TSTP Solution File: GRP228-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP228-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 11:46:25 EDT 2022

% Result   : Unsatisfiable 0.50s 0.68s
% Output   : Refutation 0.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP228-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 21:01:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.50/0.68  
% 0.50/0.68  SPASS V 3.9 
% 0.50/0.68  SPASS beiseite: Proof found.
% 0.50/0.68  % SZS status Theorem
% 0.50/0.68  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.50/0.68  SPASS derived 2790 clauses, backtracked 560 clauses, performed 11 splits and kept 1224 clauses.
% 0.50/0.68  SPASS allocated 65534 KBytes.
% 0.50/0.68  SPASS spent	0:00:00.32 on the problem.
% 0.50/0.68  		0:00:00.04 for the input.
% 0.50/0.68  		0:00:00.00 for the FLOTTER CNF translation.
% 0.50/0.68  		0:00:00.02 for inferences.
% 0.50/0.68  		0:00:00.01 for the backtracking.
% 0.50/0.68  		0:00:00.23 for the reduction.
% 0.50/0.68  
% 0.50/0.68  
% 0.50/0.68  Here is a proof with depth 4, length 487 :
% 0.50/0.68  % SZS output start Refutation
% 0.50/0.68  1[0:Inp] ||  -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.50/0.68  2[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.50/0.68  3[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.68  4[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  5[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.50/0.68  10[0:Inp] ||  -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.50/0.68  11[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.50/0.68  12[0:Inp] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c10).
% 0.50/0.68  13[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c10).
% 0.50/0.68  14[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.50/0.68  15[0:Inp] ||  -> equal(multiply(sk_c8,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c10).
% 0.50/0.68  19[0:Inp] ||  -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  20[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  21[0:Inp] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  22[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  23[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  24[0:Inp] ||  -> equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  25[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  26[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  27[0:Inp] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  28[0:Inp] ||  -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  29[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  30[0:Inp] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  31[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  32[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  37[0:Inp] ||  -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c2),sk_c10).
% 0.50/0.68  38[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.50/0.68  39[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.68  40[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  41[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.50/0.68  46[0:Inp] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** equal(multiply(w,sk_c10),v)* equal(inverse(w),sk_c10) equal(inverse(sk_c10),sk_c9) equal(inverse(x),sk_c10) equal(multiply(x,sk_c9),sk_c10)** equal(multiply(y,z),sk_c10)** equal(inverse(y),z) equal(multiply(z,sk_c9),sk_c10)** equal(inverse(x1),x2) equal(inverse(x2),z)* equal(multiply(x1,z),x2)* -> .
% 0.50/0.68  47[0:Inp] ||  -> equal(multiply(identity,u),u)**.
% 0.50/0.68  48[0:Inp] ||  -> equal(multiply(inverse(u),u),identity)**.
% 0.50/0.68  49[0:Inp] ||  -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.50/0.68  50[0:Con:46.6] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c10)** equal(multiply(y,sk_c10),x1)* equal(multiply(v,sk_c9),sk_c10)** equal(multiply(z,sk_c9),sk_c10)** equal(multiply(sk_c10,x1),sk_c9)** -> .
% 0.50/0.68  51[1:Spt:50.0,50.1,50.2,50.6,50.7,50.9] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)* equal(multiply(x,v),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.50/0.68  52[1:EqR:51.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c10)** equal(multiply(v,sk_c9),sk_c10) -> .
% 0.50/0.68  53[2:Spt:37.1] ||  -> equal(inverse(sk_c2),sk_c10)**.
% 0.50/0.68  55[3:Spt:1.1] ||  -> equal(inverse(sk_c1),sk_c10)**.
% 0.50/0.68  57[4:Spt:28.1] ||  -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  61[5:Spt:19.1] ||  -> equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.50/0.68  64[6:Spt:10.1] ||  -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.50/0.68  66[6:SpL:64.0,51.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.50/0.68  67[6:Rew:55.0,66.1] || equal(inverse(u),sk_c9)** equal(sk_c10,u) equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.50/0.68  68[6:Obv:67.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.50/0.68  72[2:SpR:53.0,48.0] ||  -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.50/0.68  73[3:SpR:55.0,48.0] ||  -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.50/0.68  84[4:SpR:57.0,49.0] ||  -> equal(multiply(sk_c2,multiply(sk_c10,u)),multiply(sk_c3,u))**.
% 0.50/0.68  86[2:SpR:72.0,49.0] ||  -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.50/0.68  87[3:SpR:73.0,49.0] ||  -> equal(multiply(sk_c10,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.50/0.68  89[0:SpR:48.0,49.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.50/0.68  91[2:Rew:47.0,86.0] ||  -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.50/0.68  92[3:Rew:47.0,87.0] ||  -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.50/0.68  93[0:Rew:47.0,89.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.50/0.68  97[4:SpR:57.0,91.0] ||  -> equal(multiply(sk_c10,sk_c3),sk_c10)**.
% 0.50/0.68  99[5:Rew:61.0,97.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.68  102[5:Rew:99.0,55.0] ||  -> equal(inverse(sk_c1),sk_c9)**.
% 0.50/0.68  103[5:Rew:99.0,57.0] ||  -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.50/0.68  104[5:Rew:99.0,61.0] ||  -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.50/0.68  105[6:Rew:99.0,64.0] ||  -> equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.50/0.68  106[5:Rew:99.0,72.0] ||  -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.50/0.68  107[5:Rew:99.0,73.0] ||  -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.50/0.68  116[6:Rew:99.0,68.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.50/0.68  121[5:Rew:99.0,92.0] ||  -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.50/0.68  125[6:Rew:99.0,116.4,99.0,116.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c9,u) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,sk_c9),sk_c9)** -> .
% 0.50/0.68  154[0:SpR:93.0,93.0] ||  -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.50/0.68  156[0:SpR:47.0,93.0] ||  -> equal(multiply(inverse(identity),u),u)**.
% 0.50/0.68  157[0:SpR:48.0,93.0] ||  -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.50/0.68  160[6:SpR:105.0,93.0] ||  -> equal(multiply(inverse(sk_c1),sk_c9),sk_c9)**.
