TSTP Solution File: GRP340-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP340-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 11:46:55 EDT 2022

% Result   : Unsatisfiable 0.44s 0.61s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP340-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.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 : Tue Jun 14 13:34:24 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.44/0.61  
% 0.44/0.61  SPASS V 3.9 
% 0.44/0.61  SPASS beiseite: Proof found.
% 0.44/0.61  % SZS status Theorem
% 0.44/0.61  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.44/0.61  SPASS derived 2118 clauses, backtracked 637 clauses, performed 12 splits and kept 1290 clauses.
% 0.44/0.61  SPASS allocated 64910 KBytes.
% 0.44/0.61  SPASS spent	0:00:00.26 on the problem.
% 0.44/0.61  		0:00:00.04 for the input.
% 0.44/0.61  		0:00:00.00 for the FLOTTER CNF translation.
% 0.44/0.61  		0:00:00.01 for inferences.
% 0.44/0.61  		0:00:00.01 for the backtracking.
% 0.44/0.61  		0:00:00.18 for the reduction.
% 0.44/0.61  
% 0.44/0.61  
% 0.44/0.61  Here is a proof with depth 5, length 535 :
% 0.44/0.61  % SZS output start Refutation
% 0.44/0.61  1[0:Inp] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.44/0.61  2[0:Inp] ||  -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  3[0:Inp] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.44/0.61  4[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  5[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.44/0.61  6[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  8[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  9[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  11[0:Inp] ||  -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  12[0:Inp] ||  -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  14[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  15[0:Inp] ||  -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  16[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  17[0:Inp] ||  -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  18[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  19[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  20[0:Inp] ||  -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  21[0:Inp] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  22[0:Inp] ||  -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  23[0:Inp] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  24[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  25[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  26[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  27[0:Inp] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  28[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  29[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  30[0:Inp] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  31[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  32[0:Inp] ||  -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  33[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61  34[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  35[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  36[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  37[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  38[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  39[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  40[0:Inp] ||  -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  41[0:Inp] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  42[0:Inp] ||  -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  43[0:Inp] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  44[0:Inp] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  45[0:Inp] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  46[0:Inp] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  47[0:Inp] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  48[0:Inp] ||  -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  49[0:Inp] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  50[0:Inp] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  51[0:Inp] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(x1),sk_c10) equal(inverse(x2),sk_c11) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(x1,sk_c9),sk_c10)** equal(multiply(x2,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.44/0.61  52[0:Inp] ||  -> equal(multiply(identity,u),u)**.
% 0.44/0.61  53[0:Inp] ||  -> equal(multiply(inverse(u),u),identity)**.
% 0.44/0.61  54[0:Inp] ||  -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.44/0.61  55[1:Spt:51.0,51.1,51.2,51.7,51.8,51.9] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** -> .
% 0.44/0.61  56[1:EqR:55.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11) -> .
% 0.44/0.61  57[2:Spt:9.1] ||  -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  59[2:SpL:57.0,55.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.61  60[3:Spt:39.1] ||  -> equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  62[4:Spt:19.1] ||  -> equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  64[5:Spt:49.1] ||  -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  69[6:Spt:29.1] ||  -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.44/0.61  71[6:SpL:69.0,55.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.44/0.61  72[6:Rew:62.0,71.1] || equal(inverse(u),sk_c10)** equal(sk_c11,u) equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.44/0.61  73[6:Obv:72.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.44/0.61  77[3:SpR:60.0,53.0] ||  -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.44/0.61  78[4:SpR:62.0,53.0] ||  -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.44/0.61  90[3:SpR:77.0,54.0] ||  -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.44/0.61  91[5:SpR:64.0,54.0] ||  -> equal(multiply(sk_c2,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.44/0.61  93[0:SpR:53.0,54.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.44/0.61  94[4:SpR:78.0,54.0] ||  -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.44/0.61  96[3:Rew:52.0,90.0] ||  -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.44/0.61  97[4:Rew:52.0,94.0] ||  -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.44/0.61  98[0:Rew:52.0,93.0] ||  -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.44/0.61  102[5:SpR:64.0,96.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.44/0.61  104[6:Rew:102.0,73.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c11)** equal(sk_c9,sk_c11) -> .
% 0.44/0.61  113[6:SpR:69.0,97.0] ||  -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.44/0.61  121[0:SpR:98.0,98.0] ||  -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.44/0.61  124[2:SpR:57.0,98.0] ||  -> equal(multiply(inverse(sk_c10),sk_c9),sk_c11)**.
% 0.44/0.61  125[3:SpR:77.0,98.0] ||  -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.44/0.61  127[5:SpR:102.0,98.0] ||  -> equal(multiply(inverse(sk_c10),sk_c9),sk_c10)**.
% 0.44/0.61  129[0:SpR:52.0,98.0] ||  -> equal(multiply(inverse(identity),u),u)**.
% 0.44/0.61  130[0:SpR:53.0,98.0] ||  -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.44/0.61  131[4:SpR:78.0,98.0] ||  -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.44/0.61  132[6:SpR:113.0,98.0] ||  -> equal(multiply(inverse(sk_c11),sk_c10),sk_c11)**.
% 0.44/0.61  139[5:Rew:124.0,127.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  142[5:Rew:139.0,62.0] ||  -> equal(inverse(sk_c1),sk_c10)**.
