TSTP Solution File: GRP338-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP338-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 0.19s 0.58s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP338-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 09:20:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.58
% 0.19/0.58 SPASS V 3.9
% 0.19/0.58 SPASS beiseite: Proof found.
% 0.19/0.58 % SZS status Theorem
% 0.19/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.58 SPASS derived 1791 clauses, backtracked 552 clauses, performed 11 splits and kept 1110 clauses.
% 0.19/0.58 SPASS allocated 64754 KBytes.
% 0.19/0.58 SPASS spent 0:00:00.24 on the problem.
% 0.19/0.58 0:00:00.04 for the input.
% 0.19/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.58 0:00:00.01 for inferences.
% 0.19/0.58 0:00:00.00 for the backtracking.
% 0.19/0.58 0:00:00.16 for the reduction.
% 0.19/0.58
% 0.19/0.58
% 0.19/0.58 Here is a proof with depth 5, length 361 :
% 0.19/0.58 % SZS output start Refutation
% 0.19/0.58 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.19/0.58 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 3[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.19/0.58 4[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.19/0.58 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 41[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 43[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 45[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 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_c10),sk_c11)** equal(multiply(x2,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.19/0.58 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.58 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.58 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.58 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)** -> .
% 0.19/0.58 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) -> .
% 0.19/0.58 57[2:Spt:9.1] || -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 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)** -> .
% 0.19/0.58 60[3:Spt:49.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 62[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 64[5:Spt:39.1] || -> equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 68[6:Spt:29.1] || -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 76[3:SpR:60.0,53.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.19/0.58 77[4:SpR:62.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.19/0.58 92[3:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.58 94[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.58 95[4:SpR:77.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.58 97[3:Rew:52.0,92.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.19/0.58 98[4:Rew:52.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.19/0.58 99[0:Rew:52.0,94.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.58 103[5:SpR:64.0,97.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.19/0.58 105[5:Rew:57.0,103.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 106[5:Rew:105.0,57.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.19/0.58 117[6:SpR:68.0,98.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.19/0.58 122[0:SpR:99.0,99.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.58 126[3:SpR:76.0,99.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.19/0.58 127[3:SpR:97.0,99.0] || -> equal(multiply(inverse(sk_c10),u),multiply(sk_c2,u))**.
% 0.19/0.58 128[5:SpR:106.0,99.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c11)**.
% 0.19/0.58 130[0:SpR:53.0,99.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.58 139[5:Rew:53.0,128.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 140[5:Rew:139.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 141[5:Rew:139.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.19/0.58 142[5:Rew:139.0,76.0] || -> equal(multiply(sk_c10,sk_c2),sk_c11)**.
% 0.19/0.58 143[5:Rew:139.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.19/0.58 150[6:Rew:140.0,117.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 156[6:Rew:150.0,62.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.58 160[6:Rew:150.0,56.3] || 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) -> .
% 0.19/0.58 165[6:Rew:150.0,139.0] || -> equal(identity,sk_c10)**.
% 0.19/0.58 166[6:Rew:150.0,140.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.58 168[6:Rew:150.0,143.0] || -> equal(multiply(sk_c10,sk_c1),sk_c10)**.
% 0.19/0.58 170[6:Rew:166.0,168.0] || -> equal(sk_c1,sk_c10)**.
% 0.19/0.58 172[6:Rew:170.0,156.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 179[6:Rew:150.0,141.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.19/0.58 181[6:Rew:165.0,130.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.19/0.58 188[6:Rew:122.0,181.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.58 199[6:Rew:188.0,160.4,150.0,160.4] || 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) -> .
% 0.19/0.58 226[6:SpR:179.0,99.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.19/0.58 230[6:Rew:188.0,226.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.58 236[6:SpR:230.0,179.0] || -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.19/0.58 854[6:SpL:179.0,199.0] || 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) -> .
% 0.19/0.58 864[6:Rew:179.0,854.1,230.0,854.1,172.0,854.0] || equal(sk_c10,u) equal(sk_c10,u) equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.58 865[6:Obv:864.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)** equal(v,sk_c10) -> .
% 0.19/0.58 950[6:SpL:236.0,865.1] || equal(inverse(u),inverse(u))* equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) -> .
% 0.19/0.58 972[6:Obv:950.1] || equal(inverse(u),sk_c10)** -> .
% 0.19/0.58 973[6:UnC:972.0,230.0] || -> .
% 0.19/0.58 979[6:Spt:973.0,29.1,68.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.19/0.58 980[6:Spt:973.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 981[5:Rew:140.0,143.0] || -> equal(sk_c1,sk_c11)**.