% 0.50/0.68  161[5:SpR:104.0,93.0] ||  -> equal(multiply(inverse(sk_c9),sk_c9),sk_c3)**.
% 0.50/0.68  162[5:SpR:106.0,93.0] ||  -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.50/0.68  163[5:SpR:107.0,93.0] ||  -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.50/0.68  167[6:Rew:102.0,160.0] ||  -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.50/0.68  168[6:Rew:167.0,125.4] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c9,u) equal(multiply(v,sk_c9),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.50/0.68  169[5:Rew:48.0,161.0] ||  -> equal(identity,sk_c3)**.
% 0.50/0.68  170[5:Rew:169.0,47.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.50/0.68  172[5:Rew:169.0,106.0] ||  -> equal(multiply(sk_c9,sk_c2),sk_c3)**.
% 0.50/0.68  182[5:Rew:169.0,162.0] ||  -> equal(multiply(inverse(sk_c9),sk_c3),sk_c2)**.
% 0.50/0.68  183[5:Rew:182.0,163.0,169.0,163.0] ||  -> equal(sk_c2,sk_c1)**.
% 0.50/0.68  185[5:Rew:183.0,103.0] ||  -> equal(multiply(sk_c1,sk_c9),sk_c3)**.
% 0.50/0.68  188[5:Rew:183.0,172.0] ||  -> equal(multiply(sk_c9,sk_c1),sk_c3)**.
% 0.50/0.68  189[5:Rew:183.0,182.0] ||  -> equal(multiply(inverse(sk_c9),sk_c3),sk_c1)**.
% 0.50/0.68  190[6:Rew:105.0,185.0] ||  -> equal(sk_c3,sk_c9)**.
% 0.50/0.68  192[6:Rew:190.0,169.0] ||  -> equal(identity,sk_c9)**.
% 0.50/0.68  193[6:Rew:190.0,170.0] ||  -> equal(multiply(sk_c9,u),u)**.
% 0.50/0.68  195[6:Rew:190.0,188.0] ||  -> equal(multiply(sk_c9,sk_c1),sk_c9)**.
% 0.50/0.68  197[6:Rew:193.0,195.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  200[6:Rew:197.0,102.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.68  206[6:Rew:197.0,192.0] ||  -> equal(identity,sk_c1)**.
% 0.50/0.68  212[6:Rew:206.0,157.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.50/0.68  217[6:Rew:154.0,212.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.68  219[6:Obv:168.4] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c9,u) equal(multiply(v,sk_c9),sk_c9)** -> .
% 0.50/0.68  220[6:Rew:217.0,219.3,197.0,219.3,197.0,219.2,197.0,219.1,197.0,219.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.50/0.68  517[6:SpL:200.0,220.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.50/0.68  520[6:Obv:517.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.68  522[6:SpL:200.0,520.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.50/0.68  525[6:Obv:522.1] ||  -> .
% 0.50/0.68  526[6:Spt:525.0,10.1,64.0] || equal(multiply(sk_c1,sk_c9),sk_c10)** -> .
% 0.50/0.68  527[6:Spt:525.0,10.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  528[6:Rew:99.0,527.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.68  529[6:Rew:104.0,189.0,528.0,189.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  530[6:Rew:529.0,99.0] ||  -> equal(sk_c10,sk_c1)**.
% 0.50/0.68  533[6:Rew:529.0,185.0] ||  -> equal(multiply(sk_c1,sk_c1),sk_c3)**.
% 0.50/0.68  536[6:Rew:533.0,526.0,529.0,526.0,530.0,526.0] || equal(sk_c3,sk_c1)** -> .
% 0.50/0.68  537[6:Rew:529.0,121.0] ||  -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.50/0.68  549[6:Rew:533.0,14.1,529.0,14.1,530.0,14.1] ||  -> equal(inverse(sk_c5),sk_c8)** equal(sk_c3,sk_c1).
% 0.50/0.68  550[6:MRR:549.1,536.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  557[6:Rew:533.0,15.1,529.0,15.1,530.0,15.1,529.0,15.0,530.0,15.0] ||  -> equal(multiply(sk_c8,sk_c1),sk_c1)** equal(sk_c3,sk_c1).
% 0.50/0.68  558[6:MRR:557.1,536.0] ||  -> equal(multiply(sk_c8,sk_c1),sk_c1)**.
% 0.50/0.68  559[6:Rew:533.0,13.1,529.0,13.1,530.0,13.1,530.0,13.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c1)** equal(sk_c3,sk_c1).
% 0.50/0.68  560[6:MRR:559.1,536.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c1)**.
% 0.50/0.68  609[6:SpR:558.0,49.0] ||  -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(sk_c1,u))**.
% 0.50/0.68  613[6:SpR:560.0,93.0] ||  -> equal(multiply(inverse(sk_c5),sk_c1),sk_c8)**.
% 0.50/0.68  615[6:Rew:558.0,613.0,550.0,613.0] ||  -> equal(sk_c8,sk_c1)**.
% 0.50/0.68  626[6:Rew:615.0,609.0] ||  -> equal(multiply(sk_c1,multiply(sk_c1,u)),multiply(sk_c1,u))**.
% 0.50/0.68  632[6:Rew:537.0,626.0] ||  -> equal(multiply(sk_c1,u),u)**.
% 0.50/0.68  633[6:Rew:632.0,533.0] ||  -> equal(sk_c3,sk_c1)**.
% 0.50/0.68  641[6:MRR:633.0,536.0] ||  -> .
% 0.50/0.68  650[5:Spt:641.0,19.1,61.0] || equal(multiply(sk_c10,sk_c3),sk_c9)** -> .
% 0.50/0.68  651[5:Spt:641.0,19.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  652[5:Rew:97.0,650.0] || equal(sk_c10,sk_c9)** -> .
% 0.50/0.68  653[0:Rew:154.0,157.0] ||  -> equal(multiply(u,identity),u)**.
% 0.50/0.68  654[4:Rew:97.0,26.1] ||  -> equal(inverse(sk_c6),sk_c8)** equal(sk_c10,sk_c9).
