TSTP Solution File: GRP208-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP208-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:46:20 EDT 2022
% Result : Unsatisfiable 0.43s 0.60s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP208-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 17:28:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.60
% 0.43/0.60 SPASS V 3.9
% 0.43/0.60 SPASS beiseite: Proof found.
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.60 SPASS derived 1954 clauses, backtracked 537 clauses, performed 13 splits and kept 1053 clauses.
% 0.43/0.60 SPASS allocated 64937 KBytes.
% 0.43/0.60 SPASS spent 0:00:00.26 on the problem.
% 0.43/0.60 0:00:00.03 for the input.
% 0.43/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.43/0.60 0:00:00.01 for inferences.
% 0.43/0.60 0:00:00.00 for the backtracking.
% 0.43/0.60 0:00:00.18 for the reduction.
% 0.43/0.60
% 0.43/0.60
% 0.43/0.60 Here is a proof with depth 5, length 416 :
% 0.43/0.60 % SZS output start Refutation
% 0.43/0.60 1[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c12)** equal(multiply(sk_c1,sk_c2),sk_c12).
% 0.43/0.60 2[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c12)**.
% 0.43/0.60 3[0:Inp] || -> equal(multiply(sk_c6,sk_c11),sk_c12)** equal(multiply(sk_c1,sk_c2),sk_c12).
% 0.43/0.60 6[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c11)** equal(multiply(sk_c1,sk_c2),sk_c12).
% 0.43/0.60 7[0:Inp] || -> equal(inverse(sk_c8),sk_c9) equal(multiply(sk_c1,sk_c2),sk_c12)**.
% 0.43/0.60 9[0:Inp] || -> equal(inverse(sk_c10),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c12)**.
% 0.43/0.60 10[0:Inp] || -> equal(multiply(sk_c10,sk_c12),sk_c11)** equal(multiply(sk_c1,sk_c2),sk_c12).
% 0.43/0.60 11[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c1),sk_c2).
% 0.43/0.60 13[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 16[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 17[0:Inp] || -> equal(inverse(sk_c8),sk_c9)** equal(inverse(sk_c1),sk_c2).
% 0.43/0.60 18[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c9,sk_c12),sk_c11)**.
% 0.43/0.60 19[0:Inp] || -> equal(inverse(sk_c10),sk_c11)** equal(inverse(sk_c1),sk_c2).
% 0.43/0.60 20[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 21[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c12)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 22[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 23[0:Inp] || -> equal(multiply(sk_c6,sk_c11),sk_c12)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 24[0:Inp] || -> equal(inverse(sk_c7),sk_c12) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 25[0:Inp] || -> equal(multiply(sk_c7,sk_c11),sk_c12)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 26[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c11)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 27[0:Inp] || -> equal(inverse(sk_c8),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 28[0:Inp] || -> equal(multiply(sk_c9,sk_c12),sk_c11)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 29[0:Inp] || -> equal(inverse(sk_c10),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 30[0:Inp] || -> equal(multiply(sk_c10,sk_c12),sk_c11)** equal(multiply(sk_c2,sk_c11),sk_c12).
% 0.43/0.60 36[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c11) equal(multiply(sk_c12,sk_c4),sk_c11)**.
% 0.43/0.60 37[0:Inp] || -> equal(inverse(sk_c8),sk_c9) equal(multiply(sk_c12,sk_c4),sk_c11)**.
% 0.43/0.60 39[0:Inp] || -> equal(inverse(sk_c10),sk_c11) equal(multiply(sk_c12,sk_c4),sk_c11)**.
% 0.43/0.60 40[0:Inp] || -> equal(multiply(sk_c10,sk_c12),sk_c11) equal(multiply(sk_c12,sk_c4),sk_c11)**.
% 0.43/0.60 46[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c11) equal(multiply(sk_c3,sk_c12),sk_c4)**.
% 0.43/0.60 47[0:Inp] || -> equal(inverse(sk_c8),sk_c9) equal(multiply(sk_c3,sk_c12),sk_c4)**.
% 0.43/0.60 49[0:Inp] || -> equal(inverse(sk_c10),sk_c11) equal(multiply(sk_c3,sk_c12),sk_c4)**.
% 0.43/0.60 50[0:Inp] || -> equal(multiply(sk_c10,sk_c12),sk_c11) equal(multiply(sk_c3,sk_c12),sk_c4)**.
% 0.43/0.60 51[0:Inp] || -> equal(inverse(sk_c3),sk_c12) equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 52[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c3),sk_c12)**.
% 0.43/0.60 53[0:Inp] || -> equal(inverse(sk_c3),sk_c12) equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 56[0:Inp] || -> equal(inverse(sk_c3),sk_c12) equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 57[0:Inp] || -> equal(inverse(sk_c8),sk_c9) equal(inverse(sk_c3),sk_c12)**.
% 0.43/0.60 58[0:Inp] || -> equal(inverse(sk_c3),sk_c12) equal(multiply(sk_c9,sk_c12),sk_c11)**.
% 0.43/0.60 59[0:Inp] || -> equal(inverse(sk_c10),sk_c11) equal(inverse(sk_c3),sk_c12)**.
% 0.43/0.60 60[0:Inp] || -> equal(inverse(sk_c3),sk_c12) equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 61[0:Inp] || equal(multiply(u,v),sk_c12)** equal(inverse(u),v) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,w),sk_c11)** equal(multiply(x,sk_c12),w)* equal(inverse(x),sk_c12) equal(multiply(y,z),sk_c12)** equal(inverse(y),z) equal(multiply(z,sk_c11),sk_c12)** equal(inverse(x1),sk_c12) equal(multiply(x1,sk_c11),sk_c12)** equal(multiply(x2,x3),sk_c11)** equal(inverse(x2),x3) equal(multiply(x3,sk_c12),sk_c11)** equal(inverse(x4),sk_c11) equal(multiply(x4,sk_c12),sk_c11)** -> .