% 0.19/0.58 982[5:Rew:981.0,62.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.19/0.58 986[6:Rew:140.0,979.0,981.0,979.0] || equal(sk_c11,sk_c10)** -> .
% 0.19/0.58 987[5:Rew:139.0,130.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.19/0.58 997[5:Rew:140.0,22.1,981.0,22.1] || -> equal(inverse(sk_c3),sk_c11)** equal(sk_c11,sk_c10).
% 0.19/0.58 998[6:MRR:997.1,986.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 999[5:Rew:122.0,987.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 1010[5:Rew:140.0,21.1,981.0,21.1,999.0,21.0] || -> equal(sk_c3,sk_c10)** equal(sk_c11,sk_c10).
% 0.19/0.58 1011[6:MRR:1010.1,986.0] || -> equal(sk_c3,sk_c10)**.
% 0.19/0.58 1012[6:Rew:1011.0,998.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.19/0.58 1013[6:Rew:1012.0,127.0] || -> equal(multiply(sk_c2,u),multiply(sk_c11,u))**.
% 0.19/0.58 1014[6:Rew:140.0,1013.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.58 1015[6:Rew:1014.0,97.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.58 1019[6:Rew:1015.0,142.0] || -> equal(sk_c2,sk_c11)**.
% 0.19/0.58 1020[6:Rew:1019.0,60.0] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.19/0.58 1022[6:Rew:982.0,1020.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 1023[6:MRR:1022.0,986.0] || -> .
% 0.19/0.58 1041[5:Spt:1023.0,39.1,64.0] || equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.19/0.58 1042[5:Spt:1023.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 1043[0:Rew:122.0,130.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.58 1045[3:Rew:1043.0,126.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.19/0.58 1049[5:MRR:36.1,1041.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 1051[5:MRR:32.1,1041.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 1055[5:MRR:35.1,1041.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 1057[5:MRR:31.1,1041.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 1059[3:Rew:1045.0,59.1] || equal(inverse(u),sk_c11)** equal(sk_c2,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)** -> .
% 0.19/0.58 1102[5:SpR:1055.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 1104[5:Rew:1049.0,1102.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 1110[5:SpR:1057.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 1112[5:Rew:1051.0,1110.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 1127[5:SpR:1104.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 1129[5:Rew:53.0,1127.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 1130[5:Rew:1129.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.19/0.58 1132[5:Rew:1129.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 1136[5:Rew:1129.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 1139[5:Rew:1132.0,1112.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 1140[5:Rew:1132.0,1130.0] || -> equal(sk_c1,sk_c11)**.
% 0.19/0.58 1149[5:Rew:1139.0,62.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.58 1162[5:Rew:1139.0,1041.0] || equal(multiply(sk_c2,sk_c10),sk_c10)** -> .
% 0.19/0.58 1170[5:Rew:1139.0,1140.0] || -> equal(sk_c1,sk_c10)**.
% 0.19/0.58 1171[5:Rew:1170.0,1149.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 1172[5:Rew:1045.0,1171.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.58 1178[5:Rew:1139.0,1136.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.58 1214[5:Rew:1178.0,1162.0,1172.0,1162.0] || equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 1215[5:Obv:1214.0] || -> .
% 0.19/0.58 1244[4:Spt:1215.0,19.1,62.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.19/0.58 1245[4:Spt:1215.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 1247[4:MRR:16.1,1244.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 1248[4:MRR:14.1,1244.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.58 1249[4:MRR:12.1,1244.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 1252[4:MRR:15.0,1244.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 1253[4:MRR:13.0,1244.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 1254[4:MRR:11.0,1244.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 1291[4:SpR:1252.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 1293[4:Rew:1247.0,1291.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 1299[4:SpR:1254.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 1301[4:Rew:1249.0,1299.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 1302[4:Rew:1301.0,1059.5] || equal(inverse(u),sk_c11)** equal(sk_c2,u) equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.19/0.58 1303[4:Obv:1302.5] || equal(inverse(u),sk_c11)** equal(sk_c2,u) equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.19/0.58 1309[4:SpR:1293.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 1311[4:Rew:53.0,1309.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 1313[4:Rew:1311.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 1314[4:Rew:1311.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 1321[4:Rew:1313.0,1301.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 1330[4:Rew:1321.0,57.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.58 1341[4:Rew:1321.0,1303.0] || equal(inverse(u),sk_c10)** equal(sk_c2,u) equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.19/0.58 1345[4:Rew:1321.0,1314.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.58 1346[4:Rew:1345.0,1253.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.58 1347[4:Rew:1346.0,1248.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.58 1350[4:Rew:1345.0,1330.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 1353[4:Rew:1350.0,1347.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 1355[4:Rew:1045.0,1353.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.58 1356[4:Rew:1355.0,1045.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 1401[4:Rew:1345.0,1341.4,1321.0,1341.4,1350.0,1341.3,1321.0,1341.2,1355.0,1341.1] || equal(inverse(u),sk_c10)** equal(sk_c10,u) equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.19/0.58 1402[4:Obv:1401.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.19/0.58 1624[4:SpL:1356.0,1402.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.19/0.58 1626[4:Obv:1624.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.58 1628[4:SpL:1356.0,1626.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 1630[4:Obv:1628.1] || -> .