% 0.50/0.68  655[5:MRR:654.1,652.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.50/0.68  656[4:Rew:97.0,25.1] ||  -> equal(inverse(sk_c7),sk_c6)** equal(sk_c10,sk_c9).
% 0.50/0.68  657[5:MRR:656.1,652.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.50/0.68  658[4:Rew:97.0,23.1] ||  -> equal(inverse(sk_c5),sk_c8)** equal(sk_c10,sk_c9).
% 0.50/0.68  659[5:MRR:658.1,652.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  663[4:Rew:97.0,27.1] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c10,sk_c9).
% 0.50/0.68  664[5:MRR:663.1,652.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.50/0.68  665[4:Rew:97.0,24.1] ||  -> equal(multiply(sk_c8,sk_c9),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  666[5:MRR:665.1,652.0] ||  -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.50/0.68  667[4:Rew:97.0,22.1] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  668[5:MRR:667.1,652.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  677[5:SpR:651.0,93.0] ||  -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.50/0.68  687[5:SpR:659.0,93.0] ||  -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.50/0.68  696[3:SpR:73.0,93.0] ||  -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.50/0.68  698[5:Rew:651.0,696.0] ||  -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.50/0.68  699[5:Rew:653.0,698.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  700[5:Rew:699.0,651.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.50/0.68  701[5:Rew:699.0,652.0] || equal(sk_c10,sk_c1)** -> .
% 0.50/0.68  702[5:Rew:699.0,666.0] ||  -> equal(multiply(sk_c8,sk_c1),sk_c10)**.
% 0.50/0.68  713[5:Rew:699.0,677.0] ||  -> equal(multiply(sk_c1,multiply(sk_c10,u)),u)**.
% 0.50/0.68  724[2:SpR:72.0,93.0] ||  -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.50/0.68  726[5:Rew:700.0,724.0] ||  -> equal(multiply(sk_c1,identity),sk_c2)**.
% 0.50/0.68  727[5:Rew:653.0,726.0] ||  -> equal(sk_c2,sk_c1)**.
% 0.50/0.68  732[5:Rew:727.0,84.0] ||  -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c3,u))**.
% 0.50/0.68  736[5:Rew:713.0,732.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.50/0.68  742[5:SpR:664.0,93.0] ||  -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.50/0.68  744[5:Rew:657.0,742.0] ||  -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.50/0.68  746[5:SpR:668.0,93.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.50/0.68  748[5:Rew:659.0,746.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.50/0.68  749[5:SpR:702.0,49.0] ||  -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(sk_c10,u))**.
% 0.50/0.68  750[5:SpR:702.0,93.0] ||  -> equal(multiply(inverse(sk_c8),sk_c10),sk_c1)**.
% 0.50/0.68  762[5:SpR:744.0,93.0] ||  -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.50/0.68  764[5:Rew:655.0,762.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.50/0.68  769[5:SpR:748.0,93.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.50/0.68  771[5:Rew:48.0,769.0] ||  -> equal(sk_c10,identity)**.
% 0.50/0.68  774[5:Rew:771.0,97.0] ||  -> equal(multiply(identity,sk_c3),identity)**.
% 0.50/0.68  776[5:Rew:771.0,701.0] || equal(identity,sk_c1)** -> .
% 0.50/0.68  777[5:Rew:771.0,700.0] ||  -> equal(inverse(identity),sk_c1)**.
% 0.50/0.68  778[5:Rew:771.0,668.0] ||  -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.50/0.68  786[5:Rew:771.0,749.0] ||  -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.50/0.68  797[5:Rew:771.0,750.0] ||  -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.50/0.68  799[5:Rew:777.0,156.0] ||  -> equal(multiply(sk_c1,u),u)**.
% 0.50/0.68  800[5:Rew:47.0,774.0] ||  -> equal(identity,sk_c3)**.
% 0.50/0.68  803[5:Rew:800.0,653.0] ||  -> equal(multiply(u,sk_c3),u)**.
% 0.50/0.68  807[5:Rew:800.0,776.0] || equal(sk_c3,sk_c1)** -> .
% 0.50/0.68  811[5:Rew:800.0,778.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c3)**.
% 0.50/0.68  818[5:Rew:803.0,797.0,800.0,797.0] ||  -> equal(inverse(sk_c8),sk_c1)**.
% 0.50/0.68  826[5:Rew:799.0,786.0,736.0,786.0,800.0,786.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.50/0.68  828[5:Rew:826.0,764.0] ||  -> equal(sk_c6,sk_c8)**.
% 0.50/0.68  829[5:Rew:826.0,687.0] ||  -> equal(multiply(sk_c5,u),u)**.
% 0.50/0.68  835[5:Rew:828.0,655.0] ||  -> equal(inverse(sk_c8),sk_c8)**.
% 0.50/0.68  840[5:Rew:818.0,835.0] ||  -> equal(sk_c8,sk_c1)**.
% 0.50/0.68  842[5:Rew:840.0,811.0] ||  -> equal(multiply(sk_c5,sk_c1),sk_c3)**.
% 0.50/0.68  852[5:Rew:829.0,842.0] ||  -> equal(sk_c3,sk_c1)**.
% 0.50/0.68  853[5:MRR:852.0,807.0] ||  -> .
% 0.50/0.68  867[4:Spt:853.0,28.1,57.0] || equal(multiply(sk_c2,sk_c10),sk_c3)** -> .
% 0.50/0.68  868[4:Spt:853.0,28.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  869[4:Rew:653.0,696.0,868.0,696.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  870[4:Rew:869.0,868.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.50/0.68  871[4:Rew:653.0,724.0,870.0,724.0] ||  -> equal(sk_c2,sk_c1)**.
% 0.50/0.68  874[4:Rew:871.0,867.0] || equal(multiply(sk_c1,sk_c10),sk_c3)** -> .
% 0.50/0.68  891[4:Rew:871.0,32.1] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c3)**.
% 0.50/0.68  892[4:MRR:891.1,874.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  907[4:Rew:871.0,31.1] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)** equal(multiply(sk_c1,sk_c10),sk_c3).
