TSTP Solution File: GRP254-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP254-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:46:32 EDT 2022
% Result : Unsatisfiable 0.58s 0.75s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP254-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:22:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.75
% 0.58/0.75 SPASS V 3.9
% 0.58/0.75 SPASS beiseite: Proof found.
% 0.58/0.75 % SZS status Theorem
% 0.58/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.75 SPASS derived 3391 clauses, backtracked 813 clauses, performed 13 splits and kept 1722 clauses.
% 0.58/0.75 SPASS allocated 65848 KBytes.
% 0.58/0.75 SPASS spent 0:00:00.40 on the problem.
% 0.58/0.75 0:00:00.03 for the input.
% 0.58/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.75 0:00:00.02 for inferences.
% 0.58/0.75 0:00:00.01 for the backtracking.
% 0.58/0.75 0:00:00.31 for the reduction.
% 0.58/0.75
% 0.58/0.75
% 0.58/0.75 Here is a proof with depth 5, length 560 :
% 0.58/0.75 % SZS output start Refutation
% 0.58/0.75 1[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c1,sk_c12),sk_c11).
% 0.58/0.75 2[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.58/0.75 5[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c1,sk_c12),sk_c11).
% 0.58/0.75 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.58/0.75 9[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.58/0.75 11[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 12[0:Inp] || -> equal(inverse(sk_c4),sk_c12)** equal(inverse(sk_c1),sk_c12).
% 0.58/0.75 13[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 14[0:Inp] || -> equal(inverse(sk_c5),sk_c11)** equal(inverse(sk_c1),sk_c12).
% 0.58/0.75 15[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 16[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c12).
% 0.58/0.75 17[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 19[0:Inp] || -> equal(inverse(sk_c7),sk_c9)** equal(inverse(sk_c1),sk_c12).
% 0.58/0.75 21[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 22[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 23[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 24[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 25[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 26[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 27[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 29[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 31[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 32[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 33[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 34[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 35[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 37[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 39[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 41[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 42[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 43[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 44[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 45[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 47[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 48[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 51[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 52[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 53[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 54[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 55[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 56[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 57[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 59[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 61[0:Inp] || equal(multiply(u,sk_c12),sk_c11)** equal(inverse(u),sk_c12) equal(multiply(v,sk_c11),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(multiply(w,sk_c12),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(inverse(x),sk_c12) equal(multiply(y,sk_c11),sk_c10)** equal(inverse(y),sk_c11) equal(multiply(z,x1),sk_c12)** equal(inverse(z),x1) equal(multiply(x1,sk_c11),sk_c12)** equal(inverse(x2),x3) equal(inverse(x3),x1)* equal(multiply(x2,x1),x3)* -> .
% 0.58/0.75 62[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.58/0.75 63[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.58/0.75 64[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.58/0.75 65[0:Con:61.6] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(x1),sk_c12) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(y,sk_c12),sk_c10)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(x1,sk_c12),sk_c11)** -> .
% 0.58/0.75 66[1:Spt:65.0,65.1,65.2,65.6,65.7,65.8] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12)** -> .
% 0.58/0.75 67[1:EqR:66.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12) -> .
% 0.58/0.75 68[2:Spt:49.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 70[3:Spt:39.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 72[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.58/0.75 74[5:Spt:59.1] || -> equal(multiply(sk_c3,sk_c12),sk_c10)**.
% 0.58/0.75 76[5:SpL:74.0,66.3] || equal(inverse(u),sk_c12)** equal(inverse(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)** -> .
% 0.58/0.75 77[5:Rew:68.0,76.1] || equal(inverse(u),sk_c12)** equal(sk_c10,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)** -> .
% 0.58/0.75 78[5:Obv:77.1] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(multiply(sk_c12,sk_c11),sk_c12)** -> .
% 0.58/0.75 79[6:Spt:29.1] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.58/0.75 85[7:Spt:9.1] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.58/0.75 90[2:SpR:68.0,63.0] || -> equal(multiply(sk_c10,sk_c3),identity)**.
% 0.58/0.75 91[3:SpR:70.0,63.0] || -> equal(multiply(sk_c11,sk_c2),identity)**.
% 0.58/0.75 92[4:SpR:72.0,63.0] || -> equal(multiply(sk_c12,sk_c1),identity)**.
% 0.58/0.75 101[6:SpR:79.0,64.0] || -> equal(multiply(sk_c2,multiply(sk_c11,u)),multiply(sk_c10,u))**.
% 0.58/0.75 105[0:SpR:63.0,64.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.58/0.75 106[2:SpR:90.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.58/0.75 107[3:SpR:91.0,64.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.58/0.75 109[2:Rew:62.0,106.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.58/0.75 110[3:Rew:62.0,107.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.58/0.75 111[0:Rew:62.0,105.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.58/0.75 113[4:SpR:92.0,64.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.58/0.75 116[4:Rew:62.0,113.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.58/0.75 119[5:SpR:74.0,109.0] || -> equal(multiply(sk_c10,sk_c10),sk_c12)**.
% 0.58/0.75 128[6:SpR:79.0,110.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.58/0.75 133[0:SpR:111.0,111.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.58/0.75 137[7:SpR:85.0,111.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c12)**.
% 0.58/0.75 139[0:SpR:63.0,111.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.58/0.75 146[4:SpR:92.0,111.0] || -> equal(multiply(inverse(sk_c12),identity),sk_c1)**.
% 0.58/0.75 153[7:Rew:72.0,137.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.58/0.75 155[7:Rew:153.0,78.4] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.58/0.75 159[0:Rew:133.0,139.0] || -> equal(multiply(u,identity),u)**.
