TSTP Solution File: GRP252-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP252-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 11:46:32 EDT 2022

% Result   : Unsatisfiable 0.37s 0.54s
% Output   : Refutation 0.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP252-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 21:48:24 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.37/0.54  
% 0.37/0.54  SPASS V 3.9 
% 0.37/0.54  SPASS beiseite: Proof found.
% 0.37/0.54  % SZS status Theorem
% 0.37/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.37/0.54  SPASS derived 1196 clauses, backtracked 300 clauses, performed 11 splits and kept 657 clauses.
% 0.37/0.54  SPASS allocated 64188 KBytes.
% 0.37/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.37/0.54  		0:00:00.04 for the input.
% 0.37/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.54  		0:00:00.01 for inferences.
% 0.37/0.54  		0:00:00.00 for the backtracking.
% 0.37/0.54  		0:00:00.10 for the reduction.
% 0.37/0.54  
% 0.37/0.54  
% 0.37/0.54  Here is a proof with depth 4, length 302 :
% 0.37/0.54  % SZS output start Refutation
% 0.37/0.54  1[0:Inp] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.37/0.54  2[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.37/0.54  3[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.37/0.54  5[0:Inp] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.37/0.54  8[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.54  9[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.37/0.54  10[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  11[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.37/0.54  12[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  13[0:Inp] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  14[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.37/0.54  16[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  17[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  18[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  19[0:Inp] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  20[0:Inp] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  21[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  22[0:Inp] ||  -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.54  23[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c9)**.
% 0.37/0.54  24[0:Inp] ||  -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  25[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.37/0.54  26[0:Inp] ||  -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  27[0:Inp] ||  -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  28[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.37/0.54  31[0:Inp] ||  -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  32[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c9)**.
% 0.37/0.54  33[0:Inp] ||  -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  34[0:Inp] ||  -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  35[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c3),sk_c9)**.
% 0.37/0.54  37[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  38[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  39[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  40[0:Inp] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  41[0:Inp] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  42[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  43[0:Inp] || equal(multiply(u,sk_c10),sk_c9)** equal(inverse(u),sk_c10) equal(multiply(v,sk_c9),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(w,sk_c8),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(sk_c8,z),sk_c9)** equal(multiply(x1,sk_c8),z)* equal(inverse(x1),sk_c8) -> .
% 0.37/0.54  44[0:Inp] ||  -> equal(multiply(identity,u),u)**.
% 0.37/0.54  45[0:Inp] ||  -> equal(multiply(inverse(u),u),identity)**.
% 0.37/0.54  46[0:Inp] ||  -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.37/0.54  47[0:Con:43.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c8),z)*+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(sk_c8,z),sk_c9)** -> .
% 0.37/0.54  48[1:Spt:47.2,47.7] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.37/0.54  49[2:Spt:35.1] ||  -> equal(inverse(sk_c3),sk_c9)**.
% 0.37/0.54  55[3:Spt:37.1] ||  -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.37/0.54  57[3:SpL:55.0,48.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.37/0.54  58[3:Obv:57.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.37/0.54  59[3:Rew:49.0,58.0] || equal(sk_c9,sk_c9)* -> .
% 0.37/0.54  60[3:Obv:59.0] ||  -> .
% 0.37/0.54  61[3:Spt:60.0,37.1,55.0] || equal(multiply(sk_c3,sk_c8),sk_c9)** -> .
% 0.37/0.54  62[3:Spt:60.0,37.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.54  63[3:MRR:42.1,61.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.54  64[3:MRR:39.1,61.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.54  65[3:MRR:41.1,61.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  66[3:MRR:40.1,61.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  67[3:MRR:38.1,61.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  77[3:SpL:67.0,48.1] || equal(inverse(sk_c5),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.37/0.54  78[3:Obv:77.1] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.37/0.54  79[3:Rew:64.0,78.0] || equal(sk_c9,sk_c8)** -> .
% 0.37/0.54  82[1:SpL:44.0,48.1] || equal(inverse(identity),sk_c9)** equal(sk_c9,sk_c8) -> .