% 0.43/0.60 62[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.43/0.60 63[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.43/0.60 64[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.43/0.60 65[0:Con:61.6] || equal(inverse(u),v) equal(inverse(w),x) equal(inverse(y),sk_c11) equal(inverse(z),sk_c12) equal(inverse(x1),sk_c12) equal(multiply(u,v),sk_c11)**+ equal(multiply(w,x),sk_c12)** equal(multiply(x1,sk_c12),x2)* equal(multiply(y,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(z,sk_c11),sk_c12)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,x2),sk_c11)** -> .
% 0.43/0.60 66[1:Spt:65.1,65.6,65.11] || equal(inverse(u),v) equal(multiply(u,v),sk_c12)**+ equal(multiply(v,sk_c11),sk_c12)** -> .
% 0.43/0.60 69[2:Spt:19.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 79[3:Spt:27.1] || -> equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 85[4:Spt:9.1] || -> equal(multiply(sk_c1,sk_c2),sk_c12)**.
% 0.43/0.60 87[4:SpL:85.0,66.1] || equal(inverse(sk_c1),sk_c2) equal(sk_c12,sk_c12) equal(multiply(sk_c2,sk_c11),sk_c12)** -> .
% 0.43/0.60 88[4:Obv:87.1] || equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c2,sk_c11),sk_c12)** -> .
% 0.43/0.60 89[4:Rew:79.0,88.1,69.0,88.0] || equal(sk_c2,sk_c2) equal(sk_c12,sk_c12)* -> .
% 0.43/0.60 90[4:Obv:89.1] || -> .
% 0.43/0.60 91[4:Spt:90.0,9.1,85.0] || equal(multiply(sk_c1,sk_c2),sk_c12)** -> .
% 0.43/0.60 92[4:Spt:90.0,9.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 95[4:MRR:2.1,91.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 100[4:MRR:3.1,91.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 101[4:MRR:1.1,91.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 124[4:SpL:101.0,66.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c12,sk_c12) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 125[4:Obv:124.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 126[4:Rew:100.0,125.1,95.0,125.0] || equal(sk_c6,sk_c6) equal(sk_c12,sk_c12)* -> .
% 0.43/0.60 127[4:Obv:126.1] || -> .
% 0.43/0.60 128[3:Spt:127.0,27.1,79.0] || equal(multiply(sk_c2,sk_c11),sk_c12)** -> .
% 0.43/0.60 129[3:Spt:127.0,27.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 132[3:MRR:22.1,128.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 137[3:MRR:23.1,128.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 138[3:MRR:21.1,128.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 161[3:SpL:138.0,66.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c12,sk_c12) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 162[3:Obv:161.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 163[3:Rew:137.0,162.1,132.0,162.0] || equal(sk_c6,sk_c6) equal(sk_c12,sk_c12)* -> .
% 0.43/0.60 164[3:Obv:163.1] || -> .
% 0.43/0.60 165[2:Spt:164.0,19.1,69.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.43/0.60 166[2:Spt:164.0,19.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 169[2:MRR:12.1,165.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 174[2:MRR:13.0,165.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 175[2:MRR:11.0,165.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 198[2:SpL:175.0,66.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c12,sk_c12) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 199[2:Obv:198.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c11),sk_c12)** -> .
% 0.43/0.60 200[2:Rew:174.0,199.1,169.0,199.0] || equal(sk_c6,sk_c6) equal(sk_c12,sk_c12)* -> .
% 0.43/0.60 201[2:Obv:200.1] || -> .
% 0.43/0.60 202[1:Spt:201.0,65.0,65.2,65.3,65.4,65.5,65.7,65.8,65.9,65.10,65.12] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)**+ equal(multiply(y,sk_c12),z)* equal(multiply(w,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(x,sk_c11),sk_c12)** equal(multiply(sk_c12,z),sk_c11)** -> .
% 0.43/0.60 203[1:SpL:62.0,202.4] || equal(inverse(identity),u) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(inverse(x),sk_c12) equal(u,sk_c11) equal(multiply(x,sk_c12),y)* equal(multiply(v,sk_c12),sk_c11)** equal(multiply(u,sk_c12),sk_c11)** equal(multiply(w,sk_c11),sk_c12)** equal(multiply(sk_c12,y),sk_c11)** -> .
% 0.43/0.60 204[2:Spt:17.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 206[3:Spt:57.1] || -> equal(inverse(sk_c3),sk_c12)**.
% 0.43/0.60 208[4:Spt:7.1] || -> equal(multiply(sk_c1,sk_c2),sk_c12)**.
% 0.43/0.60 210[4:SpL:208.0,202.4] || equal(inverse(sk_c1),sk_c2) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c12,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c2,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 211[4:Rew:204.0,210.0] || equal(sk_c2,sk_c2) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c12,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c2,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 212[4:Obv:211.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c12,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c2,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 213[5:Spt:29.1] || -> equal(multiply(sk_c2,sk_c11),sk_c12)**.
% 0.43/0.60 216[6:Spt:39.1] || -> equal(multiply(sk_c12,sk_c4),sk_c11)**.
% 0.43/0.60 220[7:Spt:47.1] || -> equal(multiply(sk_c3,sk_c12),sk_c4)**.