% 0.58/0.75 160[4:Rew:159.0,146.0] || -> equal(inverse(sk_c12),sk_c1)**.
% 0.58/0.75 163[7:Obv:155.4] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12) equal(sk_c10,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.58/0.75 166[4:SpR:160.0,63.0] || -> equal(multiply(sk_c1,sk_c12),identity)**.
% 0.58/0.75 169[7:Rew:85.0,166.0] || -> equal(identity,sk_c11)**.
% 0.58/0.75 170[7:Rew:169.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.58/0.75 172[7:Rew:169.0,90.0] || -> equal(multiply(sk_c10,sk_c3),sk_c11)**.
% 0.58/0.75 181[7:Rew:169.0,159.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.58/0.75 183[7:Rew:170.0,128.0] || -> equal(sk_c10,sk_c11)**.
% 0.58/0.75 187[7:Rew:183.0,68.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.58/0.75 188[7:Rew:183.0,74.0] || -> equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 192[7:Rew:183.0,163.2] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12) equal(sk_c11,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.58/0.75 198[7:Rew:170.0,172.0,183.0,172.0] || -> equal(sk_c3,sk_c11)**.
% 0.58/0.75 199[7:Rew:198.0,187.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.58/0.75 209[7:Rew:170.0,188.0,198.0,188.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 216[7:Rew:209.0,199.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 219[7:Rew:209.0,181.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 220[7:Rew:160.0,216.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 221[7:Rew:220.0,72.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.58/0.75 224[7:Rew:220.0,209.0] || -> equal(sk_c11,sk_c1)**.
% 0.58/0.75 234[7:Rew:220.0,219.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 246[7:Rew:234.0,192.3,220.0,192.3,224.0,192.2,220.0,192.1,220.0,192.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.58/0.75 457[7:SpL:221.0,246.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.58/0.75 459[7:Obv:457.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.58/0.75 461[7:SpL:221.0,459.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.58/0.75 463[7:Obv:461.1] || -> .
% 0.58/0.75 464[7:Spt:463.0,9.1,85.0] || equal(multiply(sk_c1,sk_c12),sk_c11)** -> .
% 0.58/0.75 465[7:Spt:463.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 466[7:Rew:166.0,464.0] || equal(identity,sk_c11)** -> .
% 0.58/0.75 473[4:Rew:166.0,2.1] || -> equal(inverse(sk_c4),sk_c12)** equal(identity,sk_c11).
% 0.58/0.75 474[7:MRR:473.1,466.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 483[4:Rew:166.0,1.1] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(identity,sk_c11).
% 0.58/0.75 484[7:MRR:483.1,466.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 501[7:SpR:474.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 514[3:SpR:91.0,111.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.58/0.75 516[3:Rew:159.0,514.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.58/0.75 521[3:SpR:516.0,111.0] || -> equal(multiply(sk_c2,multiply(sk_c11,u)),u)**.
% 0.58/0.75 523[6:Rew:101.0,521.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.58/0.75 529[6:Rew:523.0,119.0] || -> equal(sk_c10,sk_c12)**.
% 0.58/0.75 530[6:Rew:523.0,90.0] || -> equal(identity,sk_c3)**.
% 0.58/0.75 542[6:Rew:529.0,523.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 543[7:Rew:530.0,466.0] || equal(sk_c3,sk_c11)** -> .
% 0.58/0.75 545[6:Rew:530.0,92.0] || -> equal(multiply(sk_c12,sk_c1),sk_c3)**.
% 0.58/0.75 546[6:Rew:530.0,91.0] || -> equal(multiply(sk_c11,sk_c2),sk_c3)**.
% 0.58/0.75 548[6:Rew:530.0,159.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.58/0.75 554[7:Rew:542.0,501.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 557[6:Rew:542.0,545.0] || -> equal(sk_c3,sk_c1)**.
% 0.58/0.75 560[7:Rew:557.0,543.0] || equal(sk_c11,sk_c1)** -> .
% 0.58/0.75 563[6:Rew:557.0,546.0] || -> equal(multiply(sk_c11,sk_c2),sk_c1)**.
% 0.58/0.75 565[6:Rew:557.0,548.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 566[7:Rew:554.0,484.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 569[7:Rew:566.0,516.0] || -> equal(inverse(sk_c12),sk_c2)**.
% 0.58/0.75 581[7:Rew:566.0,560.0] || equal(sk_c12,sk_c1)** -> .
% 0.58/0.75 582[7:Rew:566.0,563.0] || -> equal(multiply(sk_c12,sk_c2),sk_c1)**.
% 0.58/0.75 583[7:Rew:160.0,569.0] || -> equal(sk_c2,sk_c1)**.
% 0.58/0.75 588[7:Rew:565.0,582.0,583.0,582.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 589[7:MRR:588.0,581.0] || -> .
% 0.58/0.75 620[6:Spt:589.0,29.1,79.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.58/0.75 621[6:Spt:589.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 627[6:MRR:26.1,620.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 628[6:MRR:24.1,620.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 629[6:MRR:22.1,620.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 637[6:MRR:25.1,620.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 638[6:MRR:23.1,620.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 639[6:MRR:21.1,620.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 693[6:SpR:637.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 695[6:Rew:627.0,693.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 711[6:SpR:695.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.58/0.75 713[6:Rew:63.0,711.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 717[6:Rew:713.0,166.0] || -> equal(multiply(sk_c1,sk_c12),sk_c12)**.
