0,2614.0] || equal(sk_c11,sk_c11)* -> .
% 0.39/0.61 2653[5:Obv:2652.0] || -> .
% 0.39/0.61 2674[4:Spt:2653.0,59.1,2277.0] || equal(inverse(sk_c2),sk_c12)** -> .
% 0.39/0.61 2675[4:Spt:2653.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.61 2677[4:MRR:56.1,2674.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.61 2679[4:MRR:52.1,2674.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.61 2682[4:MRR:55.0,2674.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.61 2684[4:MRR:51.0,2674.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.61 2706[4:SpR:2682.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.61 2708[4:Rew:2677.0,2706.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.61 2714[4:SpR:2684.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.61 2716[4:Rew:2679.0,2714.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.61 2722[4:SpR:2708.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.61 2724[4:Rew:63.0,2722.0] || -> equal(identity,sk_c12)**.
% 0.39/0.61 2725[4:Rew:2724.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.61 2726[4:Rew:2724.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.61 2729[4:Rew:2725.0,2684.0] || -> equal(sk_c4,sk_c11)**.
% 0.39/0.61 2730[4:Rew:2725.0,2264.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.61 2733[4:Rew:2725.0,2268.7] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,w),sk_c11)** -> .
% 0.39/0.61 2735[4:Rew:2729.0,2679.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.39/0.62 2743[4:Rew:2726.0,2716.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.62 2750[4:Rew:2743.0,2725.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.62 2751[4:Rew:2743.0,2735.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.62 2752[4:Rew:2743.0,2726.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.62 2796[4:Rew:2752.0,2733.7,2743.0,2733.7,2750.0,2733.6,2743.0,2733.6,2750.0,2733.5,2743.0,2733.5,2750.0,2733.4,2730.0,2733.4,2743.0,2733.2,2743.0,2733.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(inverse(x),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(x,sk_c11) equal(w,sk_c11) -> .
% 0.39/0.62 2797[4:Con:2796.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.62 2848[4:SpL:2751.0,2797.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.62 2850[4:Obv:2848.1] || -> .
% 0.39/0.62 2851[3:Spt:2850.0,29.1,2274.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.39/0.62 2852[3:Spt:2850.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.39/0.62 2854[3:MRR:26.1,2851.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.62 2855[3:MRR:24.1,2851.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.39/0.62 2856[3:MRR:22.1,2851.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.62 2859[3:MRR:25.0,2851.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.62 2860[3:MRR:23.0,2851.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.39/0.62 2861[3:MRR:21.0,2851.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.62 2883[3:SpR:2859.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.62 2885[3:Rew:2854.0,2883.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.62 2891[3:SpR:2861.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.62 2893[3:Rew:2856.0,2891.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.62 2899[3:SpR:2885.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.62 2901[3:Rew:63.0,2899.0] || -> equal(identity,sk_c12)**.
% 0.39/0.62 2902[3:Rew:2901.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.62 2903[3:Rew:2901.0,584.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.39/0.62 2906[3:Rew:2902.0,2893.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.62 2910[3:Rew:2902.0,2268.7] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.39/0.62 2916[3:Rew:2906.0,2264.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.39/0.62 2925[3:Rew:2906.0,2903.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.39/0.62 2926[3:Rew:2925.0,2860.0] || -> equal(sk_c5,sk_c10)**.
% 0.39/0.62 2927[3:Rew:2926.0,2855.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.39/0.62 2930[3:Rew:2925.0,2916.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.62 2933[3:Rew:2930.0,2927.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.39/0.62 2971[3:Con:2910.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(w,sk_c11),sk_c12)** -> .
% 0.39/0.62 2972[3:Rew:2925.0,2971.5,2906.0,2971.5,2925.0,2971.4,2906.0,2971.4,2925.0,2971.3,2930.0,2971.3,2906.0,2971.1] || 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) -> .
% 0.39/0.62 2973[3:Con:2972.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.39/0.62 3026[3:SpL:2933.0,2973.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.39/0.62 3028[3:Obv:3026.1] || -> .
% 0.39/0.62 3029[2:Spt:3028.0,8.1,2264.0] || equal(multiply(sk_c11,sk_c12),sk_c10)** -> .
% 0.39/0.62 3030[2:Spt:3028.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.39/0.62 3031[2:MRR:6.1,3029.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.39/0.62 3032[2:MRR:4.1,3029.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.39/0.62 3033[2:MRR:2.1,3029.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.39/0.62 3037[2:MRR:5.1,3029.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.39/0.62 3038[2:MRR:3.1,3029.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.39/0.62 3039[2:MRR:1.1,3029.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.39/0.62 3058[2:SpR:3037.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.39/0.62 3060[2:Rew:3031.0,3058.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.39/0.62 3062[2:SpR:3038.0,110.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.39/0.62 3064[2:Rew:3032.0,3062.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.39/0.62 3066[2:SpR:3039.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.39/0.62 3068[2:Rew:3033.0,3066.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.39/0.62 3077[2:SpR:3060.0,110.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.39/0.62 3079[2:Rew:63.0,3077.0] || -> equal(identity,sk_c12)**.
% 0.39/0.62 3080[2:Rew:3079.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.39/0.62 3084[2:Rew:3080.0,3068.0] || -> equal(sk_c12,sk_c11)**.
% 0.39/0.62 3094[2:Rew:3084.0,3029.0] || equal(multiply(sk_c11,sk_c11),sk_c10)** -> .
% 0.39/0.62 3097[2:Rew:3084.0,3080.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.39/0.62 3115[2:Rew:3097.0,3064.0] || -> equal(sk_c10,sk_c11)**.
% 0.39/0.62 3129[2:Rew:3097.0,3094.0,3115.0,3094.0] || equal(sk_c11,sk_c11)* -> .
% 0.39/0.62 3130[2:Obv:3129.0] || -> .
% 0.39/0.62 % SZS output end Refutation
% 0.39/0.62 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_17 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_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_45 prove_this_46 prove_this_49 prove_this_51 prove_this_52 prove_this_55 prove_this_56 prove_this_59 prove_this_61 left_identity left_inverse associativity
% 0.39/0.62
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