% 0.37/0.54  88[3:SpR:63.0,45.0] ||  -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.37/0.54  89[3:SpR:64.0,45.0] ||  -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.37/0.54  102[0:SpR:45.0,46.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.37/0.54  112[0:Rew:44.0,102.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.37/0.54  127[0:SpR:112.0,112.0] ||  -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.37/0.54  130[3:SpR:67.0,112.0] ||  -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.37/0.54  132[3:SpR:88.0,112.0] ||  -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.37/0.54  133[3:SpR:89.0,112.0] ||  -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.37/0.54  136[0:SpR:45.0,112.0] ||  -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.37/0.54  152[3:Rew:64.0,130.0] ||  -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.37/0.54  153[3:Rew:132.0,133.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.37/0.54  155[3:Rew:153.0,65.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.37/0.54  160[3:Rew:67.0,155.0] ||  -> equal(sk_c9,sk_c7)**.
% 0.37/0.54  164[3:Rew:160.0,66.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.37/0.54  166[3:Rew:160.0,79.0] || equal(sk_c7,sk_c8)** -> .
% 0.37/0.54  178[3:Rew:160.0,152.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  180[3:Rew:164.0,178.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.37/0.54  181[3:MRR:180.0,166.0] ||  -> .
% 0.37/0.54  203[0:Rew:127.0,136.0] ||  -> equal(multiply(u,identity),u)**.
% 0.37/0.54  213[2:Spt:181.0,35.1,49.0] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.37/0.54  214[2:Spt:181.0,35.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.54  215[2:MRR:32.1,213.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.54  217[2:MRR:34.0,213.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  218[2:MRR:33.0,213.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  219[2:MRR:31.0,213.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  221[2:SpR:214.0,45.0] ||  -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.37/0.54  224[2:SpR:215.0,45.0] ||  -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.37/0.54  231[2:SpR:217.0,112.0] ||  -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.37/0.54  233[2:Rew:214.0,231.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  234[2:Rew:218.0,233.0] ||  -> equal(sk_c9,sk_c8)**.
% 0.37/0.54  236[2:Rew:234.0,82.0] || equal(inverse(identity),sk_c8)** equal(sk_c9,sk_c8) -> .
% 0.37/0.54  238[2:Rew:234.0,219.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.37/0.54  243[2:Rew:234.0,236.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.37/0.54  244[2:Obv:243.1] || equal(inverse(identity),sk_c8)** -> .
% 0.37/0.54  250[2:SpR:221.0,112.0] ||  -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.37/0.54  252[2:Rew:203.0,250.0] ||  -> equal(inverse(sk_c8),sk_c6)**.
% 0.37/0.54  257[2:SpR:252.0,45.0] ||  -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.37/0.54  258[2:SpR:252.0,112.0] ||  -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.37/0.54  260[2:Rew:217.0,257.0] ||  -> equal(identity,sk_c7)**.
% 0.37/0.54  265[2:Rew:260.0,244.0] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.37/0.54  266[2:Rew:260.0,203.0] ||  -> equal(multiply(u,sk_c7),u)**.
% 0.37/0.54  267[2:Rew:260.0,224.0] ||  -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.37/0.54  272[2:SpR:238.0,46.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.37/0.54  289[2:SpR:267.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c7),sk_c5)**.
% 0.37/0.54  291[2:Rew:252.0,289.0] ||  -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.37/0.54  292[2:Rew:266.0,291.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.37/0.54  298[2:Rew:292.0,258.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.37/0.54  301[2:Rew:272.0,298.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.54  302[2:Rew:301.0,267.0] ||  -> equal(sk_c7,sk_c5)**.
% 0.37/0.54  308[2:Rew:302.0,265.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.37/0.54  314[2:Rew:215.0,308.0] || equal(sk_c8,sk_c8)* -> .
% 0.37/0.54  315[2:Obv:314.0] ||  -> .
% 0.37/0.54  318[1:Spt:315.0,47.0,47.1,47.3,47.4,47.5,47.6,47.8,47.9,47.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c8),y)*+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,y),sk_c9)** -> .
% 0.37/0.54  319[1:EqR:318.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.37/0.54  321[2:Spt:14.1] ||  -> equal(inverse(sk_c1),sk_c10)**.
% 0.37/0.54  322[2:SpR:321.0,112.0] ||  -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.37/0.54  324[3:Spt:28.1] ||  -> equal(inverse(sk_c2),sk_c9)**.