% 0.58/0.75 718[6:Rew:713.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 719[6:Rew:713.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 727[6:Rew:718.0,639.0] || -> equal(sk_c4,sk_c11)**.
% 0.58/0.75 728[6:Rew:718.0,74.0] || -> equal(sk_c3,sk_c10)**.
% 0.58/0.75 729[6:Rew:718.0,717.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 732[6:Rew:727.0,629.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.58/0.75 735[6:Rew:728.0,68.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.58/0.75 741[6:Rew:729.0,160.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.58/0.75 761[6:Rew:729.0,718.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 762[6:Rew:516.0,732.0] || -> equal(sk_c2,sk_c12)**.
% 0.58/0.75 763[6:Rew:729.0,762.0] || -> equal(sk_c2,sk_c1)**.
% 0.58/0.75 765[6:Rew:763.0,70.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.58/0.75 766[6:Rew:763.0,620.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.58/0.75 769[6:Rew:741.0,765.0] || -> equal(sk_c11,sk_c1)**.
% 0.58/0.75 770[6:Rew:769.0,628.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.58/0.75 771[6:Rew:769.0,638.0] || -> equal(multiply(sk_c5,sk_c1),sk_c10)**.
% 0.58/0.75 778[6:Rew:729.0,719.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 795[6:Rew:761.0,771.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 797[6:Rew:795.0,735.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.58/0.75 799[6:Rew:770.0,797.0] || -> equal(sk_c5,sk_c1)**.
% 0.58/0.75 801[6:Rew:799.0,795.0] || -> equal(sk_c10,sk_c1)**.
% 0.58/0.75 818[6:Rew:778.0,766.0,769.0,766.0,801.0,766.0] || equal(sk_c1,sk_c1)* -> .
% 0.58/0.75 819[6:Obv:818.0] || -> .
% 0.58/0.75 857[5:Spt:819.0,59.1,74.0] || equal(multiply(sk_c3,sk_c12),sk_c10)** -> .
% 0.58/0.75 858[5:Spt:819.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 860[5:MRR:56.1,857.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 861[5:MRR:54.1,857.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 862[5:MRR:52.1,857.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 865[5:MRR:55.1,857.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 866[5:MRR:53.1,857.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 867[5:MRR:51.1,857.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 916[5:SpR:865.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 918[5:Rew:860.0,916.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 920[5:SpR:866.0,111.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.58/0.75 922[5:Rew:861.0,920.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.58/0.75 924[5:SpR:867.0,111.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.58/0.75 926[5:Rew:862.0,924.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.58/0.75 932[5:SpR:918.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.58/0.75 934[5:Rew:63.0,932.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 936[5:Rew:934.0,92.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.58/0.75 938[5:Rew:934.0,90.0] || -> equal(multiply(sk_c10,sk_c3),sk_c12)**.
% 0.58/0.75 939[5:Rew:934.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 940[5:Rew:934.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 948[5:Rew:939.0,936.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 949[5:Rew:939.0,926.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 951[5:Rew:939.0,116.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 963[5:Rew:948.0,857.0] || equal(multiply(sk_c3,sk_c1),sk_c10)** -> .
% 0.58/0.75 974[5:Rew:948.0,938.0] || -> equal(multiply(sk_c10,sk_c3),sk_c1)**.
% 0.58/0.75 976[5:Rew:948.0,949.0] || -> equal(sk_c11,sk_c1)**.
% 0.58/0.75 980[5:Rew:976.0,866.0] || -> equal(multiply(sk_c5,sk_c1),sk_c10)**.
% 0.58/0.75 985[5:Rew:976.0,922.0] || -> equal(multiply(sk_c1,sk_c10),sk_c1)**.
% 0.58/0.75 988[5:Rew:948.0,940.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 1003[5:Rew:988.0,980.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 1007[5:Rew:1003.0,974.0] || -> equal(multiply(sk_c5,sk_c3),sk_c1)**.
% 0.58/0.75 1008[5:Rew:951.0,985.0,1003.0,985.0] || -> equal(sk_c5,sk_c1)**.
% 0.58/0.75 1010[5:Rew:1008.0,1003.0] || -> equal(sk_c10,sk_c1)**.
% 0.58/0.75 1021[5:Rew:951.0,1007.0,1008.0,1007.0] || -> equal(sk_c3,sk_c1)**.
% 0.58/0.75 1025[5:Rew:951.0,963.0,1021.0,963.0,1010.0,963.0] || equal(sk_c1,sk_c1)* -> .
% 0.58/0.75 1026[5:Obv:1025.0] || -> .
% 0.58/0.75 1057[4:Spt:1026.0,19.1,72.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.58/0.75 1058[4:Spt:1026.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 1060[4:MRR:16.1,1057.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 1061[4:MRR:14.1,1057.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 1062[4:MRR:12.1,1057.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 1065[4:MRR:15.0,1057.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 1066[4:MRR:13.0,1057.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 1067[4:MRR:11.0,1057.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 1102[4:SpR:1065.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 1104[4:Rew:1060.0,1102.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 1106[4:SpR:1066.0,111.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.58/0.75 1108[4:Rew:1061.0,1106.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.58/0.75 1110[4:SpR:1067.0,111.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.58/0.75 1112[4:Rew:1062.0,1110.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.58/0.75 1121[4:SpR:1104.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.58/0.75 1123[4:Rew:63.0,1121.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 1126[4:Rew:1123.0,62.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 1127[4:Rew:1123.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 1130[4:Rew:1123.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.58/0.75 1134[4:Rew:1126.0,1112.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 1139[4:Rew:1134.0,516.0] || -> equal(inverse(sk_c12),sk_c2)**.