% 0.43/0.60 222[7:SpL:220.0,202.4] || equal(inverse(sk_c3),sk_c12) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c4,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c12,sk_c12),sk_c11)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 223[7:Rew:206.0,222.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c4,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c12,sk_c12),sk_c11)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 224[7:Obv:223.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c4,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c12,sk_c12),sk_c11)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 226[2:SpR:204.0,63.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.43/0.60 227[3:SpR:206.0,63.0] || -> equal(multiply(sk_c12,sk_c3),identity)**.
% 0.43/0.60 232[3:SpL:227.0,202.4] || equal(inverse(sk_c12),sk_c3) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(identity,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c3,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 237[0:SpR:63.0,64.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.43/0.60 241[3:SpR:227.0,64.0] || -> equal(multiply(sk_c12,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.43/0.60 243[2:SpR:226.0,64.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.43/0.60 245[3:Rew:62.0,241.0] || -> equal(multiply(sk_c12,multiply(sk_c3,u)),u)**.
% 0.43/0.60 246[2:Rew:62.0,243.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.43/0.60 247[0:Rew:62.0,237.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.43/0.60 251[7:SpR:220.0,245.0] || -> equal(multiply(sk_c12,sk_c4),sk_c12)**.
% 0.43/0.60 253[7:Rew:216.0,251.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 256[7:Rew:253.0,208.0] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.43/0.60 257[7:Rew:253.0,213.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.43/0.60 258[7:Rew:253.0,216.0] || -> equal(multiply(sk_c11,sk_c4),sk_c11)**.
% 0.43/0.60 265[7:Rew:253.0,224.2] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c11) equal(sk_c4,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c12,sk_c12),sk_c11)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 277[7:Rew:253.0,265.8,253.0,265.7,253.0,265.6,253.0,265.5,253.0,265.4,253.0,265.1] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(sk_c4,sk_c11) equal(multiply(w,sk_c11),x)* equal(multiply(u,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,x),sk_c11)** -> .
% 0.43/0.60 278[7:Con:277.1] || equal(inverse(u),sk_c11) equal(sk_c4,sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c11),sk_c11)** -> .
% 0.43/0.60 318[7:SpR:256.0,246.0] || -> equal(multiply(sk_c2,sk_c11),sk_c2)**.
% 0.43/0.60 319[7:Rew:257.0,318.0] || -> equal(sk_c11,sk_c2)**.
% 0.43/0.60 323[7:Rew:319.0,257.0] || -> equal(multiply(sk_c2,sk_c2),sk_c2)**.
% 0.43/0.60 324[7:Rew:319.0,258.0] || -> equal(multiply(sk_c2,sk_c4),sk_c2)**.
% 0.43/0.60 334[7:Rew:319.0,278.0] || equal(inverse(u),sk_c2) equal(sk_c4,sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c11),sk_c11)** -> .
% 0.43/0.60 336[7:Rew:323.0,334.3,319.0,334.3,319.0,334.2,319.0,334.1] || equal(inverse(u),sk_c2) equal(sk_c4,sk_c2) equal(multiply(u,sk_c2),sk_c2)** equal(sk_c2,sk_c2) -> .
% 0.43/0.60 337[7:Obv:336.3] || equal(inverse(u),sk_c2) equal(sk_c4,sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.43/0.60 355[0:SpR:247.0,247.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.43/0.60 358[0:SpR:63.0,247.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.43/0.60 360[2:SpR:246.0,247.0] || -> equal(multiply(inverse(sk_c2),u),multiply(sk_c1,u))**.
% 0.43/0.60 361[7:SpR:323.0,247.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c2)**.
% 0.43/0.60 368[7:Rew:63.0,361.0] || -> equal(identity,sk_c2)**.
% 0.43/0.60 369[7:Rew:368.0,62.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.43/0.60 371[7:Rew:368.0,226.0] || -> equal(multiply(sk_c2,sk_c1),sk_c2)**.
% 0.43/0.60 375[7:Rew:369.0,324.0] || -> equal(sk_c4,sk_c2)**.
% 0.43/0.60 383[7:Rew:375.0,337.1] || equal(inverse(u),sk_c2) equal(sk_c2,sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.43/0.60 384[7:Rew:369.0,371.0] || -> equal(sk_c2,sk_c1)**.
% 0.43/0.60 385[7:Rew:384.0,204.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.43/0.60 391[7:Rew:384.0,368.0] || -> equal(identity,sk_c1)**.
% 0.43/0.60 404[7:Rew:391.0,358.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.43/0.60 410[7:Rew:355.0,404.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.43/0.60 412[7:Obv:383.1] || equal(inverse(u),sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.43/0.60 413[7:Rew:410.0,412.1,384.0,412.1,384.0,412.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.43/0.60 475[7:SpL:385.0,413.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.43/0.60 477[7:Obv:475.1] || -> .
% 0.43/0.60 478[7:Spt:477.0,47.1,220.0] || equal(multiply(sk_c3,sk_c12),sk_c4)** -> .
% 0.43/0.60 479[7:Spt:477.0,47.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 483[7:MRR:49.1,478.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 484[0:Rew:355.0,358.0] || -> equal(multiply(u,identity),u)**.
% 0.43/0.60 485[7:MRR:50.1,478.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 487[7:MRR:46.1,478.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 506[7:SpR:485.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.60 508[7:Rew:483.0,506.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.60 510[3:SpR:227.0,247.0] || -> equal(multiply(inverse(sk_c12),identity),sk_c3)**.
% 0.43/0.60 512[3:Rew:484.0,510.0] || -> equal(inverse(sk_c12),sk_c3)**.
