TSTP Solution File: GRP242-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP242-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:46:29 EDT 2022
% Result : Unsatisfiable 0.38s 0.58s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP242-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 16:12:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.38/0.58
% 0.38/0.58 SPASS V 3.9
% 0.38/0.58 SPASS beiseite: Proof found.
% 0.38/0.58 % SZS status Theorem
% 0.38/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.58 SPASS derived 1802 clauses, backtracked 757 clauses, performed 13 splits and kept 1275 clauses.
% 0.38/0.58 SPASS allocated 64860 KBytes.
% 0.38/0.58 SPASS spent 0:00:00.24 on the problem.
% 0.38/0.58 0:00:00.04 for the input.
% 0.38/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.58 0:00:00.01 for inferences.
% 0.38/0.58 0:00:00.00 for the backtracking.
% 0.38/0.58 0:00:00.16 for the reduction.
% 0.38/0.58
% 0.38/0.58
% 0.38/0.58 Here is a proof with depth 6, length 446 :
% 0.38/0.58 % SZS output start Refutation
% 0.38/0.58 1[0:Inp] || -> equal(multiply(sk_c10,sk_c9),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.38/0.58 2[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 3[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.38/0.58 4[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 5[0:Inp] || -> equal(multiply(sk_c8,sk_c11),sk_c9)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.38/0.58 6[0:Inp] || -> equal(inverse(sk_c8),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 7[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 8[0:Inp] || -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c1),sk_c11).
% 0.38/0.58 9[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c10),sk_c11)**.
% 0.38/0.58 10[0:Inp] || -> equal(inverse(sk_c7),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.38/0.58 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c8,sk_c11),sk_c9)**.
% 0.38/0.58 12[0:Inp] || -> equal(inverse(sk_c8),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.38/0.58 14[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.58 17[0:Inp] || -> equal(multiply(sk_c8,sk_c11),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.58 20[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.58 23[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c8,sk_c11),sk_c9)**.
% 0.38/0.58 25[0:Inp] || -> equal(multiply(sk_c10,sk_c9),sk_c11) equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.58 26[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.58 31[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 32[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c3),sk_c6)**.
% 0.38/0.58 37[0:Inp] || -> equal(multiply(sk_c10,sk_c9),sk_c11) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.58 38[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.58 43[0:Inp] || -> equal(inverse(sk_c5),sk_c4) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 44[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c5),sk_c4)**.
% 0.38/0.58 49[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 50[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 51[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c10),sk_c11)**.
% 0.38/0.58 52[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 53[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c8,sk_c11),sk_c9)**.
% 0.38/0.58 54[0:Inp] || -> equal(inverse(sk_c8),sk_c11) equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 55[0:Inp] || -> equal(multiply(sk_c10,sk_c9),sk_c11) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.58 56[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.58 61[0:Inp] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c11) equal(inverse(z),sk_c10) equal(inverse(x1),sk_c10) equal(inverse(x2),sk_c11) equal(inverse(sk_c10),sk_c9) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(y,sk_c11),sk_c9)** equal(multiply(z,sk_c10),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(x1,sk_c10),sk_c9)** equal(multiply(x2,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 62[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.38/0.58 63[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.38/0.58 64[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.38/0.58 65[1:Spt:61.0,61.1,61.2,61.8,61.9,61.12] || 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)** -> .
% 0.38/0.58 66[1:EqR:65.3] || 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) -> .
% 0.38/0.58 67[2:Spt:50.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.38/0.58 69[3:Spt:49.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 71[3:SpL:69.0,65.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.38/0.58 72[3:Rew:67.0,71.1] || equal(inverse(u),sk_c9)** equal(sk_c9,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.38/0.58 73[4:Spt:54.0] || -> equal(inverse(sk_c8),sk_c11)**.
% 0.38/0.58 75[5:Spt:52.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.38/0.58 77[6:Spt:53.1] || -> equal(multiply(sk_c8,sk_c11),sk_c9)**.
% 0.38/0.58 83[7:Spt:51.1] || -> equal(multiply(sk_c7,sk_c10),sk_c11)**.
% 0.38/0.58 88[2:SpR:67.0,63.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.38/0.58 89[4:SpR:73.0,63.0] || -> equal(multiply(sk_c11,sk_c8),identity)**.
% 0.38/0.58 90[5:SpR:75.0,63.0] || -> equal(multiply(sk_c10,sk_c7),identity)**.
% 0.38/0.58 92[3:Rew:88.0,72.5] || equal(inverse(u),sk_c9)** equal(sk_c9,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(identity,sk_c11) -> .
% 0.38/0.58 100[2:SpR:88.0,64.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(identity,u))**.
% 0.38/0.58 101[3:SpR:69.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.38/0.58 104[0:SpR:63.0,64.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.38/0.58 105[4:SpR:89.0,64.0] || -> equal(multiply(sk_c11,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.38/0.58 107[2:Rew:62.0,100.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.38/0.58 108[4:Rew:62.0,105.0] || -> equal(multiply(sk_c11,multiply(sk_c8,u)),u)**.