% 0.58/0.75 1141[4:Rew:1134.0,1061.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.58/0.75 1143[4:Rew:1134.0,1066.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.58/0.75 1150[4:Rew:1134.0,67.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c12),sk_c12) -> .
% 0.58/0.75 1156[4:Rew:1134.0,1108.0] || -> equal(multiply(sk_c12,sk_c10),sk_c12)**.
% 0.58/0.75 1169[4:Rew:1127.0,1143.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 1174[4:Rew:1126.0,1156.0,1169.0,1156.0] || -> equal(sk_c5,sk_c12)**.
% 0.58/0.75 1175[4:Rew:1174.0,1141.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 1178[4:Rew:1139.0,1175.0] || -> equal(sk_c2,sk_c12)**.
% 0.58/0.75 1179[4:Rew:1178.0,1139.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 1217[4:Rew:1127.0,1150.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 1262[4:SpR:133.0,1127.0] || -> equal(multiply(u,sk_c12),inverse(inverse(u)))**.
% 0.58/0.75 1263[0:SpR:133.0,111.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.58/0.75 1264[4:SpR:133.0,1130.0] || -> equal(multiply(u,inverse(u)),sk_c12)**.
% 0.58/0.75 1267[4:Rew:1127.0,1262.0] || -> equal(inverse(inverse(u)),u)**.
% 0.58/0.75 1894[4:SpL:1130.0,1217.0] || equal(inverse(sk_c12),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 1904[4:Rew:1130.0,1894.1,1267.0,1894.1,1179.0,1894.0] || equal(sk_c12,u) equal(sk_c12,u) equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 1905[4:Obv:1904.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 1990[4:SpL:1264.0,1905.1] || equal(inverse(u),inverse(u))* equal(sk_c12,sk_c12) equal(inverse(u),sk_c12) -> .
% 0.58/0.75 2012[4:Obv:1990.1] || equal(inverse(u),sk_c12)** -> .
% 0.58/0.75 2013[4:UnC:2012.0,1267.0] || -> .
% 0.58/0.75 2019[3:Spt:2013.0,39.1,70.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.58/0.75 2020[3:Spt:2013.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 2022[3:MRR:36.1,2019.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 2024[3:MRR:32.1,2019.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 2027[3:MRR:37.0,2019.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 2028[3:MRR:35.0,2019.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 2030[3:MRR:31.0,2019.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 2054[3:SpR:2022.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.58/0.75 2059[3:SpR:2024.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 2085[3:SpR:2027.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.58/0.75 2089[3:SpR:2028.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.58/0.75 2090[3:SpR:2028.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 2094[3:Rew:2022.0,2090.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 2095[3:Rew:2054.0,2089.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 2096[3:Rew:2095.0,2059.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 2099[3:Rew:2096.0,2030.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 2102[3:Rew:2099.0,2027.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.58/0.75 2108[3:Rew:2099.0,67.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c12),sk_c12) -> .
% 0.58/0.75 2114[3:Rew:2099.0,2085.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.58/0.75 2117[3:Rew:2094.0,2102.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 2119[3:Rew:2117.0,2022.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.58/0.75 2121[3:Rew:2117.0,2028.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.58/0.75 2131[3:Rew:63.0,2114.0,2117.0,2114.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 2134[3:Rew:2131.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 2135[3:Rew:2131.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.58/0.75 2137[3:Rew:2134.0,2121.0] || -> equal(sk_c6,sk_c12)**.
% 0.58/0.75 2140[3:Rew:2137.0,2119.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 2185[3:Rew:2134.0,2108.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 2238[3:SpR:2134.0,1263.0] || -> equal(multiply(u,inverse(u)),sk_c12)**.
% 0.58/0.75 2253[3:SpR:2238.0,1263.0] || -> equal(multiply(u,sk_c12),inverse(inverse(u)))**.
% 0.58/0.75 2256[3:Rew:2134.0,2253.0] || -> equal(inverse(inverse(u)),u)**.
% 0.58/0.75 2635[3:SpL:2135.0,2185.0] || equal(inverse(sk_c12),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 2645[3:Rew:2135.0,2635.1,2256.0,2635.1,2140.0,2635.0] || equal(sk_c12,u) equal(sk_c12,u) equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 2646[3:Obv:2645.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 2807[3:SpL:2238.0,2646.1] || equal(inverse(u),inverse(u))* equal(sk_c12,sk_c12) equal(inverse(u),sk_c12) -> .
% 0.58/0.75 2829[3:Obv:2807.1] || equal(inverse(u),sk_c12)** -> .
% 0.58/0.75 2830[3:UnC:2829.0,2256.0] || -> .
% 0.58/0.75 2836[2:Spt:2830.0,49.1,68.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.58/0.75 2837[2:Spt:2830.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 2839[2:MRR:46.1,2836.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 2841[2:MRR:42.1,2836.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 2844[2:MRR:47.0,2836.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 2845[2:MRR:45.0,2836.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 2847[2:MRR:41.0,2836.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 2866[2:SpR:2839.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.58/0.75 2875[2:SpR:2841.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 2889[2:SpR:2844.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.58/0.75 2893[2:SpR:2845.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.58/0.75 2894[2:SpR:2845.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 2898[2:Rew:2839.0,2894.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 2899[2:Rew:2866.0,2893.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 2901[2:Rew:2899.0,2875.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 2905[2:Rew:2901.0,2847.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 2907[2:Rew:2905.0,2844.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.58/0.75 2912[2:Rew:2905.0,67.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(multiply(v,sk_c12),sk_c12) -> .