% 0.44/0.61  144[5:Rew:139.0,78.0] ||  -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.44/0.61  146[6:Rew:139.0,113.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.44/0.61  151[6:Rew:139.0,104.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c10)** equal(sk_c9,sk_c11) -> .
% 0.44/0.61  164[6:Rew:102.0,146.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  171[5:Rew:125.0,131.0,139.0,131.0] ||  -> equal(sk_c2,sk_c1)**.
% 0.44/0.61  177[6:Rew:139.0,132.0] ||  -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.44/0.61  178[6:Rew:53.0,177.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  179[6:Rew:178.0,52.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  181[6:Rew:178.0,144.0] ||  -> equal(multiply(sk_c10,sk_c1),sk_c10)**.
% 0.44/0.61  183[6:Rew:179.0,181.0] ||  -> equal(sk_c1,sk_c10)**.
% 0.44/0.61  184[6:Rew:183.0,142.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  190[6:Rew:178.0,130.0] ||  -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.44/0.61  197[6:Rew:121.0,190.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  202[6:Rew:164.0,151.4,139.0,151.4,197.0,151.3,139.0,151.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.44/0.61  203[6:Obv:202.4] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.44/0.61  509[6:SpL:184.0,203.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.44/0.61  512[6:Obv:509.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  514[6:SpL:184.0,512.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  517[6:Obv:514.1] ||  -> .
% 0.44/0.61  518[6:Spt:517.0,29.1,69.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.44/0.61  519[6:Spt:517.0,29.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  522[6:Rew:139.0,518.0] || equal(multiply(sk_c1,sk_c10),sk_c10)** -> .
% 0.44/0.61  529[5:Rew:139.0,28.1] ||  -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  530[6:MRR:529.1,522.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61  531[5:Rew:139.0,26.1] ||  -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  532[6:MRR:531.1,522.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  537[5:Rew:171.0,91.0] ||  -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.44/0.61  538[0:Rew:121.0,130.0] ||  -> equal(multiply(u,identity),u)**.
% 0.44/0.61  540[5:Rew:139.0,30.1] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  541[6:MRR:540.1,522.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  542[5:Rew:139.0,27.1,139.0,27.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  543[6:MRR:542.1,522.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.44/0.61  544[5:Rew:139.0,25.1,139.0,25.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  545[6:MRR:544.1,522.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.44/0.61  575[6:SpR:519.0,98.0] ||  -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.44/0.61  597[6:SpR:541.0,98.0] ||  -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.44/0.61  599[6:Rew:530.0,597.0] ||  -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.44/0.61  601[5:SpR:144.0,98.0] ||  -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.44/0.61  603[5:Rew:538.0,601.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.44/0.61  608[5:SpR:603.0,98.0] ||  -> equal(multiply(sk_c1,multiply(sk_c10,u)),u)**.
% 0.44/0.61  614[6:SpR:545.0,98.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.44/0.61  616[6:Rew:543.0,614.0,532.0,614.0] ||  -> equal(sk_c8,sk_c10)**.
% 0.44/0.61  617[6:Rew:616.0,519.0] ||  -> equal(inverse(sk_c6),sk_c10)**.
% 0.44/0.61  620[6:Rew:616.0,543.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.44/0.61  622[6:Rew:616.0,575.0] ||  -> equal(multiply(sk_c10,multiply(sk_c6,u)),u)**.
% 0.44/0.61  624[6:Rew:616.0,599.0] ||  -> equal(multiply(sk_c6,sk_c6),sk_c10)**.
% 0.44/0.61  628[6:Rew:102.0,620.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  632[6:Rew:628.0,537.0] ||  -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.44/0.61  640[6:Rew:608.0,632.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  641[6:Rew:640.0,144.0] ||  -> equal(identity,sk_c1)**.
% 0.44/0.61  643[6:Rew:640.0,622.0] ||  -> equal(multiply(sk_c6,u),u)**.
% 0.44/0.61  654[6:Rew:641.0,538.0] ||  -> equal(multiply(u,sk_c1),u)**.
% 0.44/0.61  656[6:Rew:643.0,624.0] ||  -> equal(sk_c6,sk_c10)**.
% 0.44/0.61  659[6:Rew:656.0,617.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  662[6:Rew:603.0,659.0] ||  -> equal(sk_c1,sk_c10)**.
% 0.44/0.61  666[6:Rew:662.0,522.0] || equal(multiply(sk_c10,sk_c10),sk_c10)** -> .
% 0.44/0.61  672[6:Rew:662.0,654.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  679[6:Rew:672.0,666.0] || equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  680[6:Obv:679.0] ||  -> .
% 0.44/0.61  689[5:Spt:680.0,49.1,64.0] || equal(multiply(sk_c2,sk_c9),sk_c10)** -> .
% 0.44/0.61  690[5:Spt:680.0,49.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  691[4:Rew:538.0,131.0] ||  -> equal(inverse(sk_c11),sk_c1)**.
% 0.44/0.61  692[3:Rew:538.0,125.0] ||  -> equal(inverse(sk_c10),sk_c2)**.
% 0.44/0.61  693[3:Rew:692.0,124.0] ||  -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.44/0.61  694[5:Rew:693.0,689.0] || equal(sk_c11,sk_c10)** -> .
% 0.44/0.61  697[3:Rew:693.0,48.1] ||  -> equal(inverse(sk_c7),sk_c6)** equal(sk_c11,sk_c10).