% 0.37/0.54  330[4:Spt:16.1] ||  -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.37/0.54  332[4:SpR:330.0,112.0] ||  -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.37/0.54  334[4:Rew:324.0,332.0] ||  -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.37/0.54  335[5:Spt:2.1] ||  -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.37/0.54  337[5:SpR:335.0,112.0] ||  -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.37/0.54  339[5:Rew:321.0,337.0] ||  -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.37/0.54  341[4:SpR:334.0,112.0] ||  -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.37/0.54  344[4:Rew:45.0,341.0] ||  -> equal(identity,sk_c8)**.
% 0.37/0.54  345[4:Rew:344.0,44.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.54  346[4:Rew:344.0,203.0] ||  -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.54  347[4:Rew:344.0,45.0] ||  -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.54  352[4:Rew:345.0,319.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.37/0.54  368[4:Con:352.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.37/0.54  369[4:Rew:346.0,368.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.37/0.54  377[5:SpR:339.0,112.0] ||  -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.37/0.54  379[5:Rew:347.0,377.0] ||  -> equal(sk_c9,sk_c8)**.
% 0.37/0.54  380[5:Rew:379.0,324.0] ||  -> equal(inverse(sk_c2),sk_c8)**.
% 0.37/0.54  382[5:Rew:379.0,330.0] ||  -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.37/0.54  383[5:Rew:379.0,335.0] ||  -> equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.54  395[5:Rew:379.0,369.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.37/0.54  396[5:Rew:346.0,382.0] ||  -> equal(sk_c2,sk_c8)**.
% 0.37/0.54  397[5:Rew:396.0,380.0] ||  -> equal(inverse(sk_c8),sk_c8)**.
% 0.37/0.54  407[5:Rew:379.0,395.5,346.0,395.4,379.0,395.4,379.0,395.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c10) equal(u,sk_c8) equal(v,sk_c8) equal(multiply(w,sk_c10),sk_c8)** -> .
% 0.37/0.54  408[5:Con:407.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c10) equal(u,sk_c8) equal(multiply(v,sk_c10),sk_c8)**+ -> .
% 0.37/0.54  438[4:SpR:347.0,112.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.37/0.54  441[4:SpR:321.0,347.0] ||  -> equal(multiply(sk_c10,sk_c1),sk_c8)**.
% 0.37/0.54  443[4:Rew:346.0,438.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.37/0.54  447[4:SpR:441.0,112.0] ||  -> equal(multiply(inverse(sk_c10),sk_c8),sk_c1)**.
% 0.37/0.54  449[4:Rew:346.0,447.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.37/0.54  458[4:SpR:449.0,347.0] ||  -> equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.54  472[2:SpR:322.0,112.0] ||  -> equal(multiply(inverse(sk_c10),u),multiply(sk_c1,u))**.
% 0.37/0.54  657[5:SpL:383.0,408.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.37/0.54  660[5:Obv:657.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c8) -> .
% 0.37/0.54  661[5:Rew:321.0,660.1] || equal(inverse(u),sk_c8)** equal(sk_c10,sk_c10) equal(u,sk_c8) -> .
% 0.37/0.54  662[5:Obv:661.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.37/0.54  737[5:SpL:397.0,662.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.37/0.54  742[5:Obv:737.1] ||  -> .
% 0.37/0.54  743[5:Spt:742.0,2.1,335.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.37/0.54  744[5:Spt:742.0,2.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.54  750[5:Rew:458.0,743.0] || equal(sk_c9,sk_c8)** -> .
% 0.37/0.54  774[4:Rew:345.0,5.0] ||  -> equal(sk_c9,sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.37/0.54  775[4:Rew:458.0,774.1] ||  -> equal(sk_c9,sk_c7)** equal(sk_c9,sk_c8).
% 0.37/0.54  776[5:MRR:775.1,750.0] ||  -> equal(sk_c9,sk_c7)**.
% 0.37/0.54  783[5:Rew:776.0,750.0] || equal(sk_c7,sk_c8)** -> .
% 0.37/0.54  788[4:Rew:346.0,3.0] ||  -> equal(sk_c9,sk_c5) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.37/0.54  789[5:Rew:458.0,788.1,776.0,788.1,776.0,788.0] ||  -> equal(sk_c7,sk_c5) equal(sk_c7,sk_c8)**.
% 0.37/0.54  790[5:MRR:789.1,783.0] ||  -> equal(sk_c7,sk_c5)**.