% 0.58/0.75 2919[2:Rew:2905.0,2889.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.58/0.75 2922[2:Rew:2898.0,2907.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 2924[2:Rew:2922.0,2839.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.58/0.75 2926[2:Rew:2922.0,2845.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.58/0.75 2939[2:Rew:63.0,2919.0,2922.0,2919.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 2940[2:Rew:2939.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 2943[2:Rew:2939.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.58/0.75 2944[2:Rew:2940.0,2926.0] || -> equal(sk_c6,sk_c12)**.
% 0.58/0.75 2947[2:Rew:2944.0,2924.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 2985[2:Rew:2940.0,2912.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 3043[2:SpR:2940.0,1263.0] || -> equal(multiply(u,inverse(u)),sk_c12)**.
% 0.58/0.75 3060[2:SpR:2943.0,111.0] || -> equal(multiply(inverse(inverse(u)),sk_c12),u)**.
% 0.58/0.75 3077[2:Rew:2940.0,3060.0] || -> equal(inverse(inverse(u)),u)**.
% 0.58/0.75 3443[2:SpL:2943.0,2985.0] || equal(inverse(sk_c12),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 3451[2:Rew:2943.0,3443.1,3077.0,3443.1,2947.0,3443.0] || equal(sk_c12,u) equal(sk_c12,u) equal(inverse(v),u) equal(multiply(v,u),sk_c12)** equal(u,sk_c12) -> .
% 0.58/0.75 3452[2:Obv:3451.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c12)** equal(v,sk_c12) -> .
% 0.58/0.75 3612[2:SpL:3043.0,3452.1] || equal(inverse(u),inverse(u))* equal(sk_c12,sk_c12) equal(inverse(u),sk_c12) -> .
% 0.58/0.75 3634[2:Obv:3612.1] || equal(inverse(u),sk_c12)** -> .
% 0.58/0.75 3635[2:UnC:3634.0,3077.0] || -> .
% 0.58/0.75 3641[1:Spt:3635.0,65.3,65.4,65.5,65.9,65.10,65.11] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(multiply(u,sk_c12),sk_c10)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.58/0.75 3660[2:Spt:19.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.58/0.75 3661[2:SpR:3660.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.58/0.75 3662[2:SpR:3660.0,1263.0] || -> equal(multiply(sk_c1,multiply(sk_c12,u)),u)**.
% 0.58/0.75 3666[3:Spt:39.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.58/0.75 3667[3:SpR:3666.0,111.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.58/0.75 3672[4:Spt:48.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.58/0.75 3673[4:SpR:3672.0,111.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.58/0.75 3678[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.58/0.75 3679[5:SpR:3678.0,64.0] || -> equal(multiply(sk_c1,multiply(sk_c12,u)),multiply(sk_c11,u))**.
% 0.58/0.75 3680[5:SpR:3678.0,111.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c12)**.
% 0.58/0.75 3685[5:SpL:3678.0,3641.3] || equal(inverse(sk_c1),sk_c10) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(sk_c10,sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3686[5:Rew:3660.0,3680.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.58/0.75 3687[5:Rew:3662.0,3679.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.58/0.75 3689[5:Rew:3687.0,3667.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.58/0.75 3693[5:Rew:3689.0,23.1] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(sk_c10,sk_c11).
% 0.58/0.75 3694[5:Rew:3689.0,25.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(sk_c10,sk_c11).
% 0.58/0.75 3695[5:Rew:3689.0,27.1] || -> equal(multiply(sk_c9,sk_c11),sk_c12)** equal(sk_c10,sk_c11).
% 0.58/0.75 3698[5:Rew:3689.0,24.1] || -> equal(inverse(sk_c5),sk_c11)** equal(sk_c10,sk_c11).
% 0.58/0.75 3699[5:Rew:3689.0,26.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c10,sk_c11).
% 0.58/0.75 3704[5:Rew:3699.1,56.1] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3709[5:Rew:3694.1,55.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3710[5:Rew:3695.1,57.1] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3715[5:Rew:3660.0,3685.0] || equal(sk_c10,sk_c12) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(sk_c10,sk_c11) equal(multiply(u,sk_c11),sk_c10)** equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3717[5:SpR:3686.0,111.0] || -> equal(multiply(inverse(sk_c12),sk_c12),sk_c11)**.
% 0.58/0.75 3722[5:Rew:63.0,3717.0] || -> equal(identity,sk_c11)**.
% 0.58/0.75 3724[5:Rew:3722.0,159.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.58/0.75 3725[5:Rew:3722.0,63.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.58/0.75 3728[5:Rew:3724.0,3715.4] || equal(sk_c10,sk_c12) equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(sk_c10,sk_c11) equal(u,sk_c10) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3729[5:Rew:3724.0,3710.0] || -> equal(sk_c9,sk_c12) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3730[5:Rew:3724.0,3695.0] || -> equal(sk_c9,sk_c12)** equal(sk_c10,sk_c11).
% 0.58/0.75 3732[5:Rew:3724.0,3693.0] || -> equal(sk_c10,sk_c5)** equal(sk_c10,sk_c11).
% 0.58/0.75 3736[5:Rew:3730.0,3699.0] || -> equal(inverse(sk_c6),sk_c12)** equal(sk_c10,sk_c11).
% 0.58/0.75 3738[5:Rew:3730.0,3694.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)** equal(sk_c10,sk_c11).