% 0.43/0.60 514[3:Rew:512.0,232.0] || equal(sk_c3,sk_c3) equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(identity,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c3,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 517[3:Obv:514.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(identity,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c3,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 521[6:SpR:216.0,247.0] || -> equal(multiply(inverse(sk_c12),sk_c11),sk_c4)**.
% 0.43/0.60 523[6:Rew:512.0,521.0] || -> equal(multiply(sk_c3,sk_c11),sk_c4)**.
% 0.43/0.60 525[5:SpR:213.0,247.0] || -> equal(multiply(inverse(sk_c2),sk_c12),sk_c11)**.
% 0.43/0.60 527[5:Rew:360.0,525.0] || -> equal(multiply(sk_c1,sk_c12),sk_c11)**.
% 0.43/0.60 534[4:SpR:208.0,247.0] || -> equal(multiply(inverse(sk_c1),sk_c12),sk_c2)**.
% 0.43/0.60 536[4:Rew:204.0,534.0] || -> equal(multiply(sk_c2,sk_c12),sk_c2)**.
% 0.43/0.60 537[4:Rew:536.0,212.6] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c12,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(sk_c11,sk_c2) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 544[7:SpR:487.0,247.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c9)**.
% 0.43/0.60 546[7:Rew:479.0,544.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.43/0.60 577[7:SpR:546.0,247.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.43/0.60 579[7:Rew:63.0,577.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 581[7:Rew:579.0,226.0] || -> equal(multiply(sk_c2,sk_c1),sk_c11)**.
% 0.43/0.60 582[7:Rew:579.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 586[7:Rew:579.0,484.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 590[7:Rew:582.0,508.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 607[7:Rew:590.0,216.0] || -> equal(multiply(sk_c11,sk_c4),sk_c11)**.
% 0.43/0.60 608[7:Rew:590.0,213.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.43/0.60 616[7:Rew:590.0,478.0] || equal(multiply(sk_c3,sk_c11),sk_c4)** -> .
% 0.43/0.60 634[7:Rew:586.0,523.0] || -> equal(sk_c3,sk_c4)**.
% 0.43/0.60 637[7:Rew:582.0,607.0] || -> equal(sk_c4,sk_c11)**.
% 0.43/0.60 638[7:Rew:637.0,634.0] || -> equal(sk_c3,sk_c11)**.
% 0.43/0.60 641[7:Rew:586.0,608.0] || -> equal(sk_c11,sk_c2)**.
% 0.43/0.60 645[7:Rew:641.0,581.0] || -> equal(multiply(sk_c2,sk_c1),sk_c2)**.
% 0.43/0.60 646[7:Rew:641.0,582.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.43/0.60 650[7:Rew:641.0,637.0] || -> equal(sk_c4,sk_c2)**.
% 0.43/0.60 651[7:Rew:641.0,638.0] || -> equal(sk_c3,sk_c2)**.
% 0.43/0.60 668[7:Rew:646.0,645.0] || -> equal(sk_c2,sk_c1)**.
% 0.43/0.60 669[7:Rew:646.0,246.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.43/0.60 671[7:Rew:668.0,641.0] || -> equal(sk_c11,sk_c1)**.
% 0.43/0.60 674[7:Rew:668.0,650.0] || -> equal(sk_c4,sk_c1)**.
% 0.43/0.60 675[7:Rew:668.0,651.0] || -> equal(sk_c3,sk_c1)**.
% 0.43/0.60 699[7:Rew:669.0,616.0,675.0,616.0,671.0,616.0,674.0,616.0] || equal(sk_c1,sk_c1)* -> .
% 0.43/0.60 700[7:Obv:699.0] || -> .
% 0.43/0.60 755[6:Spt:700.0,39.1,216.0] || equal(multiply(sk_c12,sk_c4),sk_c11)** -> .
% 0.43/0.60 756[6:Spt:700.0,39.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 759[6:MRR:37.1,755.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 760[6:MRR:40.1,755.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 762[6:MRR:36.1,755.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 786[6:SpR:760.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.60 788[6:Rew:756.0,786.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.60 814[6:SpR:762.0,247.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c9)**.
% 0.43/0.60 816[6:Rew:759.0,814.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.43/0.60 832[6:SpR:816.0,247.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.43/0.60 834[6:Rew:63.0,832.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 837[6:Rew:834.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 838[6:Rew:834.0,484.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 845[6:Rew:837.0,788.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 861[6:Rew:845.0,527.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.43/0.60 862[6:Rew:845.0,208.0] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.43/0.60 874[6:Rew:845.0,537.1] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c12) equal(sk_c12,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(sk_c11,sk_c2) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 885[6:Rew:838.0,861.0] || -> equal(sk_c11,sk_c1)**.
% 0.43/0.60 890[6:Rew:885.0,837.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.43/0.60 891[6:Rew:885.0,845.0] || -> equal(sk_c12,sk_c1)**.
% 0.43/0.60 895[6:Rew:885.0,838.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.43/0.60 899[6:Rew:885.0,862.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.43/0.60 912[6:Rew:890.0,899.0] || -> equal(sk_c2,sk_c1)**.
% 0.43/0.60 914[6:Rew:912.0,204.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.43/0.60 952[6:Rew:890.0,874.8,891.0,874.8,885.0,874.8,895.0,874.7,885.0,874.7,891.0,874.7,885.0,874.6,912.0,874.6,895.0,874.5,891.0,874.5,885.0,874.5,895.0,874.4,891.0,874.4,891.0,874.3,885.0,874.3,891.0,874.2,885.0,874.1,885.0,874.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(sk_c1,sk_c1) equal(w,x)* equal(u,sk_c1) equal(sk_c1,sk_c1) equal(v,sk_c1) equal(x,sk_c1)* -> .