% 0.37/0.54  793[5:Rew:790.0,776.0] ||  -> equal(sk_c9,sk_c5)**.
% 0.37/0.54  796[5:Rew:790.0,783.0] || equal(sk_c8,sk_c5)** -> .
% 0.37/0.54  802[5:Rew:458.0,1.1,793.0,1.1,793.0,1.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c5)** equal(sk_c8,sk_c5).
% 0.37/0.54  803[5:MRR:802.1,796.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.37/0.54  813[5:SpR:744.0,443.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.37/0.54  818[5:Rew:449.0,813.0] ||  -> equal(sk_c4,sk_c1)**.
% 0.37/0.54  820[5:Rew:818.0,803.0] ||  -> equal(multiply(sk_c1,sk_c10),sk_c5)**.
% 0.37/0.54  823[5:Rew:458.0,820.0] ||  -> equal(sk_c8,sk_c5)**.
% 0.37/0.54  824[5:MRR:823.0,796.0] ||  -> .
% 0.37/0.54  828[4:Spt:824.0,16.1,330.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.37/0.54  829[4:Spt:824.0,16.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.54  830[4:MRR:21.1,828.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.54  831[4:MRR:18.1,828.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.54  833[4:MRR:20.1,828.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  834[4:MRR:19.1,828.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  835[4:MRR:17.1,828.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  849[4:SpR:833.0,112.0] ||  -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.37/0.54  851[4:Rew:830.0,849.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  852[4:Rew:834.0,851.0] ||  -> equal(sk_c9,sk_c8)**.
% 0.37/0.54  853[4:Rew:852.0,324.0] ||  -> equal(inverse(sk_c2),sk_c8)**.
% 0.37/0.54  855[4:Rew:852.0,828.0] || equal(multiply(sk_c2,sk_c8),sk_c8)** -> .
% 0.37/0.54  858[4:Rew:852.0,834.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  859[4:Rew:852.0,835.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.37/0.54  871[4:SpR:858.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.37/0.54  873[4:Rew:45.0,871.0] ||  -> equal(identity,sk_c7)**.
% 0.37/0.54  874[4:Rew:873.0,203.0] ||  -> equal(multiply(u,sk_c7),u)**.
% 0.37/0.54  875[4:Rew:873.0,44.0] ||  -> equal(multiply(sk_c7,u),u)**.
% 0.37/0.54  877[4:Rew:873.0,45.0] ||  -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.37/0.54  887[4:SpR:859.0,112.0] ||  -> equal(multiply(inverse(sk_c5),sk_c8),sk_c8)**.
% 0.37/0.54  889[4:Rew:831.0,887.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.37/0.54  895[4:SpR:889.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.37/0.54  897[4:Rew:877.0,895.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.37/0.54  900[4:Rew:897.0,874.0] ||  -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.54  901[4:Rew:897.0,875.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.54  903[4:Rew:897.0,877.0] ||  -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.54  904[4:Rew:900.0,859.0] ||  -> equal(sk_c8,sk_c5)**.
% 0.37/0.54  909[4:Rew:900.0,855.0] || equal(sk_c2,sk_c8)** -> .
% 0.37/0.54  913[4:Rew:904.0,853.0] ||  -> equal(inverse(sk_c2),sk_c5)**.
% 0.37/0.54  927[4:Rew:904.0,909.0] || equal(sk_c2,sk_c5)** -> .
% 0.37/0.54  929[4:Rew:904.0,901.0] ||  -> equal(multiply(sk_c5,u),u)**.
% 0.37/0.54  931[4:Rew:904.0,903.0] ||  -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.37/0.54  983[4:SpR:913.0,931.0] ||  -> equal(multiply(sk_c5,sk_c2),sk_c5)**.
% 0.37/0.54  985[4:Rew:929.0,983.0] ||  -> equal(sk_c2,sk_c5)**.
% 0.37/0.54  986[4:MRR:985.0,927.0] ||  -> .
% 0.37/0.54  993[3:Spt:986.0,28.1,324.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.37/0.54  994[3:Spt:986.0,28.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.54  995[3:MRR:25.1,993.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.54  996[3:MRR:23.1,993.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.54  997[3:MRR:27.0,993.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  998[3:MRR:26.0,993.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  999[3:MRR:24.0,993.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  1000[3:MRR:22.0,993.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.54  1008[3:SpR:997.0,112.0] ||  -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.37/0.54  1010[3:Rew:994.0,1008.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  1011[3:Rew:998.0,1010.0] ||  -> equal(sk_c9,sk_c8)**.