% 0.50/0.68  908[4:MRR:907.1,874.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  911[4:Rew:869.0,52.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c10)** equal(multiply(v,sk_c1),sk_c10) -> .
% 0.50/0.68  949[4:SpR:908.0,93.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.50/0.68  951[4:Rew:892.0,949.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.50/0.68  964[4:SpR:951.0,93.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.50/0.68  966[4:Rew:48.0,964.0] ||  -> equal(sk_c10,identity)**.
% 0.50/0.68  967[4:Rew:966.0,55.0] ||  -> equal(inverse(sk_c1),identity)**.
% 0.50/0.68  970[4:Rew:966.0,73.0] ||  -> equal(multiply(identity,sk_c1),identity)**.
% 0.50/0.68  979[4:Rew:966.0,911.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),identity)** equal(multiply(v,sk_c1),sk_c10) -> .
% 0.50/0.68  992[4:Rew:47.0,970.0] ||  -> equal(identity,sk_c1)**.
% 0.50/0.68  994[4:Rew:992.0,653.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.68  995[4:Rew:992.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.50/0.68  996[4:Rew:992.0,966.0] ||  -> equal(sk_c10,sk_c1)**.
% 0.50/0.68  997[4:Rew:992.0,967.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.68  1046[4:Rew:994.0,979.4,996.0,979.4,992.0,979.3] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c1)** equal(v,sk_c1) -> .
% 0.50/0.68  1073[4:SpR:995.0,93.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.50/0.68  1077[4:Rew:994.0,1073.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.50/0.68  1093[4:SpR:1077.0,995.0] ||  -> equal(multiply(u,inverse(u)),sk_c1)**.
% 0.50/0.68  1610[4:SpL:995.0,1046.0] || equal(inverse(sk_c1),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.68  1620[4:Rew:995.0,1610.1,1077.0,1610.1,997.0,1610.0] || equal(sk_c1,u) equal(sk_c1,u) equal(inverse(v),u) equal(multiply(v,u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.68  1621[4:Obv:1620.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c1)** equal(v,sk_c1) -> .
% 0.50/0.68  1782[4:SpL:1093.0,1621.1] || equal(inverse(u),inverse(u))* equal(sk_c1,sk_c1) equal(inverse(u),sk_c1) -> .
% 0.50/0.68  1804[4:Obv:1782.1] || equal(inverse(u),sk_c1)** -> .
% 0.50/0.68  1805[4:UnC:1804.0,1077.0] ||  -> .
% 0.50/0.68  1811[3:Spt:1805.0,1.1,55.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.50/0.68  1812[3:Spt:1805.0,1.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  1813[3:Rew:653.0,724.0,1812.0,724.0] ||  -> equal(sk_c2,sk_c9)**.
% 0.50/0.68  1815[3:Rew:1813.0,72.0] ||  -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.50/0.68  1819[3:MRR:5.1,1811.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  1825[3:MRR:4.0,1811.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  1867[3:SpR:1825.0,93.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.50/0.68  1869[3:Rew:1819.0,1867.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.50/0.68  1879[3:SpR:1869.0,93.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.50/0.68  1881[3:Rew:48.0,1879.0] ||  -> equal(sk_c10,identity)**.
% 0.50/0.68  1882[3:Rew:1881.0,1812.0] ||  -> equal(inverse(identity),sk_c9)**.
% 0.50/0.68  1886[3:Rew:1881.0,1815.0] ||  -> equal(multiply(identity,sk_c9),identity)**.
% 0.50/0.68  1895[3:Rew:1881.0,52.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c10)** equal(multiply(v,sk_c9),identity) -> .
% 0.50/0.68  1907[3:Rew:47.0,1886.0] ||  -> equal(identity,sk_c9)**.
% 0.50/0.68  1909[3:Rew:1907.0,653.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.68  1910[3:Rew:1907.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.50/0.68  1911[3:Rew:1907.0,1881.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.68  1912[3:Rew:1907.0,1882.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.68  1960[3:Rew:1909.0,1895.4,1907.0,1895.4,1911.0,1895.3] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c9)** equal(v,sk_c9) -> .
% 0.50/0.68  1988[3:SpR:1910.0,93.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.50/0.68  1992[3:Rew:1909.0,1988.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.50/0.68  2008[3:SpR:1992.0,1910.0] ||  -> equal(multiply(u,inverse(u)),sk_c9)**.
% 0.50/0.68  2525[3:SpL:1910.0,1960.0] || equal(inverse(sk_c9),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c9)** equal(u,sk_c9) -> .
% 0.50/0.68  2535[3:Rew:1910.0,2525.1,1992.0,2525.1,1912.0,2525.0] || equal(sk_c9,u) equal(sk_c9,u) equal(inverse(v),u) equal(multiply(v,u),sk_c9)** equal(u,sk_c9) -> .
% 0.50/0.68  2536[3:Obv:2535.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)** equal(v,sk_c9) -> .
% 0.50/0.68  2697[3:SpL:2008.0,2536.1] || equal(inverse(u),inverse(u))* equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) -> .
% 0.50/0.68  2719[3:Obv:2697.1] || equal(inverse(u),sk_c9)** -> .
% 0.50/0.68  2720[3:UnC:2719.0,1992.0] ||  -> .
% 0.50/0.68  2726[2:Spt:2720.0,37.1,53.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.50/0.68  2727[2:Spt:2720.0,37.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  2730[2:MRR:41.1,2726.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  2731[2:MRR:38.1,2726.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.50/0.68  2735[2:MRR:40.0,2726.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  2736[2:MRR:39.0,2726.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.68  2763[2:SpR:2735.0,93.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.50/0.68  2765[2:Rew:2730.0,2763.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.50/0.68  2767[2:SpR:2736.0,93.0] ||  -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.50/0.68  2769[2:Rew:2731.0,2767.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.50/0.68  2775[2:SpR:2765.0,93.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.50/0.68  2777[2:Rew:48.0,2775.0] ||  -> equal(sk_c10,identity)**.
% 0.50/0.68  2778[2:Rew:2777.0,2727.0] ||  -> equal(inverse(identity),sk_c9)**.