% 0.43/0.60 953[6:Obv:952.6] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(w,x)* equal(u,sk_c1) equal(v,sk_c1) equal(x,sk_c1)* -> .
% 0.43/0.60 954[6:Con:953.1] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.43/0.60 1256[6:SpL:914.0,954.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.43/0.60 1259[6:Obv:1256.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.43/0.60 1304[6:SpL:914.0,1259.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.43/0.60 1308[6:Obv:1304.1] || equal(u,sk_c1)* -> .
% 0.43/0.60 1309[6:AED:1308.0] || -> .
% 0.43/0.60 1310[5:Spt:1309.0,29.1,213.0] || equal(multiply(sk_c2,sk_c11),sk_c12)** -> .
% 0.43/0.60 1311[5:Spt:1309.0,29.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 1313[5:MRR:24.1,1310.0] || -> equal(inverse(sk_c7),sk_c12)**.
% 0.43/0.60 1314[5:MRR:22.1,1310.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 1315[5:MRR:27.1,1310.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 1316[5:MRR:30.1,1310.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 1317[5:MRR:28.1,1310.0] || -> equal(multiply(sk_c9,sk_c12),sk_c11)**.
% 0.43/0.60 1318[5:MRR:26.1,1310.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 1319[5:MRR:25.1,1310.0] || -> equal(multiply(sk_c7,sk_c11),sk_c12)**.
% 0.43/0.60 1320[5:MRR:23.1,1310.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 1321[5:MRR:21.1,1310.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 1340[5:SpR:1314.0,247.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.43/0.60 1350[5:SpR:1316.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.60 1352[5:Rew:1311.0,1350.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.60 1370[5:SpR:1318.0,247.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c9)**.
% 0.43/0.60 1372[5:Rew:1315.0,1370.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.43/0.60 1391[5:SpR:1372.0,247.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.43/0.60 1393[5:Rew:63.0,1391.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 1396[5:Rew:1393.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 1397[5:Rew:1393.0,484.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1403[5:Rew:1393.0,517.3] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(sk_c11,sk_c11) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c3,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 1404[5:Rew:1396.0,1352.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 1413[5:Rew:1404.0,512.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.43/0.60 1414[5:Rew:1404.0,1313.0] || -> equal(inverse(sk_c7),sk_c11)**.
% 0.43/0.60 1418[5:Rew:1404.0,1317.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.43/0.60 1419[5:Rew:1404.0,1319.0] || -> equal(multiply(sk_c7,sk_c11),sk_c11)**.
% 0.43/0.60 1420[5:Rew:1404.0,1320.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.43/0.60 1421[5:Rew:1404.0,1321.0] || -> equal(multiply(sk_c5,sk_c6),sk_c11)**.
% 0.43/0.60 1439[5:Rew:1397.0,1418.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 1440[5:Rew:1439.0,1315.0] || -> equal(inverse(sk_c8),sk_c11)**.
% 0.43/0.60 1441[5:Rew:1439.0,1318.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 1443[5:Rew:1397.0,1419.0] || -> equal(sk_c7,sk_c11)**.
% 0.43/0.60 1444[5:Rew:1443.0,1414.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1445[5:Rew:1413.0,1444.0] || -> equal(sk_c3,sk_c11)**.
% 0.43/0.60 1448[5:Rew:1397.0,1420.0] || -> equal(sk_c11,sk_c6)**.
% 0.43/0.60 1452[5:Rew:1448.0,1396.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.43/0.60 1453[5:Rew:1448.0,1404.0] || -> equal(sk_c12,sk_c6)**.
% 0.43/0.60 1454[5:Rew:1448.0,1397.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.43/0.60 1457[5:Rew:1448.0,1440.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.43/0.60 1459[5:Rew:1448.0,1445.0] || -> equal(sk_c3,sk_c6)**.
% 0.43/0.60 1461[5:Rew:1448.0,1421.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.43/0.60 1465[5:Rew:1448.0,1441.0] || -> equal(multiply(sk_c8,sk_c6),sk_c6)**.
% 0.43/0.60 1466[5:Rew:1452.0,1340.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.43/0.60 1467[5:Rew:1454.0,1465.0] || -> equal(sk_c8,sk_c6)**.
% 0.43/0.60 1468[5:Rew:1454.0,1461.0] || -> equal(sk_c6,sk_c5)**.
% 0.43/0.60 1469[5:Rew:1467.0,1457.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.43/0.60 1471[5:Rew:1468.0,1448.0] || -> equal(sk_c11,sk_c5)**.
% 0.43/0.60 1473[5:Rew:1468.0,1453.0] || -> equal(sk_c12,sk_c5)**.
% 0.43/0.60 1476[5:Rew:1468.0,1459.0] || -> equal(sk_c3,sk_c5)**.
% 0.43/0.60 1481[5:Rew:1468.0,1454.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.43/0.60 1483[5:Rew:1468.0,1469.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.43/0.60 1508[5:Obv:1403.3] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c12) equal(inverse(w),sk_c12) equal(multiply(w,sk_c12),x)* equal(multiply(u,sk_c12),sk_c11)** equal(multiply(sk_c3,sk_c12),sk_c11) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c12,x),sk_c11)** -> .
% 0.43/0.60 1509[5:Rew:1466.0,1508.7,1473.0,1508.7,1471.0,1508.7,1481.0,1508.6,1471.0,1508.6,1473.0,1508.6,1476.0,1508.5,1481.0,1508.5,1473.0,1508.5,1471.0,1508.5,1481.0,1508.4,1473.0,1508.4,1471.0,1508.4,1481.0,1508.3,1473.0,1508.3,1473.0,1508.2,1473.0,1508.1,1471.0,1508.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(w,x)* equal(u,sk_c5) equal(sk_c5,sk_c5) equal(v,sk_c5) equal(x,sk_c5)* -> .