% 0.19/0.58 1631[3:Spt:1630.0,49.1,60.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.19/0.58 1632[3:Spt:1630.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 1634[3:MRR:46.1,1631.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 1636[3:MRR:42.1,1631.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 1639[3:MRR:45.0,1631.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 1641[3:MRR:41.0,1631.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 1663[3:SpR:1639.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 1665[3:Rew:1634.0,1663.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 1671[3:SpR:1641.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 1673[3:Rew:1636.0,1671.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 1674[3:Rew:1673.0,59.5] || 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(sk_c11,sk_c11) -> .
% 0.19/0.58 1675[3:Obv:1674.5] || 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)** -> .
% 0.19/0.58 1681[3:SpR:1665.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 1683[3:Rew:53.0,1681.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 1684[3:Rew:1683.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 1685[3:Rew:1683.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 1690[3:Rew:1684.0,1641.0] || -> equal(sk_c3,sk_c10)**.
% 0.19/0.58 1691[3:Rew:1684.0,57.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 1692[3:Rew:1684.0,1675.4] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11)** equal(sk_c9,u) equal(v,sk_c11) -> .
% 0.19/0.58 1694[3:Rew:1690.0,1636.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.19/0.58 1702[3:Rew:1685.0,1673.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 1713[3:Rew:1702.0,1694.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 1757[3:Rew:1702.0,1692.4,1691.0,1692.3,1702.0,1692.2,1713.0,1692.1,1702.0,1692.0] || equal(inverse(u),sk_c10)** equal(sk_c10,u) equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.19/0.58 1758[3:Obv:1757.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.19/0.58 1939[3:SpL:1713.0,1758.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.19/0.58 1941[3:Obv:1939.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.58 1943[3:SpL:1713.0,1941.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 1945[3:Obv:1943.1] || -> .
% 0.19/0.58 1946[2:Spt:1945.0,9.1,57.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.19/0.58 1947[2:Spt:1945.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 1949[2:MRR:6.1,1946.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 1950[2:MRR:4.1,1946.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.58 1951[2:MRR:2.1,1946.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 1954[2:MRR:5.1,1946.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 1955[2:MRR:3.1,1946.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 1956[2:MRR:1.1,1946.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 1975[2:SpR:1954.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 1977[2:Rew:1949.0,1975.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 1979[2:SpR:1955.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.19/0.58 1981[2:Rew:1950.0,1979.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.19/0.58 1983[2:SpR:1956.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 1985[2:Rew:1951.0,1983.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 1991[2:SpR:1977.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 1993[2:Rew:53.0,1991.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 1994[2:Rew:1993.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 1995[2:Rew:1993.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2000[2:Rew:1994.0,1985.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 2010[2:Rew:2000.0,1946.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.58 2017[2:Rew:2000.0,1994.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.58 2018[2:Rew:2000.0,1995.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.58 2035[2:Rew:2017.0,1981.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 2049[2:Rew:2018.0,2010.0,2035.0,2010.0] || equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 2050[2:Obv:2049.0] || -> .
% 0.19/0.58 2069[1:Spt:2050.0,51.3,51.4,51.5,51.6,51.10,51.11,51.12,51.13,51.14] || 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_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.19/0.58 2071[2:Spt:8.1] || -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.19/0.58 2072[2:Rew:2071.0,2069.8] || 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_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** equal(sk_c9,sk_c9) -> .
% 0.19/0.58 2074[2:Obv:2072.8] || 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_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.19/0.58 2077[2:SpR:2071.0,99.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c11)**.
% 0.19/0.58 2079[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.58 2080[3:SpR:2079.0,99.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.19/0.58 2082[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.58 2083[4:SpR:2082.0,99.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.19/0.58 2085[5:Spt:29.1] || -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.19/0.58 2087[5:SpR:2085.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c10)**.
% 0.19/0.58 2089[5:Rew:2079.0,2087.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.19/0.58 2090[6:Spt:39.1] || -> equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.19/0.58 2092[6:SpR:2090.0,99.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c10)**.
% 0.19/0.58 2094[6:Rew:2071.0,2092.0,2082.0,2092.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 2096[6:Rew:2094.0,2074.4] || 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_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.19/0.58 2098[6:Rew:2094.0,2077.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c11)**.