% 0.50/0.68  2787[2:Rew:2777.0,52.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),identity)** equal(multiply(v,sk_c9),sk_c10) -> .
% 0.50/0.68  2796[2:Rew:2777.0,2769.0] ||  -> equal(multiply(identity,identity),sk_c9)**.
% 0.50/0.68  2798[2:Rew:47.0,2796.0] ||  -> equal(identity,sk_c9)**.
% 0.50/0.68  2799[2:Rew:2798.0,653.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.68  2801[2:Rew:2798.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.50/0.68  2802[2:Rew:2798.0,2777.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.68  2803[2:Rew:2798.0,2778.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.68  2845[2:Rew:2799.0,2787.4,2802.0,2787.4,2798.0,2787.3] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c9)** equal(v,sk_c9) -> .
% 0.50/0.68  2879[2:SpR:154.0,2799.0] ||  -> equal(multiply(u,sk_c9),inverse(inverse(u)))**.
% 0.50/0.68  2880[0:SpR:154.0,93.0] ||  -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.50/0.68  2881[2:SpR:154.0,2801.0] ||  -> equal(multiply(u,inverse(u)),sk_c9)**.
% 0.50/0.68  2884[2:Rew:2799.0,2879.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.50/0.68  3218[2:SpL:2801.0,2845.0] || equal(inverse(sk_c9),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c9)** equal(u,sk_c9) -> .
% 0.50/0.68  3227[2:Rew:2801.0,3218.1,2884.0,3218.1,2803.0,3218.0] || equal(sk_c9,u) equal(sk_c9,u) equal(inverse(v),u) equal(multiply(v,u),sk_c9)** equal(u,sk_c9) -> .
% 0.50/0.68  3228[2:Obv:3227.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)** equal(v,sk_c9) -> .
% 0.50/0.68  3535[2:SpL:2881.0,3228.1] || equal(inverse(u),inverse(u))* equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) -> .
% 0.50/0.68  3557[2:Obv:3535.1] || equal(inverse(u),sk_c9)** -> .
% 0.50/0.68  3558[2:UnC:3557.0,2884.0] ||  -> .
% 0.50/0.68  3564[1:Spt:3558.0,50.3,50.4,50.5,50.8,50.10,50.11] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,w),sk_c9)** -> .
% 0.50/0.68  3567[1:EqR:3564.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.68  3569[2:Spt:1.1] ||  -> equal(inverse(sk_c1),sk_c10)**.
% 0.50/0.68  3573[3:Spt:37.1] ||  -> equal(inverse(sk_c2),sk_c10)**.
% 0.50/0.68  3575[3:SpR:3573.0,2880.0] ||  -> equal(multiply(sk_c2,multiply(sk_c10,u)),u)**.
% 0.50/0.68  3577[4:Spt:28.1] ||  -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.50/0.68  3578[4:SpR:3577.0,49.0] ||  -> equal(multiply(sk_c2,multiply(sk_c10,u)),multiply(sk_c3,u))**.
% 0.50/0.68  3579[4:SpR:3577.0,93.0] ||  -> equal(multiply(inverse(sk_c2),sk_c3),sk_c10)**.
% 0.50/0.68  3581[4:SpL:3577.0,3564.3] || equal(inverse(sk_c2),sk_c10) equal(inverse(u),sk_c10) equal(inverse(sk_c10),sk_c9) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.50/0.68  3582[4:Rew:3573.0,3579.0] ||  -> equal(multiply(sk_c10,sk_c3),sk_c10)**.
% 0.50/0.68  3583[4:Rew:3582.0,21.1] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  3584[4:Rew:3582.0,22.1] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  3585[4:Rew:3582.0,24.1] ||  -> equal(multiply(sk_c8,sk_c9),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  3586[4:Rew:3582.0,27.1] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c10,sk_c9).
% 0.50/0.68  3587[4:Rew:3582.0,19.1] ||  -> equal(inverse(sk_c10),sk_c9)** equal(sk_c10,sk_c9).
% 0.50/0.68  3588[4:Rew:3582.0,20.1] ||  -> equal(inverse(sk_c4),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  3589[4:Rew:3582.0,23.1] ||  -> equal(inverse(sk_c5),sk_c8)** equal(sk_c10,sk_c9).
% 0.50/0.68  3590[4:Rew:3582.0,25.1] ||  -> equal(inverse(sk_c7),sk_c6)** equal(sk_c10,sk_c9).
% 0.50/0.68  3591[4:Rew:3582.0,26.1] ||  -> equal(inverse(sk_c6),sk_c8)** equal(sk_c10,sk_c9).
% 0.50/0.68  3592[4:Rew:3587.1,10.1] ||  -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.50/0.68  3593[4:Rew:3588.1,11.1] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.50/0.68  3597[4:Rew:3583.1,12.1] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c9).
% 0.50/0.68  3601[4:Rew:3575.0,3578.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.50/0.68  3602[4:Rew:3573.0,3581.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) equal(inverse(sk_c10),sk_c9) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.50/0.68  3603[4:Obv:3602.0] || equal(inverse(u),sk_c10) equal(inverse(sk_c10),sk_c9) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.50/0.68  3605[4:SpR:3582.0,93.0] ||  -> equal(multiply(inverse(sk_c10),sk_c10),sk_c3)**.
% 0.50/0.68  3607[4:Rew:48.0,3605.0] ||  -> equal(identity,sk_c3)**.
% 0.50/0.68  3609[4:Rew:3607.0,653.0] ||  -> equal(multiply(u,sk_c3),u)**.
% 0.50/0.68  3611[4:Rew:3607.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.50/0.68  3628[4:SpR:3611.0,93.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c3),u)**.
% 0.50/0.68  3629[4:SpR:3611.0,3609.0] ||  -> equal(inverse(sk_c3),sk_c3)**.
% 0.50/0.68  3632[4:SpR:3569.0,3611.0] ||  -> equal(multiply(sk_c10,sk_c1),sk_c3)**.
% 0.50/0.68  3637[4:Rew:3609.0,3628.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.50/0.68  3647[4:SpR:3632.0,93.0] ||  -> equal(multiply(inverse(sk_c10),sk_c3),sk_c1)**.