% 0.43/0.60 1510[5:Obv:1509.5] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(w,x)* equal(u,sk_c5) equal(v,sk_c5) equal(x,sk_c5)* -> .
% 0.43/0.60 1511[5:Con:1510.1] || equal(inverse(u),sk_c5)**+ equal(inverse(v),sk_c5)** equal(v,w)* equal(u,sk_c5) equal(w,sk_c5)* -> .
% 0.43/0.60 1608[0:SpR:355.0,247.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.43/0.60 1792[5:SpL:1483.0,1511.0] || equal(sk_c5,sk_c5) equal(inverse(u),sk_c5)** equal(u,v)* equal(sk_c5,sk_c5) equal(v,sk_c5)* -> .
% 0.43/0.60 1795[5:Obv:1792.3] || equal(inverse(u),sk_c5)**+ equal(u,v)* equal(v,sk_c5)* -> .
% 0.43/0.60 2097[5:SpL:1483.0,1795.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.43/0.60 2102[5:Obv:2097.1] || equal(u,sk_c5)* -> .
% 0.43/0.60 2103[5:AED:2102.0] || -> .
% 0.43/0.60 2104[4:Spt:2103.0,7.1,208.0] || equal(multiply(sk_c1,sk_c2),sk_c12)** -> .
% 0.43/0.60 2105[4:Spt:2103.0,7.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 2111[4:MRR:9.1,2104.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 2113[4:MRR:2.1,2104.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 2115[4:MRR:10.1,2104.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 2117[4:MRR:6.1,2104.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 2119[4:MRR:3.1,2104.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 2120[4:MRR:1.1,2104.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 2130[4:SpR:2105.0,1608.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.43/0.60 2138[4:SpR:2111.0,247.0] || -> equal(multiply(sk_c11,multiply(sk_c10,u)),u)**.
% 0.43/0.60 2144[4:SpR:2113.0,247.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.43/0.60 2158[4:SpR:2115.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.60 2160[4:Rew:2111.0,2158.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.60 2164[4:SpR:2117.0,64.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2168[4:Rew:2130.0,2164.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2169[4:Rew:2168.0,2160.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2170[4:Rew:2168.0,2138.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.43/0.60 2177[4:Rew:2169.0,227.0] || -> equal(multiply(sk_c11,sk_c3),identity)**.
% 0.43/0.60 2180[4:Rew:2169.0,2104.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.43/0.60 2185[4:Rew:2169.0,2119.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.43/0.60 2186[4:Rew:2169.0,2120.0] || -> equal(multiply(sk_c5,sk_c6),sk_c11)**.
% 0.43/0.60 2196[4:Rew:2168.0,2177.0] || -> equal(identity,sk_c3)**.
% 0.43/0.60 2199[4:Rew:2196.0,484.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.43/0.60 2257[4:SpR:2185.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c11,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2260[4:Rew:2168.0,2257.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.43/0.60 2261[4:Rew:2260.0,2144.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.43/0.60 2263[4:Rew:2261.0,2186.0] || -> equal(sk_c11,sk_c6)**.
% 0.43/0.60 2272[4:Rew:2263.0,2180.0] || equal(multiply(sk_c1,sk_c2),sk_c6)** -> .
% 0.43/0.60 2335[4:SpR:2199.0,2170.0] || -> equal(sk_c3,sk_c10)**.
% 0.43/0.60 2341[4:Rew:2335.0,2199.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.43/0.60 2402[4:SpR:2341.0,247.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.43/0.60 2408[4:SpR:2341.0,2260.0] || -> equal(sk_c10,sk_c6)**.
% 0.43/0.60 2411[4:SpR:2341.0,2261.0] || -> equal(sk_c10,sk_c5)**.
% 0.43/0.60 2419[4:Rew:2408.0,2341.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.43/0.60 2429[4:Rew:2408.0,2411.0] || -> equal(sk_c6,sk_c5)**.
% 0.43/0.60 2434[4:Rew:2429.0,2272.0] || equal(multiply(sk_c1,sk_c2),sk_c5)** -> .
% 0.43/0.60 2442[4:Rew:2429.0,2408.0] || -> equal(sk_c10,sk_c5)**.
% 0.43/0.60 2454[4:Rew:2429.0,2419.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.43/0.60 2457[4:Rew:2442.0,2402.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.43/0.60 2508[4:SpR:355.0,2454.0] || -> equal(multiply(u,sk_c5),inverse(inverse(u)))**.
% 0.43/0.60 2514[4:Rew:2454.0,2508.0] || -> equal(inverse(inverse(u)),u)**.
% 0.43/0.60 2525[4:SpR:204.0,2514.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.43/0.60 2540[4:SpR:2525.0,2457.0] || -> equal(multiply(sk_c1,sk_c2),sk_c5)**.
% 0.43/0.60 2541[4:MRR:2540.0,2434.0] || -> .
% 0.43/0.60 2544[3:Spt:2541.0,57.1,206.0] || equal(inverse(sk_c3),sk_c12)** -> .
% 0.43/0.60 2545[3:Spt:2541.0,57.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.60 2547[3:MRR:52.1,2544.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.60 2548[3:MRR:59.1,2544.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 2549[3:MRR:60.0,2544.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.60 2550[3:MRR:58.0,2544.0] || -> equal(multiply(sk_c9,sk_c12),sk_c11)**.