% 0.38/0.58 109[0:Rew:62.0,104.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.38/0.58 111[5:SpR:90.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.38/0.58 114[5:Rew:62.0,111.0] || -> equal(multiply(sk_c10,multiply(sk_c7,u)),u)**.
% 0.38/0.58 119[3:SpR:69.0,107.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.38/0.58 120[5:SpR:90.0,107.0] || -> equal(multiply(sk_c9,identity),sk_c7)**.
% 0.38/0.58 127[5:SpR:120.0,64.0] || -> equal(multiply(sk_c9,multiply(identity,u)),multiply(sk_c7,u))**.
% 0.38/0.58 130[5:Rew:62.0,127.0] || -> equal(multiply(sk_c7,u),multiply(sk_c9,u))**.
% 0.38/0.58 131[7:Rew:130.0,83.0] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.38/0.58 133[5:Rew:130.0,114.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.38/0.58 134[7:Rew:88.0,131.0] || -> equal(identity,sk_c11)**.
% 0.38/0.58 135[7:Rew:134.0,62.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 136[7:Rew:134.0,63.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.38/0.58 138[7:Rew:134.0,89.0] || -> equal(multiply(sk_c11,sk_c8),sk_c11)**.
% 0.38/0.58 140[7:Rew:134.0,120.0] || -> equal(multiply(sk_c9,sk_c11),sk_c7)**.
% 0.38/0.58 153[7:Rew:135.0,138.0] || -> equal(sk_c8,sk_c11)**.
% 0.38/0.58 154[7:Rew:153.0,73.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 155[7:Rew:153.0,77.0] || -> equal(multiply(sk_c11,sk_c11),sk_c9)**.
% 0.38/0.58 156[7:Rew:119.0,140.0] || -> equal(sk_c7,sk_c9)**.
% 0.38/0.58 157[7:Rew:156.0,75.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.38/0.58 162[7:Rew:135.0,155.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 169[7:Rew:162.0,157.0] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.38/0.58 170[7:Rew:154.0,169.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 174[7:Rew:170.0,66.4] || 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_c11),sk_c11) -> .
% 0.38/0.58 215[0:SpR:109.0,109.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.38/0.58 217[0:SpR:64.0,109.0] || -> equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(v,w))),w)**.
% 0.38/0.58 219[7:SpR:136.0,109.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.38/0.58 223[7:Rew:215.0,219.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.38/0.58 227[7:Rew:223.0,174.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(v,sk_c11) -> .
% 0.38/0.58 250[7:SpR:215.0,223.0] || -> equal(multiply(u,sk_c11),inverse(inverse(u)))**.
% 0.38/0.58 251[0:SpR:215.0,109.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.38/0.58 252[7:SpR:215.0,136.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.38/0.58 256[7:Rew:223.0,250.0] || -> equal(inverse(inverse(u)),u)**.
% 0.38/0.58 308[0:SpR:251.0,217.0] || -> equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w))**.
% 0.38/0.58 312[0:SpR:109.0,217.0] || -> equal(multiply(inverse(multiply(inverse(u),u)),v),v)**.
% 0.38/0.58 740[7:SpL:136.0,227.0] || equal(inverse(sk_c11),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.38/0.58 750[7:Rew:136.0,740.1,256.0,740.1,154.0,740.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.38/0.58 751[7:Obv:750.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.38/0.58 912[7:SpL:252.0,751.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.38/0.58 934[7:Obv:912.1] || equal(inverse(u),sk_c11)** -> .
% 0.38/0.58 935[7:UnC:934.0,256.0] || -> .
% 0.38/0.58 941[7:Spt:935.0,51.1,83.0] || equal(multiply(sk_c7,sk_c10),sk_c11)** -> .
% 0.38/0.58 942[7:Spt:935.0,51.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 943[7:Rew:130.0,941.0] || equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.38/0.58 944[7:Rew:88.0,943.0] || equal(identity,sk_c11)** -> .
% 0.38/0.58 953[5:Rew:133.0,101.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 956[5:Rew:953.0,108.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.38/0.58 957[5:Rew:953.0,89.0] || -> equal(identity,sk_c8)**.
% 0.38/0.58 958[5:Rew:957.0,120.0] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.38/0.58 960[5:Rew:957.0,88.0] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.38/0.58 963[7:Rew:957.0,944.0] || equal(sk_c8,sk_c11)** -> .
% 0.38/0.58 964[6:Rew:956.0,77.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 971[6:Rew:953.0,958.0,964.0,958.0] || -> equal(sk_c8,sk_c7)**.
% 0.38/0.58 972[6:Rew:971.0,73.0] || -> equal(inverse(sk_c7),sk_c11)**.
% 0.38/0.58 974[7:Rew:971.0,963.0] || equal(sk_c7,sk_c11)** -> .