% 0.44/0.61  698[5:MRR:697.1,694.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61  699[3:Rew:693.0,46.1] ||  -> equal(inverse(sk_c5),sk_c8)** equal(sk_c11,sk_c10).
% 0.44/0.61  700[5:MRR:699.1,694.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  703[3:Rew:693.0,42.1] ||  -> equal(inverse(sk_c3),sk_c11)** equal(sk_c11,sk_c10).
% 0.44/0.61  704[5:MRR:703.1,694.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  705[3:Rew:693.0,50.1] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c11,sk_c10).
% 0.44/0.61  706[5:MRR:705.1,694.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  707[3:Rew:693.0,47.1] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(sk_c11,sk_c10).
% 0.44/0.61  708[5:MRR:707.1,694.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  709[3:Rew:693.0,45.1] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c11,sk_c10).
% 0.44/0.61  710[5:MRR:709.1,694.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  713[3:Rew:693.0,41.1] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(sk_c11,sk_c10).
% 0.44/0.61  714[5:MRR:713.1,694.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  733[5:SpR:700.0,98.0] ||  -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.44/0.61  745[5:SpR:706.0,98.0] ||  -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.44/0.61  747[5:Rew:698.0,745.0] ||  -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.44/0.61  761[5:SpR:708.0,54.0] ||  -> equal(multiply(sk_c8,multiply(sk_c10,u)),multiply(sk_c11,u))**.
% 0.44/0.61  762[5:SpR:708.0,98.0] ||  -> equal(multiply(inverse(sk_c8),sk_c11),sk_c10)**.
% 0.44/0.61  765[5:SpR:710.0,98.0] ||  -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.61  767[5:Rew:700.0,765.0] ||  -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.61  779[5:SpR:747.0,98.0] ||  -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.44/0.61  781[5:Rew:690.0,779.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.44/0.61  783[5:SpR:767.0,98.0] ||  -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.44/0.61  785[5:Rew:53.0,783.0] ||  -> equal(identity,sk_c11)**.
% 0.44/0.61  788[5:Rew:785.0,538.0] ||  -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.61  789[5:Rew:785.0,52.0] ||  -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.61  790[5:Rew:785.0,129.0] ||  -> equal(multiply(inverse(sk_c11),u),u)**.
% 0.44/0.61  796[5:Rew:788.0,714.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.61  799[5:Rew:788.0,762.0] ||  -> equal(inverse(sk_c8),sk_c10)**.
% 0.44/0.61  800[5:Rew:796.0,704.0] ||  -> equal(inverse(sk_c10),sk_c11)**.
% 0.44/0.61  809[5:Rew:692.0,800.0] ||  -> equal(sk_c2,sk_c11)**.
% 0.44/0.61  810[5:Rew:809.0,60.0] ||  -> equal(inverse(sk_c11),sk_c10)**.
% 0.44/0.61  816[5:Rew:691.0,810.0] ||  -> equal(sk_c1,sk_c10)**.
% 0.44/0.61  818[5:Rew:816.0,691.0] ||  -> equal(inverse(sk_c11),sk_c10)**.
% 0.44/0.61  824[5:Rew:789.0,761.0] ||  -> equal(multiply(sk_c8,multiply(sk_c10,u)),u)**.
% 0.44/0.61  833[5:Rew:818.0,790.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  840[5:Rew:833.0,824.0] ||  -> equal(multiply(sk_c8,u),u)**.
% 0.44/0.61  842[5:Rew:840.0,781.0] ||  -> equal(sk_c6,sk_c8)**.
% 0.44/0.61  843[5:Rew:840.0,733.0] ||  -> equal(multiply(sk_c5,u),u)**.
% 0.44/0.61  848[5:Rew:842.0,690.0] ||  -> equal(inverse(sk_c8),sk_c8)**.
% 0.44/0.61  853[5:Rew:799.0,848.0] ||  -> equal(sk_c8,sk_c10)**.
% 0.44/0.61  855[5:Rew:853.0,710.0] ||  -> equal(multiply(sk_c5,sk_c10),sk_c11)**.
% 0.44/0.61  865[5:Rew:843.0,855.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  866[5:MRR:865.0,694.0] ||  -> .
% 0.44/0.61  882[4:Spt:866.0,19.1,62.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.44/0.61  883[4:Spt:866.0,19.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  885[3:Rew:699.1,16.1] ||  -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c10)**.
% 0.44/0.61  897[3:Rew:707.1,17.0] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  898[3:Rew:709.1,15.0] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  941[0:SpR:53.0,98.0] ||  -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.44/0.61  942[0:SpR:53.0,538.0] ||  -> equal(inverse(identity),identity)**.
% 0.44/0.61  944[4:SpR:883.0,53.0] ||  -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.44/0.61  950[0:Rew:538.0,941.0] ||  -> equal(inverse(inverse(u)),u)**.
% 0.44/0.61  959[5:Spt:697.1] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  960[5:Rew:959.0,882.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.44/0.61  964[5:Rew:959.0,56.3] || 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_c10),sk_c11) -> .
% 0.44/0.61  970[5:Rew:959.0,897.1] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.44/0.61  972[5:Rew:959.0,898.1] ||  -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.44/0.61  981[5:MRR:885.1,960.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  986[5:MRR:970.0,960.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.44/0.61  987[5:MRR:972.0,960.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c10)**.
% 0.44/0.61  992[5:Rew:959.0,964.4] || 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_c10),sk_c10) -> .