% 0.50/0.68  3649[4:Rew:3609.0,3647.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.50/0.68  3652[4:Rew:3649.0,3603.1] || equal(inverse(u),sk_c10) equal(sk_c9,sk_c1) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.50/0.68  3653[4:Rew:3649.0,3592.0] ||  -> equal(sk_c9,sk_c1) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.50/0.68  3654[4:Rew:3649.0,3587.0] ||  -> equal(sk_c9,sk_c1) equal(sk_c10,sk_c9)**.
% 0.50/0.68  3658[4:Rew:3654.0,3585.0] ||  -> equal(multiply(sk_c8,sk_c1),sk_c10)** equal(sk_c10,sk_c9).
% 0.50/0.68  3659[4:Rew:3653.0,3597.0] ||  -> equal(multiply(sk_c4,sk_c1),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c9).
% 0.50/0.68  3664[4:SpR:3649.0,3611.0] ||  -> equal(multiply(sk_c1,sk_c10),sk_c3)**.
% 0.50/0.68  3677[5:Spt:3654.1] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.68  3678[5:Rew:3677.0,3569.0] ||  -> equal(inverse(sk_c1),sk_c9)**.
% 0.50/0.68  3679[5:Rew:3677.0,3632.0] ||  -> equal(multiply(sk_c9,sk_c1),sk_c3)**.
% 0.50/0.68  3680[5:Rew:3677.0,3649.0] ||  -> equal(inverse(sk_c9),sk_c1)**.
% 0.50/0.68  3683[5:Rew:3677.0,3593.0] ||  -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.50/0.68  3685[5:Rew:3677.0,3659.0] ||  -> equal(multiply(sk_c4,sk_c1),sk_c9)** equal(multiply(sk_c1,sk_c9),sk_c9).
% 0.50/0.68  3690[5:Rew:3677.0,3652.0] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c1) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.50/0.68  3692[5:Rew:3677.0,3664.0] ||  -> equal(multiply(sk_c1,sk_c9),sk_c3)**.
% 0.50/0.68  3693[5:Rew:3692.0,3653.1] ||  -> equal(sk_c9,sk_c1) equal(sk_c3,sk_c9)**.
% 0.50/0.68  3698[5:Rew:3692.0,3683.1] ||  -> equal(inverse(sk_c4),sk_c9)** equal(sk_c3,sk_c9).
% 0.50/0.68  3700[5:Rew:3692.0,3685.1] ||  -> equal(multiply(sk_c4,sk_c1),sk_c9)** equal(sk_c3,sk_c9).
% 0.50/0.68  3702[5:Rew:3677.0,3690.4,3677.0,3690.3] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c1) equal(sk_c3,v) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(sk_c9,v),sk_c9)** -> .
% 0.50/0.68  3722[6:Spt:3693.1] ||  -> equal(sk_c3,sk_c9)**.
% 0.50/0.68  3724[6:Rew:3722.0,3601.0] ||  -> equal(multiply(sk_c9,u),u)**.
% 0.50/0.68  3725[6:Rew:3722.0,3609.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.68  3727[6:Rew:3722.0,3629.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.68  3732[6:Rew:3722.0,3702.2] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c1) equal(sk_c9,v) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(sk_c9,v),sk_c9)** -> .
% 0.50/0.68  3733[6:Rew:3680.0,3727.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  3735[6:Rew:3733.0,3678.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.68  3744[6:Rew:3733.0,3724.0] ||  -> equal(multiply(sk_c1,u),u)**.
% 0.50/0.68  3745[6:Rew:3733.0,3725.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.68  3750[6:Rew:3744.0,3732.4,3733.0,3732.4,3745.0,3732.3,3733.0,3732.3,3733.0,3732.2,3733.0,3732.1,3733.0,3732.0] || equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(sk_c1,v)* equal(u,sk_c1) equal(v,sk_c1)* -> .
% 0.50/0.68  3751[6:Obv:3750.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) equal(v,sk_c1)* -> .
% 0.50/0.68  3752[6:Con:3751.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.68  3801[6:SpL:3735.0,3752.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.50/0.68  3803[6:Obv:3801.1] ||  -> .
% 0.50/0.68  3804[6:Spt:3803.0,3693.1,3722.0] || equal(sk_c3,sk_c9)** -> .
% 0.50/0.68  3805[6:Spt:3803.0,3693.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  3807[6:Rew:3805.0,3680.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.68  3809[6:Rew:3805.0,3804.0] || equal(sk_c3,sk_c1)** -> .
% 0.50/0.68  3810[6:Rew:3805.0,3679.0] ||  -> equal(multiply(sk_c1,sk_c1),sk_c3)**.
% 0.50/0.68  3818[6:Rew:3805.0,3698.1,3805.0,3698.0] ||  -> equal(inverse(sk_c4),sk_c1)** equal(sk_c3,sk_c1).
% 0.50/0.68  3819[6:MRR:3818.1,3809.0] ||  -> equal(inverse(sk_c4),sk_c1)**.
% 0.50/0.68  3826[6:Rew:3805.0,3700.1,3805.0,3700.0] ||  -> equal(multiply(sk_c4,sk_c1),sk_c1)** equal(sk_c3,sk_c1).
% 0.50/0.68  3827[6:MRR:3826.1,3809.0] ||  -> equal(multiply(sk_c4,sk_c1),sk_c1)**.
% 0.50/0.68  3879[6:SpR:3819.0,3637.0] ||  -> equal(inverse(sk_c1),sk_c4)**.
% 0.50/0.68  3881[6:Rew:3807.0,3879.0] ||  -> equal(sk_c4,sk_c1)**.
% 0.50/0.68  3883[6:Rew:3881.0,3827.0] ||  -> equal(multiply(sk_c1,sk_c1),sk_c1)**.
% 0.50/0.68  3884[6:Rew:3810.0,3883.0] ||  -> equal(sk_c3,sk_c1)**.
% 0.50/0.68  3885[6:MRR:3884.0,3809.0] ||  -> .
% 0.50/0.68  3888[5:Spt:3885.0,3654.1,3677.0] || equal(sk_c10,sk_c9)** -> .