% 0.38/0.58 976[6:Rew:75.0,972.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 981[6:Rew:953.0,960.0,964.0,960.0,976.0,960.0,971.0,960.0] || -> equal(sk_c7,sk_c11)**.
% 0.38/0.58 982[7:MRR:981.0,974.0] || -> .
% 0.38/0.58 1029[6:Spt:982.0,53.1,77.0] || equal(multiply(sk_c8,sk_c11),sk_c9)** -> .
% 0.38/0.58 1030[6:Spt:982.0,53.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 1031[6:Rew:956.0,1029.0] || equal(sk_c9,sk_c11)** -> .
% 0.38/0.58 1044[5:Rew:956.0,23.1] || -> equal(inverse(sk_c2),sk_c10)** equal(sk_c9,sk_c11).
% 0.38/0.58 1045[6:MRR:1044.1,1031.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.58 1046[5:Rew:956.0,11.1] || -> equal(inverse(sk_c1),sk_c11)** equal(sk_c9,sk_c11).
% 0.38/0.58 1047[6:MRR:1046.1,1031.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 1055[5:Rew:956.0,17.0] || -> equal(sk_c9,sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.58 1056[6:MRR:1055.0,1031.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.58 1057[5:Rew:956.0,5.0] || -> equal(sk_c9,sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 1058[6:MRR:1057.0,1031.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 1072[2:SpR:67.0,251.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.38/0.58 1091[6:SpR:1045.0,251.0] || -> equal(multiply(sk_c2,multiply(sk_c10,u)),u)**.
% 0.38/0.58 1093[6:SpR:1047.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 1096[6:Rew:953.0,1093.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 1097[6:Rew:1096.0,1058.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 1105[6:Rew:1097.0,1091.0] || -> equal(multiply(sk_c2,multiply(sk_c11,u)),u)**.
% 0.38/0.58 1108[6:Rew:1097.0,1056.0] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.38/0.58 1138[6:Rew:953.0,1105.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.58 1139[6:Rew:1138.0,1108.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 1140[6:MRR:1139.0,1031.0] || -> .
% 0.38/0.58 1154[5:Spt:1140.0,52.0,75.0] || equal(inverse(sk_c7),sk_c10)** -> .
% 0.38/0.58 1155[5:Spt:1140.0,52.1] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 1159[5:MRR:10.0,1154.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 1164[5:MRR:4.0,1154.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 1165[3:Rew:1072.0,101.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 1166[4:Rew:1165.0,89.0] || -> equal(identity,sk_c8)**.
% 0.38/0.58 1170[4:Rew:1166.0,88.0] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.38/0.58 1171[4:Rew:1166.0,63.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.38/0.58 1174[4:Rew:1166.0,92.5] || equal(inverse(u),sk_c9)** equal(sk_c9,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(sk_c8,sk_c11) -> .
% 0.38/0.58 1201[5:SpR:1159.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 1204[5:Rew:1165.0,1201.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 1205[5:Rew:1204.0,1164.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 1208[5:Rew:1205.0,69.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.38/0.58 1215[5:Rew:1205.0,1170.0] || -> equal(multiply(sk_c9,sk_c11),sk_c8)**.
% 0.38/0.58 1226[5:Rew:1165.0,1208.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 1228[5:Rew:1226.0,1174.0] || equal(inverse(u),sk_c11)** equal(sk_c9,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(sk_c8,sk_c11) -> .
% 0.38/0.58 1231[5:Rew:1165.0,1215.0,1226.0,1215.0] || -> equal(sk_c8,sk_c11)**.
% 0.38/0.58 1235[5:Rew:1231.0,1171.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.38/0.58 1241[5:Rew:1231.0,1228.5,1226.0,1228.4,1226.0,1228.2,1226.0,1228.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.38/0.58 1242[5:Obv:1241.5] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.38/0.58 1351[5:SpR:1235.0,251.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.38/0.58 1353[5:SpR:1159.0,1235.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.38/0.58 1363[5:Rew:1351.0,1242.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.38/0.58 1364[5:Rew:1165.0,1353.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 1365[5:Rew:1364.0,1159.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.38/0.58 1400[5:Rew:1364.0,1363.3,1364.0,1363.2,1364.0,1363.1,1364.0,1363.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.38/0.58 1554[5:SpL:1365.0,1400.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.38/0.58 1556[5:Obv:1554.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.38/0.58 1558[5:SpL:1365.0,1556.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 1560[5:Obv:1558.1] || -> .
% 0.38/0.58 1561[4:Spt:1560.0,54.0,73.0] || equal(inverse(sk_c8),sk_c11)** -> .
% 0.38/0.58 1562[4:Spt:1560.0,54.1] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 1566[4:MRR:12.0,1561.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 1571[4:MRR:6.0,1561.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 1572[0:Rew:63.0,312.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.38/0.58 1588[4:SpR:1566.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 1591[4:Rew:1165.0,1588.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 1592[4:Rew:1591.0,1571.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 1595[4:Rew:1592.0,69.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.38/0.58 1596[4:Rew:1592.0,88.0] || -> equal(multiply(sk_c9,sk_c11),identity)**.