% 0.44/0.61  1010[4:SpR:944.0,98.0] ||  -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.44/0.61  1012[4:Rew:538.0,1010.0] ||  -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.61  1015[4:SpR:1012.0,53.0] ||  -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.44/0.61  1039[5:SpR:986.0,98.0] ||  -> equal(multiply(inverse(sk_c8),sk_c10),sk_c10)**.
% 0.44/0.61  1041[5:Rew:1012.0,1039.0] ||  -> equal(multiply(sk_c6,sk_c10),sk_c10)**.
% 0.44/0.61  1043[5:SpR:987.0,98.0] ||  -> equal(multiply(inverse(sk_c5),sk_c10),sk_c8)**.
% 0.44/0.61  1045[5:Rew:986.0,1043.0,981.0,1043.0] ||  -> equal(sk_c8,sk_c10)**.
% 0.44/0.61  1046[5:Rew:1045.0,883.0] ||  -> equal(inverse(sk_c6),sk_c10)**.
% 0.44/0.61  1049[5:Rew:1045.0,1012.0] ||  -> equal(inverse(sk_c10),sk_c6)**.
% 0.44/0.61  1056[5:Rew:1045.0,1015.0] ||  -> equal(multiply(sk_c6,sk_c10),identity)**.
% 0.44/0.61  1061[5:Rew:692.0,1049.0] ||  -> equal(sk_c2,sk_c6)**.
% 0.44/0.61  1062[5:Rew:1061.0,692.0] ||  -> equal(inverse(sk_c10),sk_c6)**.
% 0.44/0.61  1078[5:Rew:1041.0,1056.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  1080[5:Rew:1078.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  1081[5:Rew:1078.0,53.0] ||  -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.44/0.61  1082[5:Rew:1078.0,942.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  1089[5:Rew:1062.0,1082.0] ||  -> equal(sk_c6,sk_c10)**.
% 0.44/0.61  1093[5:Rew:1089.0,1046.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  1108[5:Rew:1080.0,992.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c10)** equal(v,sk_c10) -> .
% 0.44/0.61  1153[0:SpR:950.0,98.0] ||  -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.44/0.61  1169[5:SpR:950.0,1081.0] ||  -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.44/0.61  1494[5:SpL:1081.0,1108.0] || equal(inverse(sk_c10),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  1503[5:Rew:1081.0,1494.1,950.0,1494.1,1093.0,1494.0] || equal(sk_c10,u) equal(sk_c10,u) equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  1504[5:Obv:1503.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)** equal(v,sk_c10) -> .
% 0.44/0.61  1811[5:SpL:1169.0,1504.1] || equal(inverse(u),inverse(u))* equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) -> .
% 0.44/0.61  1833[5:Obv:1811.1] || equal(inverse(u),sk_c10)** -> .
% 0.44/0.61  1834[5:UnC:1833.0,1093.0] ||  -> .
% 0.44/0.61  1840[5:Spt:1834.0,697.1,959.0] || equal(sk_c11,sk_c10)** -> .
% 0.44/0.61  1841[5:Spt:1834.0,697.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61  1842[5:MRR:699.1,1840.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  1844[5:MRR:703.1,1840.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  1847[5:MRR:709.1,1840.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  1849[5:MRR:713.1,1840.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  1883[5:SpR:1842.0,950.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61  1886[5:Rew:1012.0,1883.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.44/0.61  1890[5:Rew:1886.0,1015.0] ||  -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.44/0.61  1894[5:Rew:1847.0,1890.0] ||  -> equal(identity,sk_c11)**.
% 0.44/0.61  1897[5:Rew:1894.0,77.0] ||  -> equal(multiply(sk_c10,sk_c2),sk_c11)**.
% 0.44/0.61  1898[5:Rew:1894.0,538.0] ||  -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.61  1905[5:Rew:1898.0,1849.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.61  1907[5:Rew:1905.0,1844.0] ||  -> equal(inverse(sk_c10),sk_c11)**.
% 0.44/0.61  1912[5:Rew:692.0,1907.0] ||  -> equal(sk_c2,sk_c11)**.
% 0.44/0.61  1918[5:Rew:1912.0,1897.0] ||  -> equal(multiply(sk_c10,sk_c11),sk_c11)**.
% 0.44/0.61  1925[5:Rew:1898.0,1918.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  1926[5:MRR:1925.0,1840.0] ||  -> .
% 0.44/0.61  1934[3:Spt:1926.0,39.1,60.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.44/0.61  1935[3:Spt:1926.0,39.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  1936[3:MRR:38.1,1934.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61  1937[3:MRR:36.1,1934.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  1938[3:MRR:34.1,1934.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  1939[3:MRR:32.1,1934.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  1940[3:MRR:40.0,1934.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  1941[3:MRR:37.0,1934.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  1942[3:MRR:35.0,1934.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  1944[3:MRR:31.0,1934.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  1946[3:SpR:1935.0,950.0] ||  -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.61  1956[3:SpR:1936.0,950.0] ||  -> equal(inverse(sk_c6),sk_c7)**.
% 0.44/0.61  1959[3:Rew:1935.0,1956.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.44/0.61  1961[3:Rew:1959.0,1940.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.44/0.61  1966[3:SpR:1937.0,950.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61  1967[3:SpR:1937.0,1153.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.61  1969[3:Rew:1946.0,1966.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.44/0.61  1971[3:Rew:1969.0,1946.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61  1974[3:Rew:1969.0,1961.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.44/0.61  1977[3:SpR:1938.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61  1980[3:Rew:1977.0,124.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c11)**.