% 0.43/0.60 2551[3:MRR:56.0,2544.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.60 2553[3:MRR:53.0,2544.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.60 2554[3:MRR:51.0,2544.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.60 2559[3:SpR:2545.0,1608.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.43/0.60 2564[3:SpR:2547.0,247.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.43/0.60 2576[3:SpR:2549.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.60 2578[3:Rew:2548.0,2576.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.60 2580[3:SpR:2550.0,247.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c12)**.
% 0.43/0.60 2582[3:SpR:2551.0,64.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2583[3:SpR:2551.0,247.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c9)**.
% 0.43/0.60 2585[3:Rew:2545.0,2583.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.43/0.60 2586[3:Rew:2559.0,2582.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2587[3:Rew:2586.0,2578.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.60 2595[3:Rew:2587.0,2550.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.43/0.60 2597[3:Rew:2587.0,2553.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.43/0.60 2598[3:Rew:2587.0,2554.0] || -> equal(multiply(sk_c5,sk_c6),sk_c11)**.
% 0.43/0.60 2601[3:Rew:2587.0,203.2] || equal(inverse(identity),u) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(u,sk_c11) equal(multiply(x,sk_c12),y)* equal(multiply(v,sk_c12),sk_c11)** equal(multiply(u,sk_c12),sk_c11)** equal(multiply(w,sk_c11),sk_c12)** equal(multiply(sk_c12,y),sk_c11)** -> .
% 0.43/0.60 2606[3:Rew:2587.0,2580.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c11)**.
% 0.43/0.60 2607[3:Rew:2585.0,2595.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 2613[3:Rew:63.0,2606.0,2607.0,2606.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 2615[3:Rew:2613.0,484.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2616[3:Rew:2613.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2620[3:Rew:2615.0,2597.0] || -> equal(sk_c11,sk_c6)**.
% 0.43/0.60 2625[3:Rew:2620.0,2587.0] || -> equal(sk_c12,sk_c6)**.
% 0.43/0.60 2629[3:Rew:2620.0,2598.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.43/0.60 2630[3:Rew:2620.0,2613.0] || -> equal(identity,sk_c6)**.
% 0.43/0.60 2632[3:Rew:2620.0,2615.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.43/0.60 2637[3:Rew:2620.0,2616.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.43/0.60 2638[3:Rew:2637.0,2564.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.43/0.60 2640[3:Rew:2632.0,2629.0] || -> equal(sk_c6,sk_c5)**.
% 0.43/0.60 2641[3:Rew:2640.0,2547.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.43/0.60 2642[3:Rew:2640.0,2620.0] || -> equal(sk_c11,sk_c5)**.
% 0.43/0.60 2644[3:Rew:2640.0,2625.0] || -> equal(sk_c12,sk_c5)**.
% 0.43/0.60 2646[3:Rew:2640.0,2630.0] || -> equal(identity,sk_c5)**.
% 0.43/0.60 2653[3:Rew:2640.0,2632.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.43/0.60 2665[3:Rew:2638.0,2601.9,2644.0,2601.9,2642.0,2601.9,2653.0,2601.8,2642.0,2601.8,2644.0,2601.8,2653.0,2601.7,2644.0,2601.7,2642.0,2601.7,2653.0,2601.6,2644.0,2601.6,2642.0,2601.6,2653.0,2601.5,2644.0,2601.5,2642.0,2601.4,2644.0,2601.3,2642.0,2601.2,2642.0,2601.1,2641.0,2601.0,2646.0,2601.0] || equal(sk_c5,u)* equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(inverse(x),sk_c5)** equal(u,sk_c5)* equal(x,y)* equal(v,sk_c5) equal(u,sk_c5)* equal(w,sk_c5) equal(y,sk_c5)* -> .
% 0.43/0.60 2666[3:Obv:2665.4] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(w,x)* equal(u,sk_c5) equal(y,sk_c5)* equal(v,sk_c5) equal(x,sk_c5)* -> .
% 0.43/0.60 2667[3:Con:2666.1] || equal(inverse(u),sk_c5)**+ equal(inverse(v),sk_c5)** equal(v,w)* equal(u,sk_c5) equal(w,sk_c5)* -> .
% 0.43/0.61 2754[3:SpL:2641.0,2667.0] || equal(sk_c5,sk_c5) equal(inverse(u),sk_c5)** equal(u,v)* equal(sk_c5,sk_c5) equal(v,sk_c5)* -> .
% 0.43/0.61 2755[3:Obv:2754.3] || equal(inverse(u),sk_c5)**+ equal(u,v)* equal(v,sk_c5)* -> .
% 0.43/0.61 2843[3:SpL:2641.0,2755.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.43/0.61 2846[3:Obv:2843.1] || equal(u,sk_c5)* -> .
% 0.43/0.61 2847[3:AED:2846.0] || -> .
% 0.43/0.61 2848[2:Spt:2847.0,17.1,204.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.43/0.61 2849[2:Spt:2847.0,17.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.43/0.61 2851[2:MRR:12.1,2848.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.43/0.61 2852[2:MRR:19.1,2848.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.61 2853[2:MRR:20.0,2848.0] || -> equal(multiply(sk_c10,sk_c12),sk_c11)**.
% 0.43/0.61 2854[2:MRR:18.0,2848.0] || -> equal(multiply(sk_c9,sk_c12),sk_c11)**.
% 0.43/0.61 2855[2:MRR:16.0,2848.0] || -> equal(multiply(sk_c8,sk_c9),sk_c11)**.