% 0.58/0.75 3740[5:Rew:3729.0,3704.0] || -> equal(inverse(sk_c6),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3742[5:Rew:3729.0,3709.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12) equal(multiply(sk_c3,sk_c12),sk_c11)**.
% 0.58/0.75 3747[6:Spt:3730.1] || -> equal(sk_c10,sk_c11)**.
% 0.58/0.75 3749[6:Rew:3747.0,3673.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.58/0.75 3753[6:Rew:3747.0,3728.3] || equal(sk_c10,sk_c12) equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(sk_c11,sk_c11) equal(u,sk_c10) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3757[6:Rew:3687.0,3749.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.58/0.75 3759[6:Rew:3757.0,3742.1] || -> equal(multiply(sk_c6,sk_c12),sk_c12)** equal(sk_c11,sk_c12).
% 0.58/0.75 3761[6:Rew:3757.0,3740.1] || -> equal(inverse(sk_c6),sk_c12)** equal(sk_c11,sk_c12).
% 0.58/0.75 3762[6:Rew:3757.0,3729.1] || -> equal(sk_c9,sk_c12)** equal(sk_c11,sk_c12).
% 0.58/0.75 3772[6:Obv:3753.3] || equal(sk_c10,sk_c12) equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(u,sk_c10) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3773[6:Rew:3747.0,3772.3,3747.0,3772.0] || equal(sk_c11,sk_c12) equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(u,sk_c11) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3812[7:Spt:3762.1] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 3814[7:Rew:3812.0,3678.0] || -> equal(multiply(sk_c1,sk_c12),sk_c12)**.
% 0.58/0.75 3819[7:Rew:3812.0,3724.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 3822[7:Rew:3812.0,3773.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(u,sk_c11) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3830[7:Rew:3819.0,3814.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 3831[7:Rew:3830.0,3660.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.58/0.75 3833[7:Rew:3830.0,3812.0] || -> equal(sk_c11,sk_c1)**.
% 0.58/0.75 3839[7:Rew:3830.0,3819.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 3846[7:Obv:3822.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c12) equal(u,sk_c11) equal(multiply(v,sk_c12),sk_c11)** -> .
% 0.58/0.75 3847[7:Rew:3839.0,3846.3,3830.0,3846.3,3833.0,3846.3,3833.0,3846.2,3830.0,3846.1,3833.0,3846.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.58/0.75 3848[7:Con:3847.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.58/0.75 3988[7:SpL:3831.0,3848.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.58/0.75 3990[7:Obv:3988.1] || -> .
% 0.58/0.75 3991[7:Spt:3990.0,3762.1,3812.0] || equal(sk_c11,sk_c12)** -> .
% 0.58/0.75 3992[7:Spt:3990.0,3762.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 3995[7:MRR:3761.1,3991.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.58/0.75 4001[7:MRR:3759.1,3991.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.58/0.75 4036[7:SpR:3995.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c12,u)),u)**.
% 0.58/0.75 4083[7:SpR:4001.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c12,u)),multiply(sk_c12,u))**.
% 0.58/0.75 4090[7:Rew:4036.0,4083.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 4104[7:Rew:4090.0,3661.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 4123[7:Rew:4104.0,3678.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 4124[7:MRR:4123.0,3991.0] || -> .
% 0.58/0.75 4139[6:Spt:4124.0,3730.1,3747.0] || equal(sk_c10,sk_c11)** -> .
% 0.58/0.75 4140[6:Spt:4124.0,3730.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 4141[6:MRR:3732.1,4139.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 4143[6:Rew:4141.0,4139.0] || equal(sk_c5,sk_c11)** -> .
% 0.58/0.75 4146[6:Rew:4141.0,3698.1] || -> equal(inverse(sk_c5),sk_c11)** equal(sk_c5,sk_c11).
% 0.58/0.75 4147[6:MRR:4146.1,4143.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 4150[6:Rew:4141.0,3736.1] || -> equal(inverse(sk_c6),sk_c12)** equal(sk_c5,sk_c11).
% 0.58/0.75 4151[6:MRR:4150.1,4143.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.58/0.75 4158[6:Rew:4141.0,3738.1] || -> equal(multiply(sk_c6,sk_c12),sk_c12)** equal(sk_c5,sk_c11).
% 0.58/0.75 4159[6:MRR:4158.1,4143.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.58/0.75 4202[6:SpR:4151.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c12,u)),u)**.
% 0.58/0.75 4239[6:SpR:4159.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c12,u)),multiply(sk_c12,u))**.
% 0.58/0.75 4246[6:Rew:4202.0,4239.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 4252[6:Rew:4246.0,3661.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 4265[6:Rew:4252.0,3678.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 4270[6:Rew:4265.0,4143.0] || equal(sk_c5,sk_c12)** -> .
% 0.58/0.75 4271[6:Rew:4265.0,4147.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.58/0.75 4274[6:Rew:4265.0,3725.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.58/0.75 4344[6:SpR:3660.0,4274.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.58/0.75 4349[6:SpR:4271.0,4274.0] || -> equal(multiply(sk_c12,sk_c5),sk_c12)**.
% 0.58/0.75 4352[6:Rew:4246.0,4344.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 4360[6:Rew:4352.0,4270.0] || equal(sk_c5,sk_c1)** -> .
% 0.58/0.75 4387[6:Rew:4252.0,4349.0,4352.0,4349.0] || -> equal(sk_c5,sk_c1)**.
% 0.58/0.75 4388[6:MRR:4387.0,4360.0] || -> .
% 0.58/0.75 4415[5:Spt:4388.0,9.1,3678.0] || equal(multiply(sk_c1,sk_c12),sk_c11)** -> .