% 0.38/0.58 1612[4:Rew:1165.0,1595.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 1614[4:Rew:1612.0,92.0] || equal(inverse(u),sk_c11)** equal(sk_c9,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(identity,sk_c11) -> .
% 0.38/0.58 1616[4:Rew:1165.0,1596.0,1612.0,1596.0] || -> equal(identity,sk_c11)**.
% 0.38/0.58 1618[4:Rew:1616.0,63.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.38/0.58 1628[4:Rew:1616.0,1614.5,1612.0,1614.4,1612.0,1614.2,1612.0,1614.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.38/0.58 1629[4:Obv:1628.5] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.38/0.58 1725[4:SpR:1618.0,251.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.38/0.58 1727[4:SpR:1566.0,1618.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.38/0.58 1737[4:Rew:1725.0,1629.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.38/0.58 1738[4:Rew:1165.0,1727.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 1739[4:Rew:1738.0,1566.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.38/0.58 1771[4:Rew:1738.0,1737.3,1738.0,1737.2,1738.0,1737.1,1738.0,1737.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.38/0.58 1933[4:SpL:1739.0,1771.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.38/0.58 1935[4:Obv:1933.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.38/0.58 1937[4:SpL:1739.0,1935.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 1939[4:Obv:1937.1] || -> .
% 0.38/0.58 1940[3:Spt:1939.0,49.1,69.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 1941[3:Spt:1939.0,49.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 1942[3:MRR:43.1,1940.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.38/0.58 1943[3:MRR:31.1,1940.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.38/0.58 1945[3:MRR:7.1,1940.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 1946[3:MRR:55.0,1940.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.58 1947[3:MRR:37.0,1940.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.58 1948[3:MRR:25.0,1940.0] || -> equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.58 1950[3:MRR:1.0,1940.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 1951[3:SpR:1941.0,109.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.38/0.58 1961[3:SpR:1943.0,251.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.38/0.58 1966[3:SpR:1945.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 1977[3:SpR:1946.0,109.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.38/0.58 1981[3:Rew:1942.0,1977.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.38/0.58 1989[3:SpR:1948.0,64.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c11,u))**.
% 0.38/0.58 1990[3:SpR:1948.0,109.0] || -> equal(multiply(inverse(sk_c3),sk_c11),sk_c6)**.
% 0.38/0.58 1994[3:Rew:1943.0,1990.0] || -> equal(multiply(sk_c6,sk_c11),sk_c6)**.
% 0.38/0.58 1995[3:Rew:1961.0,1989.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 1996[3:Rew:1995.0,1966.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 1999[3:Rew:1996.0,1950.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 2000[3:Rew:1999.0,67.0] || -> equal(inverse(sk_c11),sk_c9)**.
% 0.38/0.58 2003[3:Rew:1999.0,1947.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.38/0.58 2004[3:Rew:1999.0,1940.0] || equal(multiply(sk_c11,sk_c9),sk_c11)** -> .
% 0.38/0.58 2022[3:Rew:1994.0,2003.0] || -> equal(sk_c6,sk_c11)**.
% 0.38/0.58 2023[3:Rew:2022.0,1941.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.38/0.58 2027[3:Rew:2022.0,1951.0] || -> equal(multiply(sk_c11,multiply(sk_c4,u)),u)**.
% 0.38/0.58 2032[3:Rew:2022.0,1981.0] || -> equal(multiply(sk_c4,sk_c4),sk_c11)**.
% 0.38/0.58 2036[3:Rew:1995.0,2004.0] || equal(sk_c9,sk_c11)** -> .
% 0.38/0.58 2051[3:Rew:1995.0,2027.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.38/0.58 2052[3:Rew:2051.0,2032.0] || -> equal(sk_c4,sk_c11)**.
% 0.38/0.58 2056[3:Rew:2052.0,2023.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 2059[3:Rew:2000.0,2056.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2060[3:MRR:2059.0,2036.0] || -> .
% 0.38/0.58 2077[2:Spt:2060.0,50.0,67.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.38/0.58 2078[2:Spt:2060.0,50.1] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 2079[2:MRR:44.0,2077.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.38/0.58 2080[2:MRR:32.0,2077.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.38/0.58 2081[2:MRR:20.0,2077.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.58 2082[2:MRR:8.0,2077.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 2083[2:MRR:56.0,2077.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.58 2084[2:MRR:38.0,2077.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.58 2085[2:MRR:26.0,2077.0] || -> equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.58 2086[2:MRR:14.0,2077.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.58 2087[2:MRR:2.0,2077.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 2088[2:SpR:2078.0,109.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.38/0.58 2095[2:SpR:2080.0,251.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.38/0.58 2097[2:SpR:2081.0,109.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.58 2100[2:SpR:2082.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 2104[2:SpR:2083.0,109.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.38/0.58 2108[2:Rew:2079.0,2104.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.38/0.58 2115[2:SpR:2085.0,64.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c11,u))**.