% 0.43/0.61 2857[2:MRR:13.0,2848.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.43/0.61 2858[2:MRR:11.0,2848.0] || -> equal(multiply(sk_c5,sk_c6),sk_c12)**.
% 0.43/0.61 2860[2:SpR:2849.0,1608.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.43/0.61 2865[2:SpR:2851.0,247.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.43/0.61 2872[2:SpR:2853.0,247.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c12)**.
% 0.43/0.61 2874[2:Rew:2852.0,2872.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.43/0.61 2876[2:SpR:2854.0,247.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c12)**.
% 0.43/0.61 2878[2:SpR:2855.0,64.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.61 2879[2:SpR:2855.0,247.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c9)**.
% 0.43/0.61 2881[2:Rew:2849.0,2879.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.43/0.61 2882[2:Rew:2860.0,2878.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.61 2883[2:Rew:2882.0,2874.0] || -> equal(sk_c12,sk_c11)**.
% 0.43/0.61 2890[2:Rew:2883.0,2854.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.43/0.61 2892[2:Rew:2883.0,2857.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.43/0.61 2893[2:Rew:2883.0,2858.0] || -> equal(multiply(sk_c5,sk_c6),sk_c11)**.
% 0.43/0.61 2895[2:Rew:2883.0,203.2] || equal(inverse(identity),u) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(u,sk_c11) equal(multiply(x,sk_c12),y)* equal(multiply(v,sk_c12),sk_c11)** equal(multiply(u,sk_c12),sk_c11)** equal(multiply(w,sk_c11),sk_c12)** equal(multiply(sk_c12,y),sk_c11)** -> .
% 0.43/0.61 2900[2:Rew:2883.0,2876.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c11)**.
% 0.43/0.61 2901[2:Rew:2881.0,2890.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.61 2907[2:Rew:63.0,2900.0,2901.0,2900.0] || -> equal(identity,sk_c11)**.
% 0.43/0.61 2909[2:Rew:2907.0,484.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.61 2913[2:Rew:2909.0,2892.0] || -> equal(sk_c11,sk_c6)**.
% 0.43/0.61 2917[2:Rew:2913.0,2882.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.43/0.61 2918[2:Rew:2913.0,2883.0] || -> equal(sk_c12,sk_c6)**.
% 0.43/0.61 2921[2:Rew:2913.0,2893.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.43/0.61 2922[2:Rew:2913.0,2907.0] || -> equal(identity,sk_c6)**.
% 0.43/0.61 2923[2:Rew:2913.0,2909.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.43/0.61 2928[2:Rew:2917.0,2865.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.43/0.61 2930[2:Rew:2923.0,2921.0] || -> equal(sk_c6,sk_c5)**.
% 0.43/0.61 2931[2:Rew:2930.0,2851.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.43/0.61 2932[2:Rew:2930.0,2913.0] || -> equal(sk_c11,sk_c5)**.
% 0.43/0.61 2934[2:Rew:2930.0,2918.0] || -> equal(sk_c12,sk_c5)**.
% 0.43/0.61 2936[2:Rew:2930.0,2922.0] || -> equal(identity,sk_c5)**.
% 0.43/0.61 2941[2:Rew:2930.0,2923.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.43/0.61 2950[2:Rew:2928.0,2895.9,2934.0,2895.9,2932.0,2895.9,2941.0,2895.8,2932.0,2895.8,2934.0,2895.8,2941.0,2895.7,2934.0,2895.7,2932.0,2895.7,2941.0,2895.6,2934.0,2895.6,2932.0,2895.6,2941.0,2895.5,2934.0,2895.5,2932.0,2895.4,2934.0,2895.3,2932.0,2895.2,2932.0,2895.1,2931.0,2895.0,2936.0,2895.0] || equal(sk_c5,u)* equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(inverse(x),sk_c5)** equal(u,sk_c5)* equal(x,y)* equal(v,sk_c5) equal(u,sk_c5)* equal(w,sk_c5) equal(y,sk_c5)* -> .
% 0.43/0.61 2951[2:Obv:2950.4] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c5)** equal(inverse(w),sk_c5)** equal(w,x)* equal(u,sk_c5) equal(y,sk_c5)* equal(v,sk_c5) equal(x,sk_c5)* -> .
% 0.43/0.61 2952[2:Con:2951.1] || equal(inverse(u),sk_c5)**+ equal(inverse(v),sk_c5)** equal(v,w)* equal(u,sk_c5) equal(w,sk_c5)* -> .
% 0.43/0.61 3068[2:SpL:2931.0,2952.0] || equal(sk_c5,sk_c5) equal(inverse(u),sk_c5)** equal(u,v)* equal(sk_c5,sk_c5) equal(v,sk_c5)* -> .
% 0.43/0.61 3070[2:Obv:3068.3] || equal(inverse(u),sk_c5)**+ equal(u,v)* equal(v,sk_c5)* -> .
% 0.43/0.61 3179[2:SpL:2931.0,3070.0] || equal(sk_c5,sk_c5)* equal(sk_c5,u)* equal(u,sk_c5)* -> .
% 0.43/0.61 3182[2:Obv:3179.1] || equal(u,sk_c5)* -> .
% 0.43/0.61 3183[2:AED:3182.0] || -> .
% 0.43/0.61 % SZS output end Refutation
% 0.43/0.61 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_6 prove_this_7 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_36 prove_this_37 prove_this_39 prove_this_40 prove_this_46 prove_this_47 prove_this_49 prove_this_50 prove_this_51 prove_this_52 prove_this_53 prove_this_56 prove_this_57 prove_this_58 prove_this_59 prove_this_60 prove_this_61 left_identity left_inverse associativity
% 0.43/0.61
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