% 0.44/0.61  1981[3:Rew:1977.0,59.1] || equal(inverse(u),sk_c11)** equal(sk_c4,u) equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.61  1983[3:SpR:1939.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  1984[3:SpR:1939.0,1153.0] ||  -> equal(multiply(sk_c3,multiply(sk_c11,u)),u)**.
% 0.44/0.61  2006[3:SpR:1942.0,54.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.61  2007[3:SpR:1942.0,98.0] ||  -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.61  2009[3:Rew:1937.0,2007.0] ||  -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.61  2010[3:Rew:1967.0,2006.0] ||  -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.61  2011[3:Rew:2010.0,1981.5] || equal(inverse(u),sk_c11)** equal(sk_c4,u) equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c10) -> .
% 0.44/0.61  2013[3:Rew:2010.0,1984.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.61  2016[3:Rew:2013.0,1944.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  2017[3:Rew:2016.0,1939.0] ||  -> equal(inverse(sk_c3),sk_c10)**.
% 0.44/0.61  2018[3:Rew:2016.0,1983.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.61  2020[3:Rew:2016.0,1941.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.44/0.61  2027[3:Rew:2016.0,1980.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.44/0.61  2029[3:Rew:2016.0,2009.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.44/0.61  2030[3:Rew:2016.0,2010.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  2031[3:Rew:1977.0,2018.0] ||  -> equal(sk_c4,sk_c3)**.
% 0.44/0.61  2033[3:Rew:2031.0,1977.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.61  2037[3:Rew:2013.0,2027.0,2031.0,2027.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  2039[3:Rew:2020.0,2029.0] ||  -> equal(sk_c8,sk_c10)**.
% 0.44/0.61  2042[3:Rew:2039.0,1971.0] ||  -> equal(inverse(sk_c10),sk_c5)**.
% 0.44/0.61  2043[3:Rew:2039.0,1974.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.44/0.61  2048[3:Rew:2033.0,2042.0] ||  -> equal(sk_c5,sk_c3)**.
% 0.44/0.61  2053[3:Rew:2030.0,2043.0,2048.0,2043.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.61  2055[3:Rew:2053.0,2017.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2056[3:Rew:2053.0,2031.0] ||  -> equal(sk_c4,sk_c10)**.
% 0.44/0.61  2068[3:Rew:2016.0,2011.5,2016.0,2011.4,2037.0,2011.3,2016.0,2011.2,2056.0,2011.1,2016.0,2011.0] || equal(inverse(u),sk_c10)** equal(sk_c10,u) equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.44/0.61  2069[3:Obv:2068.5] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.44/0.61  2099[0:SpR:538.0,1153.0] ||  -> equal(multiply(u,inverse(u)),identity)**.
% 0.44/0.61  2105[3:SpR:2030.0,538.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  2110[3:Rew:2105.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  2118[3:Rew:2110.0,2069.3] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.44/0.61  2320[3:SpL:2055.0,2118.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.44/0.61  2322[3:Obv:2320.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  2325[3:SpL:2055.0,2322.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  2327[3:Obv:2325.1] ||  -> .
% 0.44/0.61  2328[2:Spt:2327.0,9.1,57.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.44/0.61  2329[2:Spt:2327.0,9.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  2331[2:MRR:6.1,2328.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  2332[2:MRR:4.1,2328.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  2333[2:MRR:2.1,2328.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  2336[2:MRR:5.1,2328.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  2337[2:MRR:3.1,2328.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61  2338[2:MRR:1.1,2328.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  2361[2:SpR:2331.0,1153.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.61  2371[2:SpR:2332.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61  2374[2:SpR:2333.0,98.0] ||  -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.61  2375[2:SpR:2333.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  2394[2:SpR:2336.0,54.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.61  2398[2:Rew:2361.0,2394.0] ||  -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.61  2399[2:Rew:2398.0,2374.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.61  2402[2:Rew:2399.0,2338.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  2405[2:Rew:2402.0,2375.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.61  2407[2:Rew:2402.0,2328.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.44/0.61  2415[2:Rew:2402.0,2398.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  2416[2:Rew:2371.0,2405.0] ||  -> equal(sk_c4,sk_c3)**.
% 0.44/0.61  2419[2:Rew:2416.0,2337.0] ||  -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.44/0.61  2435[2:Rew:2399.0,2419.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  2445[2:Rew:2415.0,2407.0,2435.0,2407.0] || equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  2446[2:Obv:2445.0] ||  -> .
% 0.44/0.61  2457[1:Spt:2446.0,51.3,51.4,51.5,51.6,51.10,51.11,51.12,51.13,51.14] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.44/0.61  2459[2:Spt:8.1] ||  -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.44/0.61  2460[2:Rew:2459.0,2457.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** equal(sk_c9,sk_c9) -> .
% 0.44/0.61  2462[2:Obv:2460.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.44/0.61  2465[2:SpR:2459.0,98.0] ||  -> equal(multiply(inverse(sk_c10),sk_c9),sk_c11)**.
% 0.44/0.61  2467[3:Spt:19.1] ||  -> equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.61  2469[3:SpR:2467.0,950.0] ||  -> equal(inverse(sk_c11),sk_c1)**.
% 0.44/0.61  2472[4:Spt:39.1] ||  -> equal(inverse(sk_c2),sk_c10)**.