% 0.38/0.58 2116[2:SpR:2085.0,109.0] || -> equal(multiply(inverse(sk_c3),sk_c11),sk_c6)**.
% 0.38/0.58 2120[2:Rew:2080.0,2116.0] || -> equal(multiply(sk_c6,sk_c11),sk_c6)**.
% 0.38/0.58 2121[2:Rew:2095.0,2115.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 2122[2:Rew:2121.0,2100.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 2125[2:Rew:2122.0,2087.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 2127[2:Rew:2125.0,2077.0] || equal(inverse(sk_c11),sk_c9)** -> .
% 0.38/0.58 2128[2:Rew:2125.0,2084.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.38/0.58 2129[2:Rew:2125.0,2086.0] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.38/0.58 2135[2:Rew:2125.0,2097.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.38/0.58 2140[2:Rew:2120.0,2128.0] || -> equal(sk_c6,sk_c11)**.
% 0.38/0.58 2141[2:Rew:2140.0,2078.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.38/0.58 2145[2:Rew:2140.0,2088.0] || -> equal(multiply(sk_c11,multiply(sk_c4,u)),u)**.
% 0.38/0.58 2150[2:Rew:2140.0,2108.0] || -> equal(multiply(sk_c4,sk_c4),sk_c11)**.
% 0.38/0.58 2159[2:Rew:2121.0,2135.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.58 2160[2:Rew:2159.0,2129.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2161[2:Rew:2160.0,2127.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.38/0.58 2163[2:Rew:2121.0,2145.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.38/0.58 2164[2:Rew:2163.0,2150.0] || -> equal(sk_c4,sk_c11)**.
% 0.38/0.58 2168[2:Rew:2164.0,2141.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 2171[2:MRR:2168.0,2161.0] || -> .
% 0.38/0.58 2184[1:Spt:2171.0,61.3,61.4,61.5,61.6,61.7,61.10,61.11,61.13,61.14,61.15] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c11),sk_c9)**+ equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 2186[2:Spt:44.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.38/0.58 2187[2:Rew:2186.0,2184.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(sk_c9,sk_c9) equal(multiply(u,sk_c11),sk_c9)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 2189[2:Obv:2187.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c9)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 2192[2:SpR:2186.0,251.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.38/0.58 2194[3:Spt:43.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.38/0.58 2196[3:Rew:2194.0,2189.8] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c9)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(sk_c11,sk_c11) -> .
% 0.38/0.58 2197[3:Obv:2196.8] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,sk_c11),sk_c9)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** -> .
% 0.38/0.58 2199[3:SpR:2194.0,64.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.38/0.58 2200[3:SpR:2194.0,109.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c9)**.
% 0.38/0.58 2204[3:Rew:2186.0,2200.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.38/0.58 2205[3:Rew:2192.0,2199.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.58 2206[4:Spt:52.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.38/0.58 2210[5:Spt:54.0] || -> equal(inverse(sk_c8),sk_c11)**.
% 0.38/0.58 2211[5:SpR:2210.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c8,u)),u)**.
% 0.38/0.58 2214[5:Rew:2205.0,2211.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.38/0.58 2215[5:Rew:2214.0,5.0] || -> equal(sk_c9,sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 2220[5:Rew:2214.0,11.1] || -> equal(inverse(sk_c1),sk_c11)** equal(sk_c9,sk_c11).
% 0.38/0.58 2226[6:Spt:51.1] || -> equal(multiply(sk_c7,sk_c10),sk_c11)**.
% 0.38/0.58 2229[6:SpR:2226.0,308.0] || -> equal(multiply(inverse(sk_c11),multiply(sk_c7,u)),multiply(inverse(sk_c10),u))**.
% 0.38/0.58 2234[6:Rew:2186.0,2229.0] || -> equal(multiply(inverse(sk_c11),multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.38/0.58 2236[3:SpR:2204.0,109.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.38/0.58 2240[3:Rew:63.0,2236.0] || -> equal(identity,sk_c11)**.
% 0.38/0.58 2242[3:Rew:2240.0,1572.0] || -> equal(multiply(inverse(sk_c11),u),u)**.
% 0.38/0.58 2243[3:Rew:2240.0,63.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.38/0.58 2244[6:Rew:2242.0,2234.0] || -> equal(multiply(sk_c7,u),multiply(sk_c9,u))**.
% 0.38/0.58 2246[6:Rew:2244.0,2226.0] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.38/0.58 2257[3:SpR:2243.0,251.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.38/0.58 2259[3:SpR:2186.0,2243.0] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.38/0.58 2260[4:SpR:2206.0,2243.0] || -> equal(multiply(sk_c10,sk_c7),sk_c11)**.