% 0.50/0.68  3889[5:Spt:3885.0,3654.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.68  3890[5:Rew:3889.0,3888.0] || equal(sk_c10,sk_c1)** -> .
% 0.50/0.68  3893[5:Rew:3889.0,3589.1] ||  -> equal(inverse(sk_c5),sk_c8)** equal(sk_c10,sk_c1).
% 0.50/0.68  3894[5:MRR:3893.1,3890.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  3895[5:Rew:3889.0,3590.1] ||  -> equal(inverse(sk_c7),sk_c6)** equal(sk_c10,sk_c1).
% 0.50/0.68  3896[5:MRR:3895.1,3890.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.50/0.68  3897[5:Rew:3889.0,3591.1] ||  -> equal(inverse(sk_c6),sk_c8)** equal(sk_c10,sk_c1).
% 0.50/0.68  3898[5:MRR:3897.1,3890.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.50/0.68  3899[5:Rew:3889.0,3584.1] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)** equal(sk_c10,sk_c1).
% 0.50/0.68  3900[5:MRR:3899.1,3890.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  3901[5:Rew:3889.0,3586.1] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c10,sk_c1).
% 0.50/0.68  3902[5:MRR:3901.1,3890.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.50/0.68  3905[5:Rew:3889.0,3658.1] ||  -> equal(multiply(sk_c8,sk_c1),sk_c10)** equal(sk_c10,sk_c1).
% 0.50/0.68  3906[5:MRR:3905.1,3890.0] ||  -> equal(multiply(sk_c8,sk_c1),sk_c10)**.
% 0.50/0.68  3936[5:SpR:3894.0,2880.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.50/0.68  3937[5:SpR:3894.0,3637.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.50/0.68  3942[5:SpR:3896.0,3637.0] ||  -> equal(inverse(sk_c6),sk_c7)**.
% 0.50/0.68  3944[5:Rew:3898.0,3942.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.50/0.68  3945[5:Rew:3944.0,3896.0] ||  -> equal(inverse(sk_c8),sk_c6)**.
% 0.50/0.68  3946[5:Rew:3944.0,3902.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.50/0.68  3947[5:Rew:3937.0,3945.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.50/0.68  3949[5:Rew:3947.0,3946.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.50/0.68  3954[5:SpR:3900.0,49.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.50/0.68  3958[5:Rew:3936.0,3954.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.50/0.68  3965[5:Rew:3958.0,3632.0] ||  -> equal(sk_c3,sk_c1)**.
% 0.50/0.68  3969[5:Rew:3965.0,3609.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.68  3978[5:Rew:3969.0,3906.0] ||  -> equal(sk_c10,sk_c8)**.
% 0.50/0.68  3979[5:Rew:3978.0,3649.0] ||  -> equal(inverse(sk_c8),sk_c1)**.
% 0.50/0.68  3981[5:Rew:3978.0,3890.0] || equal(sk_c8,sk_c1)** -> .
% 0.50/0.68  3984[5:Rew:3978.0,3958.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.50/0.68  3985[5:Rew:3937.0,3979.0] ||  -> equal(sk_c5,sk_c1)**.
% 0.50/0.68  3991[5:Rew:3985.0,3949.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c1)**.
% 0.50/0.68  3995[5:Rew:3984.0,3991.0] ||  -> equal(sk_c8,sk_c1)**.
% 0.50/0.68  3996[5:MRR:3995.0,3981.0] ||  -> .
% 0.50/0.68  4005[4:Spt:3996.0,28.1,3577.0] || equal(multiply(sk_c2,sk_c10),sk_c3)** -> .
% 0.50/0.68  4006[4:Spt:3996.0,28.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.68  4009[4:MRR:32.1,4005.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.68  4010[4:MRR:29.1,4005.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.50/0.68  4013[4:MRR:31.1,4005.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.68  4014[4:MRR:30.1,4005.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.68  4015[4:Rew:4006.0,3567.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(sk_c9,sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.68  4016[4:Obv:4015.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.69  4022[4:SpR:4006.0,2880.0] ||  -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.50/0.69  4037[4:SpR:4009.0,2880.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.50/0.69  4039[4:SpR:4010.0,93.0] ||  -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.50/0.69  4049[4:SpR:4013.0,49.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.50/0.69  4053[4:Rew:4037.0,4049.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.50/0.69  4054[4:Rew:4053.0,4039.0] ||  -> equal(multiply(sk_c4,u),u)**.
% 0.50/0.69  4055[4:Rew:4053.0,4022.0] ||  -> equal(multiply(sk_c9,u),u)**.
% 0.50/0.69  4058[4:Rew:4053.0,4016.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.50/0.69  4066[4:Rew:4054.0,4014.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.69  4067[4:Rew:4066.0,4006.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.69  4068[4:Rew:4066.0,3569.0] ||  -> equal(inverse(sk_c1),sk_c9)**.
% 0.50/0.69  4104[4:Rew:4066.0,4058.3,4066.0,4058.2,4066.0,4058.1,4066.0,4058.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4105[4:Con:4104.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4155[4:SpR:4054.0,653.0] ||  -> equal(identity,sk_c4)**.
% 0.50/0.69  4159[4:Rew:4155.0,653.0] ||  -> equal(multiply(u,sk_c4),u)**.
% 0.50/0.69  4160[4:Rew:4155.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.50/0.69  4177[4:SpR:4067.0,4160.0] ||  -> equal(multiply(sk_c9,sk_c9),sk_c4)**.
% 0.50/0.69  4178[4:SpR:4068.0,4160.0] ||  -> equal(multiply(sk_c9,sk_c1),sk_c4)**.
% 0.50/0.69  4183[4:Rew:4055.0,4177.0] ||  -> equal(sk_c4,sk_c9)**.
% 0.50/0.69  4188[4:Rew:4183.0,4159.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.69  4190[4:Rew:4055.0,4178.0] ||  -> equal(sk_c4,sk_c1)**.