% 0.58/0.75 4416[5:Spt:4388.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 4418[5:MRR:6.1,4415.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 4420[5:MRR:2.1,4415.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 4423[5:MRR:5.1,4415.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 4425[5:MRR:1.1,4415.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 4452[5:SpR:4418.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.58/0.75 4461[5:SpR:4420.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 4482[5:SpR:4423.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.58/0.75 4489[5:Rew:4452.0,4482.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 4494[5:Rew:4489.0,4461.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 4495[5:Rew:4489.0,3661.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 4499[5:Rew:4494.0,4425.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 4503[5:Rew:4499.0,4415.0] || equal(multiply(sk_c1,sk_c12),sk_c12)** -> .
% 0.58/0.75 4537[5:Rew:4495.0,4503.0] || equal(sk_c12,sk_c12)* -> .
% 0.58/0.75 4538[5:Obv:4537.0] || -> .
% 0.58/0.75 4604[4:Spt:4538.0,48.1,3672.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.58/0.75 4605[4:Spt:4538.0,48.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.58/0.75 4606[4:MRR:46.1,4604.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 4607[4:MRR:44.1,4604.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 4608[4:MRR:42.1,4604.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 4611[4:MRR:47.0,4604.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 4612[4:MRR:45.0,4604.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 4613[4:MRR:43.0,4604.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 4614[4:MRR:41.0,4604.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 4626[4:SpR:4606.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.58/0.75 4631[4:SpR:4607.0,1263.0] || -> equal(multiply(sk_c5,multiply(sk_c11,u)),u)**.
% 0.58/0.75 4635[4:SpR:4608.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 4656[4:SpR:4611.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.58/0.75 4661[4:SpR:4612.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.58/0.75 4662[4:SpR:4612.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 4667[4:Rew:4606.0,4662.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 4668[4:Rew:4626.0,4661.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 4671[4:Rew:4668.0,4635.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 4672[4:Rew:4668.0,3661.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 4678[4:Rew:4671.0,4614.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 4681[4:Rew:4678.0,4611.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.58/0.75 4684[4:Rew:4678.0,4631.0] || -> equal(multiply(sk_c5,multiply(sk_c12,u)),u)**.
% 0.58/0.75 4685[4:Rew:4678.0,4613.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.58/0.75 4690[4:Rew:4678.0,3641.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c12),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.58/0.75 4693[4:Rew:4678.0,4656.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.58/0.75 4697[4:Rew:4667.0,4681.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 4715[4:Rew:63.0,4693.0,4697.0,4693.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 4717[4:Rew:4715.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 4722[4:Rew:4717.0,4685.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 4740[4:Rew:4668.0,4684.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.58/0.75 4770[4:Rew:4717.0,4690.5,4678.0,4690.5,4717.0,4690.4,4678.0,4690.4,4722.0,4690.4,4717.0,4690.3,4722.0,4690.3,4722.0,4690.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.58/0.75 4857[4:SpR:4717.0,4671.0] || -> equal(sk_c4,sk_c12)**.
% 0.58/0.75 4858[4:SpR:4717.0,4672.0] || -> equal(sk_c12,sk_c1)**.
% 0.58/0.75 4859[4:Rew:4857.0,4608.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.58/0.75 4873[4:Rew:4858.0,4717.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.58/0.75 4875[4:Rew:4858.0,4770.1] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.58/0.75 4877[4:Rew:4858.0,4859.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.58/0.75 4895[4:Rew:4858.0,4875.5,4858.0,4875.2] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c1) -> .
% 0.58/0.75 4972[4:SpR:4873.0,4740.0] || -> equal(sk_c5,sk_c1)**.
% 0.58/0.75 4981[4:Rew:4972.0,4895.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c1) -> .
% 0.58/0.75 4990[4:Con:4981.1] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c5) equal(v,sk_c1) -> .
% 0.58/0.75 4991[4:Rew:4972.0,4990.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.58/0.75 4992[4:Con:4991.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.58/0.75 5029[4:SpL:4877.0,4992.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.58/0.75 5031[4:Obv:5029.1] || -> .
% 0.58/0.75 5032[3:Spt:5031.0,39.1,3666.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.58/0.75 5033[3:Spt:5031.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.58/0.75 5035[3:MRR:36.1,5032.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.58/0.75 5036[3:MRR:34.1,5032.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.58/0.75 5037[3:MRR:32.1,5032.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.58/0.75 5039[3:MRR:37.0,5032.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.58/0.75 5040[3:MRR:35.0,5032.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.58/0.75 5041[3:MRR:33.0,5032.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.58/0.75 5042[3:MRR:31.0,5032.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.58/0.75 5059[3:SpR:5035.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.58/0.75 5068[3:SpR:5037.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.58/0.75 5084[3:SpR:5039.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.58/0.75 5089[3:SpR:5040.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.58/0.75 5090[3:SpR:5040.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.58/0.75 5095[3:Rew:5035.0,5090.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.58/0.75 5096[3:Rew:5059.0,5089.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.58/0.75 5101[3:Rew:5096.0,5068.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.58/0.75 5102[3:Rew:5096.0,3661.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.58/0.75 5106[3:Rew:5101.0,5042.0] || -> equal(sk_c11,sk_c12)**.
% 0.58/0.75 5107[3:Rew:5106.0,5036.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.58/0.75 5109[3:Rew:5106.0,5039.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.58/0.75 5110[3:Rew:5106.0,5041.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.58/0.75 5111[3:Rew:5106.0,3641.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c12),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.58/0.75 5117[3:Rew:5106.0,5084.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.58/0.75 5121[3:Rew:5095.0,5109.0] || -> equal(sk_c9,sk_c12)**.