% 0.37/0.54  1013[3:Rew:1011.0,998.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  1014[3:Rew:1011.0,999.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.37/0.54  1015[3:Rew:1011.0,1000.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c8)**.
% 0.37/0.54  1017[3:Rew:1011.0,319.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.37/0.54  1019[3:Rew:1011.0,1017.7,1011.0,1017.6,1011.0,1017.5,1011.0,1017.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(x,sk_c10),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.37/0.54  1020[3:Con:1019.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c10),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.37/0.54  1027[3:SpR:1013.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.37/0.54  1029[3:Rew:45.0,1027.0] ||  -> equal(identity,sk_c7)**.
% 0.37/0.54  1030[3:Rew:1029.0,44.0] ||  -> equal(multiply(sk_c7,u),u)**.
% 0.37/0.54  1031[3:Rew:1029.0,203.0] ||  -> equal(multiply(u,sk_c7),u)**.
% 0.37/0.54  1032[3:Rew:1029.0,45.0] ||  -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.37/0.54  1038[3:SpR:1014.0,112.0] ||  -> equal(multiply(inverse(sk_c5),sk_c8),sk_c8)**.
% 0.37/0.54  1040[3:Rew:995.0,1038.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.37/0.54  1046[3:SpR:1040.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.37/0.54  1048[3:Rew:1032.0,1046.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.37/0.54  1049[3:Rew:1048.0,997.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.37/0.54  1051[3:Rew:1048.0,1030.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.54  1052[3:Rew:1048.0,1031.0] ||  -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.54  1053[3:Rew:1048.0,1032.0] ||  -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.54  1060[3:Rew:1051.0,1020.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c10),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.37/0.54  1063[3:Rew:1052.0,1014.0] ||  -> equal(sk_c8,sk_c5)**.
% 0.37/0.54  1064[3:Rew:1052.0,1049.0] ||  -> equal(sk_c6,sk_c8)**.
% 0.37/0.54  1065[3:Rew:1063.0,994.0] ||  -> equal(inverse(sk_c6),sk_c5)**.
% 0.37/0.54  1069[3:Rew:1063.0,1015.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.37/0.54  1073[3:Rew:1063.0,1052.0] ||  -> equal(multiply(u,sk_c5),u)**.
% 0.37/0.54  1074[3:Rew:1063.0,1064.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.37/0.54  1075[3:Rew:1074.0,1065.0] ||  -> equal(inverse(sk_c5),sk_c5)**.
% 0.37/0.54  1078[3:Rew:1063.0,1053.0] ||  -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.37/0.54  1081[3:Con:1060.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c10) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c10),sk_c8)** -> .
% 0.37/0.54  1082[3:Rew:1063.0,1081.3,1073.0,1081.2,1063.0,1081.2,1063.0,1081.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c10) equal(u,sk_c5) equal(multiply(v,sk_c10),sk_c5)**+ -> .
% 0.37/0.54  1102[3:SpR:996.0,1078.0] ||  -> equal(multiply(sk_c10,sk_c4),sk_c5)**.
% 0.37/0.54  1114[3:SpR:1102.0,112.0] ||  -> equal(multiply(inverse(sk_c10),sk_c5),sk_c4)**.
% 0.37/0.54  1116[3:Rew:1073.0,1114.0,472.0,1114.0] ||  -> equal(sk_c4,sk_c1)**.
% 0.37/0.54  1118[3:Rew:1116.0,1069.0] ||  -> equal(multiply(sk_c1,sk_c10),sk_c5)**.
% 0.37/0.54  1169[0:SpR:127.0,112.0] ||  -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.37/0.54  1453[3:SpL:1118.0,1082.3] || equal(inverse(u),sk_c5)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c5) equal(sk_c5,sk_c5) -> .
% 0.37/0.54  1456[3:Obv:1453.3] || equal(inverse(u),sk_c5)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c5) -> .
% 0.37/0.54  1457[3:Rew:321.0,1456.1] || equal(inverse(u),sk_c5)** equal(sk_c10,sk_c10) equal(u,sk_c5) -> .
% 0.37/0.54  1458[3:Obv:1457.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.37/0.54  1515[3:SpL:1075.0,1458.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.37/0.54  1520[3:Obv:1515.1] ||  -> .