% 0.38/0.58 2261[5:SpR:2210.0,2243.0] || -> equal(multiply(sk_c11,sk_c8),sk_c11)**.
% 0.38/0.58 2266[3:Rew:2257.0,2197.7] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11)** equal(multiply(u,sk_c11),sk_c9)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(x,sk_c10) -> .
% 0.38/0.58 2267[5:Rew:2257.0,2215.1] || -> equal(sk_c9,sk_c11)** equal(sk_c10,sk_c1).
% 0.38/0.58 2268[5:Rew:2205.0,2261.0] || -> equal(sk_c8,sk_c11)**.
% 0.38/0.58 2269[5:Rew:2268.0,2210.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 2283[3:Rew:2257.0,2266.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11)** equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(x,sk_c10) -> .
% 0.38/0.58 2294[6:SpR:2246.0,109.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c10)**.
% 0.38/0.58 2298[6:Rew:2257.0,2294.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.38/0.58 2303[7:Spt:2267.1] || -> equal(sk_c10,sk_c1)**.
% 0.38/0.58 2304[7:Rew:2303.0,2186.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.38/0.58 2313[7:Rew:2303.0,2283.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c1) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11)** equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(w,sk_c10),sk_c9)** equal(x,sk_c10) -> .
% 0.38/0.58 2314[7:Rew:2303.0,2298.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.38/0.58 2315[7:Rew:2304.0,2220.0] || -> equal(sk_c9,sk_c11)** equal(sk_c9,sk_c11)**.
% 0.38/0.58 2316[7:Obv:2315.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2319[7:Rew:2316.0,2314.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.38/0.58 2322[7:Rew:2269.0,2319.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 2326[7:Rew:2322.0,2269.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.38/0.58 2328[7:Rew:2322.0,2257.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.38/0.58 2330[7:Rew:2322.0,2316.0] || -> equal(sk_c9,sk_c1)**.
% 0.38/0.58 2341[7:Rew:2303.0,2313.7,2328.0,2313.6,2303.0,2313.6,2330.0,2313.6,2328.0,2313.5,2303.0,2313.5,2322.0,2313.5,2330.0,2313.4,2322.0,2313.3,2303.0,2313.2,2322.0,2313.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.38/0.58 2342[7:Con:2341.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.38/0.58 2384[7:SpL:2326.0,2342.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 2386[7:Obv:2384.1] || -> .
% 0.38/0.58 2387[7:Spt:2386.0,2267.1,2303.0] || equal(sk_c10,sk_c1)** -> .
% 0.38/0.58 2388[7:Spt:2386.0,2267.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2389[7:Rew:2388.0,2186.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.38/0.58 2390[7:Rew:2388.0,2298.0] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.38/0.58 2391[7:Rew:2390.0,2269.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.58 2393[7:Rew:2391.0,2389.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 2406[7:Rew:2391.0,2283.7,2257.0,2283.6,2391.0,2283.6,2388.0,2283.6,2257.0,2283.5,2391.0,2283.5,2388.0,2283.4,2391.0,2283.2,2391.0,2283.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(inverse(x),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) equal(x,sk_c11) -> .
% 0.38/0.58 2407[7:Con:2406.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.38/0.58 2446[3:SpR:2243.0,2257.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.58 2458[7:SpL:2393.0,2407.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.38/0.58 2459[7:Obv:2458.1] || -> .
% 0.38/0.58 2460[6:Spt:2459.0,51.1,2226.0] || equal(multiply(sk_c7,sk_c10),sk_c11)** -> .
% 0.38/0.58 2461[6:Spt:2459.0,51.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 2469[6:MRR:9.1,2460.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 2474[3:Rew:2257.0,3.1] || -> equal(multiply(sk_c7,sk_c10),sk_c11)** equal(sk_c10,sk_c1).
% 0.38/0.58 2475[6:MRR:2474.0,2460.0] || -> equal(sk_c10,sk_c1)**.
% 0.38/0.58 2476[6:Rew:2475.0,2186.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.38/0.58 2478[6:Rew:2475.0,2194.0] || -> equal(multiply(sk_c1,sk_c9),sk_c11)**.
% 0.38/0.58 2479[6:Rew:2475.0,2260.0] || -> equal(multiply(sk_c1,sk_c7),sk_c11)**.
% 0.38/0.58 2481[6:Rew:2475.0,2460.0] || equal(multiply(sk_c7,sk_c1),sk_c11)** -> .
% 0.38/0.58 2491[6:Rew:2469.0,2476.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2492[6:Rew:2491.0,2478.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.38/0.58 2493[6:Rew:2257.0,2492.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 2496[6:Rew:2493.0,2257.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.38/0.58 2497[6:Rew:2493.0,2205.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.58 2504[6:Rew:2493.0,2479.0] || -> equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.38/0.58 2514[6:Rew:2497.0,2504.0] || -> equal(sk_c7,sk_c1)**.
% 0.38/0.58 2524[6:Rew:2496.0,2481.0,2514.0,2481.0,2493.0,2481.0] || equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 2525[6:Obv:2524.0] || -> .