% 0.44/0.61  2474[4:SpR:2472.0,950.0] ||  -> equal(inverse(sk_c10),sk_c2)**.
% 0.44/0.61  2477[4:Rew:2474.0,2465.0] ||  -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.44/0.61  2478[4:Rew:2477.0,41.1] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(sk_c11,sk_c10).
% 0.44/0.61  2479[4:Rew:2477.0,43.1] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(sk_c11,sk_c10).
% 0.44/0.61  2483[4:Rew:2477.0,42.1] ||  -> equal(inverse(sk_c3),sk_c11)** equal(sk_c11,sk_c10).
% 0.44/0.61  2484[4:Rew:2477.0,44.1] ||  -> equal(inverse(sk_c4),sk_c10)** equal(sk_c11,sk_c10).
% 0.44/0.61  2487[4:Rew:2477.0,49.1] ||  -> equal(inverse(sk_c6),sk_c8)** equal(sk_c11,sk_c10).
% 0.44/0.61  2488[4:Rew:2483.1,22.1] ||  -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2489[4:Rew:2484.1,24.1] ||  -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2492[4:Rew:2487.1,29.1] ||  -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2493[4:Rew:2478.1,21.1] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2494[4:Rew:2479.1,23.1] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2532[3:SpR:2467.0,2099.0] ||  -> equal(multiply(sk_c1,sk_c11),identity)**.
% 0.44/0.61  2534[3:SpR:2469.0,2099.0] ||  -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.44/0.61  2571[5:Spt:2483.1] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  2572[5:Rew:2571.0,2459.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.44/0.61  2573[5:Rew:2571.0,2467.0] ||  -> equal(inverse(sk_c1),sk_c10)**.
% 0.44/0.61  2574[5:Rew:2571.0,2469.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.44/0.61  2575[5:Rew:2571.0,2477.0] ||  -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.44/0.61  2576[5:Rew:2571.0,2532.0] ||  -> equal(multiply(sk_c1,sk_c10),identity)**.
% 0.44/0.61  2578[5:Rew:2571.0,2462.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.44/0.61  2584[5:Rew:2571.0,2488.0] ||  -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2585[5:Rew:2571.0,2493.0] ||  -> equal(multiply(sk_c3,sk_c10),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.44/0.61  2588[5:Rew:2474.0,2574.0] ||  -> equal(sk_c2,sk_c1)**.
% 0.44/0.61  2590[5:Rew:2588.0,2474.0] ||  -> equal(inverse(sk_c10),sk_c1)**.
% 0.44/0.61  2595[5:Rew:2588.0,2575.0] ||  -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.44/0.61  2597[5:Rew:2576.0,2494.1] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(identity,sk_c10).
% 0.44/0.61  2598[5:Rew:2576.0,2492.1] ||  -> equal(inverse(sk_c6),sk_c8)** equal(identity,sk_c10).
% 0.44/0.61  2601[5:Rew:2576.0,2489.1] ||  -> equal(inverse(sk_c4),sk_c10)** equal(identity,sk_c10).
% 0.44/0.61  2603[5:Rew:2576.0,2584.1] ||  -> equal(inverse(sk_c3),sk_c10)** equal(identity,sk_c10).
% 0.44/0.61  2604[5:Rew:2576.0,2585.1] ||  -> equal(multiply(sk_c3,sk_c10),sk_c10)** equal(identity,sk_c10).
% 0.44/0.61  2607[5:Rew:2571.0,2578.7,2571.0,2578.5,2571.0,2578.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c10)** -> .
% 0.44/0.61  2608[5:Con:2607.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** -> .
% 0.44/0.61  2629[6:Spt:2598.1] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  2630[6:Rew:2629.0,942.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2631[6:Rew:2629.0,52.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  2632[6:Rew:2629.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  2638[6:Rew:2590.0,2630.0] ||  -> equal(sk_c1,sk_c10)**.
% 0.44/0.61  2640[6:Rew:2638.0,2573.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2646[6:Rew:2631.0,2572.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  2648[6:Rew:2646.0,2608.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** -> .
% 0.44/0.61  2657[6:Con:2648.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.44/0.61  2658[6:Rew:2632.0,2657.3,2646.0,2657.3,2632.0,2657.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) -> .
% 0.44/0.61  2659[6:Con:2658.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  2706[6:SpL:2640.0,2659.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  2707[6:Obv:2706.1] ||  -> .
% 0.44/0.61  2708[6:Spt:2707.0,2598.1,2629.0] || equal(identity,sk_c10)** -> .
% 0.44/0.61  2709[6:Spt:2707.0,2598.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  2712[6:MRR:2601.1,2708.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  2713[6:MRR:2603.1,2708.0] ||  -> equal(inverse(sk_c3),sk_c10)**.
% 0.44/0.61  2715[6:MRR:2597.1,2708.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61  2716[6:MRR:2604.1,2708.0] ||  -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.44/0.61  2760[6:SpR:2712.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61  2763[6:Rew:2590.0,2760.0] ||  -> equal(sk_c1,sk_c4)**.
% 0.44/0.61  2768[6:Rew:2763.0,2576.0] ||  -> equal(multiply(sk_c4,sk_c10),identity)**.
% 0.44/0.61  2769[6:Rew:2763.0,2595.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.44/0.61  2773[6:Rew:2715.0,2768.0] ||  -> equal(identity,sk_c9)**.
% 0.44/0.61  2774[6:Rew:2773.0,2708.0] || equal(sk_c9,sk_c10)** -> .