% 0.37/0.54  1521[2:Spt:1520.0,14.1,321.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.37/0.54  1522[2:Spt:1520.0,14.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.54  1523[2:MRR:11.1,1521.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.54  1524[2:MRR:9.1,1521.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.54  1526[2:MRR:13.0,1521.0] ||  -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.37/0.54  1527[2:MRR:12.0,1521.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.37/0.54  1528[2:MRR:10.0,1521.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.37/0.54  1529[2:MRR:8.0,1521.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.54  1537[2:SpR:1522.0,1169.0] ||  -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.37/0.54  1540[2:SpR:1523.0,1169.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.37/0.54  1546[2:SpR:1526.0,112.0] ||  -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.37/0.54  1548[2:Rew:1522.0,1546.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  1549[2:Rew:1527.0,1548.0] ||  -> equal(sk_c9,sk_c8)**.
% 0.37/0.54  1550[2:Rew:1549.0,1527.0] ||  -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.37/0.54  1551[2:Rew:1549.0,1528.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.37/0.54  1552[2:Rew:1549.0,1529.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c8)**.
% 0.37/0.54  1554[2:Rew:1549.0,319.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.37/0.54  1557[2:Rew:1549.0,1554.7,1549.0,1554.6,1549.0,1554.5,1549.0,1554.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(x,sk_c10),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.37/0.54  1558[2:Con:1557.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c10),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.37/0.54  1565[2:SpR:1550.0,112.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.37/0.54  1567[2:Rew:45.0,1565.0] ||  -> equal(identity,sk_c7)**.
% 0.37/0.54  1568[2:Rew:1567.0,203.0] ||  -> equal(multiply(u,sk_c7),u)**.
% 0.37/0.54  1571[2:Rew:1567.0,45.0] ||  -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.37/0.54  1573[2:SpR:1551.0,46.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.37/0.54  1577[2:Rew:1540.0,1573.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.54  1580[2:Rew:1577.0,1537.0] ||  -> equal(multiply(sk_c6,u),u)**.
% 0.37/0.54  1582[2:Rew:1577.0,1558.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c10),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.37/0.54  1585[2:Rew:1580.0,1526.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.37/0.54  1588[2:Rew:1585.0,1568.0] ||  -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.54  1590[2:Rew:1585.0,1571.0] ||  -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.54  1591[2:Con:1582.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c10) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c10),sk_c8)** -> .
% 0.37/0.54  1592[2:Rew:1588.0,1591.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c10) equal(u,sk_c8) equal(multiply(v,sk_c10),sk_c8)** -> .
% 0.37/0.54  1611[2:SpR:1523.0,1590.0] ||  -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.37/0.54  1617[2:Rew:1577.0,1611.0] ||  -> equal(sk_c8,sk_c5)**.
% 0.37/0.54  1618[2:Rew:1617.0,1523.0] ||  -> equal(inverse(sk_c5),sk_c5)**.
% 0.37/0.54  1622[2:Rew:1617.0,1552.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.37/0.54  1626[2:Rew:1617.0,1592.0] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c10) equal(u,sk_c8) equal(multiply(v,sk_c10),sk_c8)** -> .
% 0.37/0.54  1635[2:Rew:1617.0,1626.3,1617.0,1626.2] || equal(inverse(u),sk_c5)** equal(inverse(v),sk_c10) equal(u,sk_c5) equal(multiply(v,sk_c10),sk_c5)**+ -> .
% 0.37/0.55  1840[2:SpL:1622.0,1635.3] || equal(inverse(u),sk_c5)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c5) equal(sk_c5,sk_c5) -> .
% 0.37/0.55  1842[2:Obv:1840.3] || equal(inverse(u),sk_c5)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c5) -> .
% 0.37/0.55  1843[2:Rew:1524.0,1842.1] || equal(inverse(u),sk_c5)** equal(sk_c10,sk_c10) equal(u,sk_c5) -> .
% 0.37/0.55  1844[2:Obv:1843.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.37/0.55  1929[2:SpL:1618.0,1844.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.37/0.55  1934[2:Obv:1929.1] ||  -> .
% 0.37/0.55  % SZS output end Refutation
% 0.37/0.55  Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_5 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 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_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 left_identity left_inverse associativity
% 0.37/0.55  
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