% 0.38/0.58 2537[5:Spt:2525.0,54.0,2210.0] || equal(inverse(sk_c8),sk_c11)** -> .
% 0.38/0.58 2538[5:Spt:2525.0,54.1] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 2547[5:MRR:12.0,2537.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 2552[3:Rew:2257.0,6.1] || -> equal(inverse(sk_c8),sk_c11)** equal(sk_c10,sk_c1).
% 0.38/0.58 2553[5:MRR:2552.0,2537.0] || -> equal(sk_c10,sk_c1)**.
% 0.38/0.58 2555[5:Rew:2553.0,2186.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.38/0.58 2556[5:Rew:2553.0,2259.0] || -> equal(multiply(sk_c9,sk_c1),sk_c11)**.
% 0.38/0.58 2568[5:Rew:2547.0,2555.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2569[5:Rew:2205.0,2556.0,2568.0,2556.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 2571[5:Rew:2569.0,2446.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.38/0.58 2573[5:Rew:2569.0,2257.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.38/0.58 2579[5:Rew:2569.0,2568.0] || -> equal(sk_c9,sk_c1)**.
% 0.38/0.58 2625[5:Rew:2553.0,2283.7,2573.0,2283.6,2553.0,2283.6,2579.0,2283.6,2573.0,2283.5,2553.0,2283.5,2569.0,2283.5,2579.0,2283.4,2569.0,2283.3,2553.0,2283.2,2553.0,2283.1,2569.0,2283.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.38/0.58 2626[5:Con:2625.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.38/0.58 2694[5:SpL:2571.0,2626.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 2695[5:Obv:2694.1] || -> .
% 0.38/0.58 2696[4:Spt:2695.0,52.0,2206.0] || equal(inverse(sk_c7),sk_c10)** -> .
% 0.38/0.58 2697[4:Spt:2695.0,52.1] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 2704[4:MRR:10.0,2696.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 2712[3:Rew:2257.0,4.1] || -> equal(inverse(sk_c7),sk_c10)** equal(sk_c10,sk_c1).
% 0.38/0.58 2713[4:MRR:2712.0,2696.0] || -> equal(sk_c10,sk_c1)**.
% 0.38/0.58 2714[4:Rew:2713.0,2186.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.38/0.58 2715[4:Rew:2713.0,2194.0] || -> equal(multiply(sk_c1,sk_c9),sk_c11)**.
% 0.38/0.58 2725[4:Rew:2704.0,2714.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.58 2727[4:Rew:2257.0,2715.0,2725.0,2715.0] || -> equal(sk_c11,sk_c1)**.
% 0.38/0.58 2729[4:Rew:2727.0,2446.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.38/0.58 2730[4:Rew:2727.0,2257.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.38/0.58 2737[4:Rew:2727.0,2725.0] || -> equal(sk_c9,sk_c1)**.
% 0.38/0.58 2775[4:Rew:2713.0,2283.7,2730.0,2283.6,2713.0,2283.6,2737.0,2283.6,2730.0,2283.5,2713.0,2283.5,2727.0,2283.5,2737.0,2283.4,2727.0,2283.3,2713.0,2283.2,2713.0,2283.1,2727.0,2283.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.38/0.58 2776[4:Con:2775.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.38/0.58 2843[4:SpL:2729.0,2776.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.38/0.58 2844[4:Obv:2843.1] || -> .
% 0.38/0.58 2845[3:Spt:2844.0,43.1,2194.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.38/0.58 2846[3:Spt:2844.0,43.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.38/0.58 2847[3:MRR:31.1,2845.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.38/0.58 2849[3:MRR:7.1,2845.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.58 2850[3:MRR:49.1,2845.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.58 2851[3:MRR:55.0,2845.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.58 2852[3:MRR:37.0,2845.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.58 2853[3:MRR:25.0,2845.0] || -> equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.58 2855[3:MRR:1.0,2845.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.58 2863[3:SpR:2847.0,251.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.38/0.58 2868[3:SpR:2849.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.58 2872[3:SpR:2850.0,251.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.38/0.58 2875[3:SpR:2851.0,109.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.38/0.58 2879[3:Rew:2846.0,2875.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.38/0.58 2887[3:SpR:2853.0,64.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c11,u))**.
% 0.38/0.58 2888[3:SpR:2853.0,109.0] || -> equal(multiply(inverse(sk_c3),sk_c11),sk_c6)**.
% 0.38/0.59 2892[3:Rew:2847.0,2888.0] || -> equal(multiply(sk_c6,sk_c11),sk_c6)**.
% 0.38/0.59 2893[3:Rew:2863.0,2887.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.59 2894[3:Rew:2893.0,2868.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.59 2897[3:Rew:2894.0,2855.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.59 2898[3:Rew:2897.0,2186.0] || -> equal(inverse(sk_c11),sk_c9)**.