% 0.50/0.69  4191[4:Rew:4183.0,4190.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.69  4195[4:Rew:4191.0,4067.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.69  4202[4:Rew:4191.0,4105.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4216[4:Rew:4191.0,4188.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.69  4222[4:Rew:4216.0,4202.1,4191.0,4202.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.69  4259[4:SpL:4195.0,4222.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.50/0.69  4260[4:Obv:4259.1] ||  -> .
% 0.50/0.69  4261[3:Spt:4260.0,37.1,3573.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.50/0.69  4262[3:Spt:4260.0,37.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.69  4265[3:MRR:41.1,4261.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.69  4266[3:MRR:38.1,4261.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.50/0.69  4269[3:MRR:40.0,4261.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.69  4270[3:MRR:39.0,4261.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.69  4271[3:Rew:4262.0,3567.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(sk_c9,sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.69  4272[3:Obv:4271.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.69  4278[3:SpR:4262.0,2880.0] ||  -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.50/0.69  4290[3:SpR:4265.0,2880.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.50/0.69  4292[3:SpR:4266.0,93.0] ||  -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.50/0.69  4302[3:SpR:4269.0,49.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.50/0.69  4306[3:Rew:4290.0,4302.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.50/0.69  4307[3:Rew:4306.0,4292.0] ||  -> equal(multiply(sk_c4,u),u)**.
% 0.50/0.69  4308[3:Rew:4306.0,4278.0] ||  -> equal(multiply(sk_c9,u),u)**.
% 0.50/0.69  4311[3:Rew:4306.0,4272.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.50/0.69  4317[3:Rew:4307.0,4270.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.69  4318[3:Rew:4317.0,4262.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.69  4319[3:Rew:4317.0,3569.0] ||  -> equal(inverse(sk_c1),sk_c9)**.
% 0.50/0.69  4353[3:Rew:4317.0,4311.3,4317.0,4311.2,4317.0,4311.1,4317.0,4311.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4354[3:Con:4353.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4399[3:SpR:4307.0,653.0] ||  -> equal(identity,sk_c4)**.
% 0.50/0.69  4402[3:Rew:4399.0,653.0] ||  -> equal(multiply(u,sk_c4),u)**.
% 0.50/0.69  4406[3:Rew:4399.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.50/0.69  4427[3:SpR:4318.0,4406.0] ||  -> equal(multiply(sk_c9,sk_c9),sk_c4)**.
% 0.50/0.69  4428[3:SpR:4319.0,4406.0] ||  -> equal(multiply(sk_c9,sk_c1),sk_c4)**.
% 0.50/0.69  4432[3:Rew:4308.0,4427.0] ||  -> equal(sk_c4,sk_c9)**.
% 0.50/0.69  4437[3:Rew:4432.0,4402.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.69  4439[3:Rew:4308.0,4428.0] ||  -> equal(sk_c4,sk_c1)**.
% 0.50/0.69  4440[3:Rew:4432.0,4439.0] ||  -> equal(sk_c9,sk_c1)**.
% 0.50/0.69  4444[3:Rew:4440.0,4318.0] ||  -> equal(inverse(sk_c1),sk_c1)**.
% 0.50/0.69  4450[3:Rew:4440.0,4354.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4463[3:Rew:4440.0,4437.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.50/0.69  4469[3:Rew:4463.0,4450.1,4440.0,4450.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.50/0.69  4516[3:SpL:4444.0,4469.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.50/0.69  4518[3:Obv:4516.1] ||  -> .
% 0.50/0.69  4519[2:Spt:4518.0,1.1,3569.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.50/0.69  4520[2:Spt:4518.0,1.0] ||  -> equal(inverse(sk_c10),sk_c9)**.
% 0.50/0.69  4523[2:MRR:5.1,4519.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.50/0.69  4524[2:MRR:2.1,4519.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.50/0.69  4527[2:MRR:4.0,4519.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.50/0.69  4528[2:MRR:3.0,4519.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.50/0.69  4529[2:Rew:4520.0,3567.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(sk_c9,sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.69  4530[2:Obv:4529.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.50/0.69  4535[2:SpR:4520.0,93.0] ||  -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.50/0.69  4545[2:SpR:4523.0,2880.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.50/0.69  4547[2:SpR:4524.0,93.0] ||  -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.50/0.69  4557[2:SpR:4527.0,49.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.50/0.69  4561[2:Rew:4545.0,4557.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.50/0.69  4562[2:Rew:4561.0,4547.0] ||  -> equal(multiply(sk_c4,u),u)**.
% 0.50/0.69  4563[2:Rew:4561.0,4535.0] ||  -> equal(multiply(sk_c9,u),u)**.
% 0.50/0.69  4569[2:Rew:4561.0,4530.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.50/0.69  4570[2:Rew:4562.0,4528.0] ||  -> equal(sk_c10,sk_c9)**.
% 0.50/0.69  4571[2:Rew:4570.0,4520.0] ||  -> equal(inverse(sk_c9),sk_c9)**.
% 0.50/0.69  4605[2:Rew:4570.0,4569.3,4570.0,4569.2,4570.0,4569.1,4570.0,4569.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4606[2:Con:4605.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.50/0.69  4646[2:SpR:4562.0,653.0] ||  -> equal(identity,sk_c4)**.
% 0.50/0.69  4650[2:Rew:4646.0,653.0] ||  -> equal(multiply(u,sk_c4),u)**.
% 0.50/0.69  4651[2:Rew:4646.0,48.0] ||  -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.50/0.69  4662[2:SpR:4571.0,4651.0] ||  -> equal(multiply(sk_c9,sk_c9),sk_c4)**.
% 0.50/0.69  4665[2:Rew:4563.0,4662.0] ||  -> equal(sk_c4,sk_c9)**.
% 0.50/0.69  4670[2:Rew:4665.0,4650.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.50/0.69  4678[2:Rew:4670.0,4606.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.50/0.69  4725[2:SpL:4571.0,4678.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.50/0.69  4727[2:Obv:4725.1] ||  -> .
% 0.50/0.69  % SZS output end Refutation
% 0.50/0.69  Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 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_31 prove_this_32 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_46 left_identity left_inverse associativity
% 0.50/0.69  
%------------------------------------------------------------------------------