% 0.44/0.61  2776[6:Rew:2773.0,538.0] ||  -> equal(multiply(u,sk_c9),u)**.
% 0.44/0.61  2782[6:Rew:2776.0,2769.0] ||  -> equal(sk_c4,sk_c10)**.
% 0.44/0.61  2785[6:Rew:2782.0,2712.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2798[6:SpR:2713.0,950.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.61  2801[6:Rew:2785.0,2798.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.61  2803[6:Rew:2801.0,2716.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.44/0.61  2804[6:Rew:2572.0,2803.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  2805[6:MRR:2804.0,2774.0] ||  -> .
% 0.44/0.61  2808[5:Spt:2805.0,2483.1,2571.0] || equal(sk_c11,sk_c10)** -> .
% 0.44/0.61  2809[5:Spt:2805.0,2483.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  2810[5:MRR:2484.1,2808.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  2814[5:MRR:2478.1,2808.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  2815[5:MRR:2479.1,2808.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61  2820[5:SpR:2809.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  2823[5:Rew:2469.0,2820.0] ||  -> equal(sk_c1,sk_c3)**.
% 0.44/0.61  2824[5:Rew:2823.0,2469.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  2826[5:Rew:2823.0,2534.0] ||  -> equal(multiply(sk_c11,sk_c3),identity)**.
% 0.44/0.61  2827[5:Rew:2823.0,2532.0] ||  -> equal(multiply(sk_c3,sk_c11),identity)**.
% 0.44/0.61  2830[5:Rew:2814.0,2827.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  2832[5:Rew:2830.0,52.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  2833[5:Rew:2830.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  2839[5:Rew:2830.0,2826.0] ||  -> equal(multiply(sk_c11,sk_c3),sk_c10)**.
% 0.44/0.61  2848[5:Rew:2832.0,2459.0] ||  -> equal(sk_c9,sk_c11)**.
% 0.44/0.61  2849[5:Rew:2848.0,2815.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c11)**.
% 0.44/0.61  2860[5:Rew:2833.0,2849.0] ||  -> equal(sk_c4,sk_c11)**.
% 0.44/0.61  2861[5:Rew:2860.0,2810.0] ||  -> equal(inverse(sk_c11),sk_c10)**.
% 0.44/0.61  2862[5:Rew:2824.0,2861.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.61  2867[5:Rew:2862.0,2839.0] ||  -> equal(multiply(sk_c11,sk_c10),sk_c10)**.
% 0.44/0.61  2872[5:Rew:2833.0,2867.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  2873[5:MRR:2872.0,2808.0] ||  -> .
% 0.44/0.61  2884[4:Spt:2873.0,39.1,2472.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.44/0.61  2885[4:Spt:2873.0,39.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  2888[4:MRR:34.1,2884.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  2889[4:MRR:32.1,2884.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  2893[4:MRR:33.0,2884.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61  2894[4:MRR:31.0,2884.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  2935[4:SpR:2888.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61  2940[4:SpR:2889.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  2943[4:Rew:2469.0,2940.0] ||  -> equal(sk_c1,sk_c3)**.
% 0.44/0.61  2946[4:Rew:2943.0,2532.0] ||  -> equal(multiply(sk_c3,sk_c11),identity)**.
% 0.44/0.61  2950[4:Rew:2894.0,2946.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.61  2951[4:Rew:2950.0,942.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2952[4:Rew:2950.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.61  2953[4:Rew:2950.0,52.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.61  2957[4:Rew:2935.0,2951.0] ||  -> equal(sk_c4,sk_c10)**.
% 0.44/0.61  2958[4:Rew:2957.0,2888.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.61  2959[4:Rew:2957.0,2893.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.44/0.61  2966[4:Rew:2952.0,2462.7] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11)** equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(x,sk_c11) -> .
% 0.44/0.61  2979[4:Rew:2953.0,2459.0] ||  -> equal(sk_c9,sk_c11)**.
% 0.44/0.61  2980[4:Rew:2953.0,2959.0,2979.0,2959.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.61  2987[4:Rew:2980.0,2979.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.61  3007[4:Rew:2980.0,2966.7,2952.0,2966.6,2987.0,2966.6,2952.0,2966.5,2980.0,2966.5,2952.0,2966.4,2987.0,2966.4,2980.0,2966.3,2980.0,2966.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c10) -> .
% 0.44/0.61  3008[4:Con:3007.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.61  3051[4:SpL:2958.0,3008.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.44/0.61  3052[4:Obv:3051.1] ||  -> .
% 0.44/0.61  3053[3:Spt:3052.0,19.1,2467.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.44/0.61  3054[3:Spt:3052.0,19.0] ||  -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.61  3055[3:MRR:18.1,3053.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61  3056[3:MRR:16.1,3053.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61  3057[3:MRR:14.1,3053.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61  3058[3:MRR:12.1,3053.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61  3059[3:MRR:20.0,3053.0] ||  -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61  3060[3:MRR:17.0,3053.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61  3061[3:MRR:15.0,3053.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61  3063[3:MRR:11.0,3053.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61  3065[3:SpR:3054.0,950.0] ||  -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.61  3075[3:SpR:3055.0,950.0] ||  -> equal(inverse(sk_c6),sk_c7)**.
% 0.44/0.61  3078[3:Rew:3054.0,3075.0] ||  -> equal(sk_c7,sk_c8)**.