% 0.38/0.59 2900[3:Rew:2897.0,2852.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.38/0.59 2901[3:Rew:2897.0,2845.0] || equal(multiply(sk_c11,sk_c9),sk_c11)** -> .
% 0.38/0.59 2910[3:Rew:2892.0,2900.0] || -> equal(sk_c6,sk_c11)**.
% 0.38/0.59 2912[3:Rew:2910.0,2850.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.38/0.59 2917[3:Rew:2910.0,2872.0] || -> equal(multiply(sk_c4,multiply(sk_c11,u)),u)**.
% 0.38/0.59 2920[3:Rew:2910.0,2879.0] || -> equal(multiply(sk_c4,sk_c4),sk_c11)**.
% 0.38/0.59 2924[3:Rew:2893.0,2901.0] || equal(sk_c9,sk_c11)** -> .
% 0.38/0.59 2935[3:Rew:2893.0,2917.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.38/0.59 2936[3:Rew:2935.0,2920.0] || -> equal(sk_c4,sk_c11)**.
% 0.38/0.59 2940[3:Rew:2936.0,2912.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.59 2943[3:Rew:2898.0,2940.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.59 2944[3:MRR:2943.0,2924.0] || -> .
% 0.38/0.59 2953[2:Spt:2944.0,44.0,2186.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.38/0.59 2954[2:Spt:2944.0,44.1] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.38/0.59 2955[2:MRR:32.0,2953.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.38/0.59 2956[2:MRR:20.0,2953.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.59 2957[2:MRR:8.0,2953.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.38/0.59 2958[2:MRR:50.0,2953.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.38/0.59 2959[2:MRR:56.0,2953.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.38/0.59 2960[2:MRR:38.0,2953.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.38/0.59 2961[2:MRR:26.0,2953.0] || -> equal(multiply(sk_c3,sk_c6),sk_c11)**.
% 0.38/0.59 2962[2:MRR:14.0,2953.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.59 2963[2:MRR:2.0,2953.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.38/0.59 2968[2:SpR:2955.0,251.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.38/0.59 2970[2:SpR:2956.0,109.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.59 2973[2:SpR:2957.0,109.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.38/0.59 2977[2:SpR:2958.0,251.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.38/0.59 2980[2:SpR:2959.0,109.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.38/0.59 2984[2:Rew:2954.0,2980.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.38/0.59 2991[2:SpR:2961.0,64.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c11,u))**.
% 0.38/0.59 2992[2:SpR:2961.0,109.0] || -> equal(multiply(inverse(sk_c3),sk_c11),sk_c6)**.
% 0.38/0.59 2996[2:Rew:2955.0,2992.0] || -> equal(multiply(sk_c6,sk_c11),sk_c6)**.
% 0.38/0.59 2997[2:Rew:2968.0,2991.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.38/0.59 2998[2:Rew:2997.0,2973.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.38/0.59 3001[2:Rew:2998.0,2963.0] || -> equal(sk_c10,sk_c11)**.
% 0.38/0.59 3003[2:Rew:3001.0,2953.0] || equal(inverse(sk_c11),sk_c9)** -> .
% 0.38/0.59 3004[2:Rew:3001.0,2960.0] || -> equal(multiply(sk_c6,sk_c11),sk_c11)**.
% 0.38/0.59 3005[2:Rew:3001.0,2962.0] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.38/0.59 3006[2:Rew:3001.0,2970.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.38/0.59 3011[2:Rew:2996.0,3004.0] || -> equal(sk_c6,sk_c11)**.
% 0.38/0.59 3013[2:Rew:3011.0,2958.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.38/0.59 3018[2:Rew:3011.0,2977.0] || -> equal(multiply(sk_c4,multiply(sk_c11,u)),u)**.
% 0.38/0.59 3021[2:Rew:3011.0,2984.0] || -> equal(multiply(sk_c4,sk_c4),sk_c11)**.
% 0.38/0.59 3030[2:Rew:2997.0,3006.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.59 3031[2:Rew:3030.0,3005.0] || -> equal(sk_c9,sk_c11)**.
% 0.38/0.59 3032[2:Rew:3031.0,3003.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.38/0.59 3036[2:Rew:2997.0,3018.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.38/0.59 3037[2:Rew:3036.0,3021.0] || -> equal(sk_c4,sk_c11)**.
% 0.38/0.59 3041[2:Rew:3037.0,3013.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.38/0.59 3044[2:MRR:3041.0,3032.0] || -> .
% 0.38/0.59 % SZS output end Refutation
% 0.38/0.59 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_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_14 prove_this_17 prove_this_20 prove_this_23 prove_this_25 prove_this_26 prove_this_31 prove_this_32 prove_this_37 prove_this_38 prove_this_43 prove_this_44 prove_this_49 prove_this_50 prove_this_51 prove_this_52 prove_this_53 prove_this_54 prove_this_55 prove_this_56 prove_this_61 left_identity left_inverse associativity
% 0.38/0.59
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