% 0.58/0.75 5139[3:Rew:63.0,5117.0,5121.0,5117.0] || -> equal(identity,sk_c12)**.
% 0.58/0.75 5140[3:Rew:5139.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.58/0.75 5143[3:Rew:5139.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.58/0.75 5146[3:Rew:5140.0,5110.0] || -> equal(sk_c10,sk_c5)**.
% 0.58/0.75 5189[3:Rew:5140.0,5111.5,5106.0,5111.5,5140.0,5111.4,5106.0,5111.4,5146.0,5111.4,5140.0,5111.3,5146.0,5111.3,5146.0,5111.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.58/0.75 5227[3:SpR:3660.0,5143.0] || -> equal(multiply(sk_c12,sk_c1),sk_c12)**.
% 0.59/0.76 5229[3:SpR:5107.0,5143.0] || -> equal(multiply(sk_c12,sk_c5),sk_c12)**.
% 0.59/0.76 5231[3:Rew:5096.0,5227.0] || -> equal(sk_c12,sk_c1)**.
% 0.59/0.76 5232[3:Rew:5231.0,3660.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.59/0.76 5246[3:Rew:5231.0,5189.1] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.59/0.76 5251[3:Rew:5102.0,5229.0,5231.0,5229.0] || -> equal(sk_c5,sk_c1)**.
% 0.59/0.76 5274[3:Rew:5231.0,5246.5,5251.0,5246.4,5251.0,5246.3,5231.0,5246.2,5251.0,5246.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.59/0.76 5275[3:Con:5274.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.59/0.76 5328[3:SpL:5232.0,5275.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.59/0.76 5329[3:Obv:5328.1] || -> .
% 0.59/0.76 5330[2:Spt:5329.0,19.1,3660.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.59/0.76 5331[2:Spt:5329.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.59/0.76 5333[2:MRR:16.1,5330.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.59/0.76 5334[2:MRR:14.1,5330.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.59/0.76 5335[2:MRR:12.1,5330.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.59/0.76 5337[2:MRR:17.0,5330.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.59/0.76 5338[2:MRR:15.0,5330.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.59/0.76 5339[2:MRR:13.0,5330.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.59/0.76 5340[2:MRR:11.0,5330.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.59/0.76 5352[2:SpR:5333.0,1263.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.59/0.76 5361[2:SpR:5335.0,111.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.59/0.76 5377[2:SpR:5337.0,111.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.59/0.76 5382[2:SpR:5338.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.59/0.76 5383[2:SpR:5338.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.59/0.76 5388[2:Rew:5333.0,5383.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.59/0.76 5389[2:Rew:5352.0,5382.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.59/0.76 5391[2:Rew:5389.0,5361.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.59/0.76 5395[2:Rew:5391.0,5340.0] || -> equal(sk_c11,sk_c12)**.
% 0.59/0.76 5396[2:Rew:5395.0,5334.0] || -> equal(inverse(sk_c5),sk_c12)**.
% 0.59/0.76 5397[2:Rew:5395.0,5337.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.59/0.76 5398[2:Rew:5395.0,5339.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.59/0.76 5399[2:Rew:5395.0,3641.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(u,sk_c12),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c12),sk_c11)** -> .
% 0.59/0.76 5405[2:Rew:5395.0,5377.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.59/0.76 5409[2:Rew:5388.0,5397.0] || -> equal(sk_c9,sk_c12)**.
% 0.59/0.76 5411[2:Rew:5409.0,5333.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.59/0.76 5413[2:Rew:5409.0,5338.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.59/0.76 5427[2:Rew:63.0,5405.0,5409.0,5405.0] || -> equal(identity,sk_c12)**.
% 0.59/0.76 5429[2:Rew:5427.0,159.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.59/0.76 5430[2:Rew:5427.0,63.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.59/0.76 5432[2:Rew:5429.0,5413.0] || -> equal(sk_c6,sk_c12)**.
% 0.59/0.76 5434[2:Rew:5429.0,5398.0] || -> equal(sk_c10,sk_c5)**.
% 0.59/0.76 5435[2:Rew:5432.0,5411.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.59/0.76 5476[2:Rew:5429.0,5399.5,5395.0,5399.5,5429.0,5399.4,5395.0,5399.4,5434.0,5399.4,5429.0,5399.3,5434.0,5399.3,5434.0,5399.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.59/0.76 5542[2:SpR:5396.0,5430.0] || -> equal(multiply(sk_c12,sk_c5),sk_c12)**.
% 0.59/0.76 5548[2:Rew:5389.0,5542.0] || -> equal(sk_c5,sk_c12)**.
% 0.59/0.76 5553[2:Rew:5548.0,5476.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(inverse(w),sk_c12)** equal(u,sk_c5) equal(v,sk_c5) equal(w,sk_c12) -> .
% 0.59/0.76 5565[2:Con:5553.1] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(u,sk_c5) equal(v,sk_c12) -> .
% 0.59/0.76 5566[2:Rew:5548.0,5565.2] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) -> .
% 0.59/0.76 5567[2:Con:5566.1] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.59/0.76 5591[2:SpL:5435.0,5567.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.59/0.76 5592[2:Obv:5591.1] || -> .
% 0.59/0.76 % SZS output end Refutation
% 0.59/0.76 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_29 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_48 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_59 prove_this_61 left_identity left_inverse associativity
% 0.59/0.76
%------------------------------------------------------------------------------