% 0.44/0.61  3080[3:Rew:3078.0,3059.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.44/0.61  3085[3:SpR:3056.0,950.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61  3086[3:SpR:3056.0,1153.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.61  3088[3:Rew:3065.0,3085.0] ||  -> equal(sk_c6,sk_c5)**.
% 0.44/0.61  3090[3:Rew:3088.0,3065.0] ||  -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61  3093[3:Rew:3088.0,3080.0] ||  -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.44/0.61  3095[3:SpR:3057.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61  3098[3:Rew:3095.0,2465.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c11)**.
% 0.44/0.61  3100[3:SpR:3058.0,98.0] ||  -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.61  3101[3:SpR:3058.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61  3124[3:SpR:3061.0,54.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.61  3125[3:SpR:3061.0,98.0] ||  -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.61  3127[3:Rew:3056.0,3125.0] ||  -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.62  3128[3:Rew:3086.0,3124.0] ||  -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.62  3129[3:Rew:3128.0,3100.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.62  3133[3:Rew:3129.0,3063.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.62  3134[3:Rew:3133.0,3058.0] ||  -> equal(inverse(sk_c3),sk_c10)**.
% 0.44/0.62  3136[3:Rew:3133.0,3101.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.62  3138[3:Rew:3133.0,3060.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.44/0.62  3140[3:Rew:3133.0,2462.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.44/0.62  3142[3:Rew:3133.0,3098.0] ||  -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.44/0.62  3144[3:Rew:3133.0,3127.0] ||  -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.44/0.62  3145[3:Rew:3133.0,3128.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.62  3146[3:Rew:3095.0,3136.0] ||  -> equal(sk_c4,sk_c3)**.
% 0.44/0.62  3148[3:Rew:3146.0,3095.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.62  3152[3:Rew:3129.0,3142.0,3146.0,3142.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.62  3154[3:Rew:3138.0,3144.0] ||  -> equal(sk_c8,sk_c10)**.
% 0.44/0.62  3157[3:Rew:3154.0,3090.0] ||  -> equal(inverse(sk_c10),sk_c5)**.
% 0.44/0.62  3158[3:Rew:3154.0,3093.0] ||  -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.44/0.62  3163[3:Rew:3148.0,3157.0] ||  -> equal(sk_c5,sk_c3)**.
% 0.44/0.62  3168[3:Rew:3145.0,3158.0,3163.0,3158.0] ||  -> equal(sk_c3,sk_c10)**.
% 0.44/0.62  3170[3:Rew:3168.0,3134.0] ||  -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.62  3183[3:Rew:3133.0,3140.7,3152.0,3140.6,3133.0,3140.5,3152.0,3140.4,3133.0,3140.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c10),sk_c10)** equal(multiply(x,sk_c10),sk_c10)** -> .
% 0.44/0.62  3184[3:Con:3183.1] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.44/0.62  3217[3:SpR:3145.0,538.0] ||  -> equal(identity,sk_c10)**.
% 0.44/0.62  3222[3:Rew:3217.0,538.0] ||  -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.62  3226[3:Rew:3222.0,3184.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.44/0.62  3258[3:SpL:3170.0,3226.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.44/0.62  3259[3:Obv:3258.1] ||  -> .
% 0.44/0.62  3260[2:Spt:3259.0,8.1,2459.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.44/0.62  3261[2:Spt:3259.0,8.0] ||  -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.62  3262[2:MRR:6.1,3260.0] ||  -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.62  3263[2:MRR:4.1,3260.0] ||  -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.62  3264[2:MRR:2.1,3260.0] ||  -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.62  3268[2:MRR:5.1,3260.0] ||  -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.62  3269[2:MRR:3.1,3260.0] ||  -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.62  3270[2:MRR:1.1,3260.0] ||  -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.62  3289[2:SpR:3262.0,1153.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.62  3299[2:SpR:3263.0,950.0] ||  -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.62  3302[2:SpR:3264.0,98.0] ||  -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.62  3303[2:SpR:3264.0,950.0] ||  -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.62  3322[2:SpR:3268.0,54.0] ||  -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.62  3326[2:Rew:3289.0,3322.0] ||  -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.62  3327[2:Rew:3326.0,3302.0] ||  -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.62  3330[2:Rew:3327.0,3270.0] ||  -> equal(sk_c11,sk_c10)**.
% 0.44/0.62  3333[2:Rew:3330.0,3303.0] ||  -> equal(inverse(sk_c10),sk_c3)**.
% 0.44/0.62  3335[2:Rew:3330.0,3260.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.44/0.62  3338[2:Rew:3330.0,3326.0] ||  -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.62  3339[2:Rew:3299.0,3333.0] ||  -> equal(sk_c4,sk_c3)**.
% 0.44/0.62  3342[2:Rew:3339.0,3269.0] ||  -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.44/0.62  3358[2:Rew:3327.0,3342.0] ||  -> equal(sk_c9,sk_c10)**.
% 0.44/0.62  3368[2:Rew:3338.0,3335.0,3358.0,3335.0] || equal(sk_c10,sk_c10)* -> .
% 0.44/0.62  3369[2:Obv:3368.0] ||  -> .
% 0.44/0.62  % SZS output end Refutation
% 0.44/0.62  Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_11 prove_this_12 prove_this_14 prove_this_15 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_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_48 prove_this_49 prove_this_50 prove_this_51 left_identity left_inverse associativity
% 0.44/0.62  
%------------------------------------------------------------------------------