% 0.19/0.58 2100[6:Rew:53.0,2098.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2101[6:Rew:2100.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2105[6:Rew:2101.0,2089.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 2108[6:Rew:2105.0,2090.0] || -> equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.19/0.58 2112[6:Rew:2105.0,2101.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.58 2115[6:Rew:2112.0,2108.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.58 2117[6:Rew:2115.0,2082.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.58 2126[6:Rew:2112.0,2096.7,2105.0,2096.7,2112.0,2096.6,2105.0,2096.6,2112.0,2096.5,2105.0,2096.5,2112.0,2096.4,2105.0,2096.3,2105.0,2096.1] || 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) -> .
% 0.19/0.58 2127[6:Con:2126.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.58 2156[6:SpL:2117.0,2127.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 2157[6:Obv:2156.1] || -> .
% 0.19/0.58 2158[6:Spt:2157.0,39.1,2090.0] || equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.19/0.58 2159[6:Spt:2157.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 2161[6:MRR:36.1,2158.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 2166[6:MRR:35.1,2158.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2201[6:SpR:2166.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2203[6:Rew:2161.0,2201.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2217[6:SpR:2203.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2219[6:Rew:53.0,2217.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2220[6:Rew:2219.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2224[6:Rew:2220.0,2089.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 2243[6:Rew:2224.0,2158.0] || equal(multiply(sk_c2,sk_c10),sk_c10)** -> .
% 0.19/0.58 2249[6:Rew:2224.0,2220.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.58 2271[6:Rew:2249.0,2083.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.58 2284[6:Rew:2271.0,2243.0] || equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 2285[6:Obv:2284.0] || -> .
% 0.19/0.58 2305[5:Spt:2285.0,29.1,2085.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.19/0.58 2306[5:Spt:2285.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 2308[5:MRR:26.1,2305.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 2310[5:MRR:22.1,2305.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 2313[5:MRR:25.1,2305.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2315[5:MRR:21.1,2305.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 2339[5:SpR:2313.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2341[5:Rew:2308.0,2339.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2347[5:SpR:2315.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 2349[5:Rew:2310.0,2347.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 2358[5:SpR:2341.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2360[5:Rew:53.0,2358.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2361[5:Rew:2360.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2365[5:Rew:2361.0,2349.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 2367[5:Rew:2361.0,2080.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.58 2380[5:Rew:2365.0,2305.0] || equal(multiply(sk_c1,sk_c10),sk_c10)** -> .
% 0.19/0.58 2420[5:Rew:2367.0,2380.0] || equal(sk_c10,sk_c10)* -> .
% 0.19/0.58 2421[5:Obv:2420.0] || -> .
% 0.19/0.58 2439[4:Spt:2421.0,49.1,2082.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.19/0.58 2440[4:Spt:2421.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 2442[4:MRR:46.1,2439.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 2443[4:MRR:44.1,2439.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.58 2444[4:MRR:42.1,2439.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 2447[4:MRR:45.0,2439.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2448[4:MRR:43.0,2439.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 2449[4:MRR:41.0,2439.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 2473[4:SpR:2447.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2475[4:Rew:2442.0,2473.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2481[4:SpR:2449.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 2483[4:Rew:2444.0,2481.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 2492[4:SpR:2475.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2494[4:Rew:53.0,2492.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2495[4:Rew:2494.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2496[4:Rew:2494.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2499[4:Rew:2495.0,2483.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.58 2508[4:Rew:2499.0,2071.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.58 2514[4:Rew:2499.0,2074.1] || 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_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.19/0.59 2519[4:Rew:2499.0,2496.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.59 2520[4:Rew:2519.0,2448.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.59 2521[4:Rew:2520.0,2443.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.59 2524[4:Rew:2519.0,2508.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.59 2527[4:Rew:2524.0,2521.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.59 2565[4:Rew:2519.0,2514.7,2499.0,2514.7,2519.0,2514.6,2499.0,2514.6,2519.0,2514.5,2499.0,2514.5,2519.0,2514.4,2524.0,2514.4,2499.0,2514.3] || 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) -> .
% 0.19/0.59 2566[4:Con:2565.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.59 2655[4:SpL:2527.0,2566.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.59 2657[4:Obv:2655.1] || -> .
% 0.19/0.59 2658[3:Spt:2657.0,19.1,2079.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.19/0.59 2659[3:Spt:2657.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.59 2661[3:MRR:16.1,2658.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.59 2662[3:MRR:14.1,2658.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.59 2663[3:MRR:12.1,2658.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.59 2666[3:MRR:15.0,2658.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.59 2667[3:MRR:13.0,2658.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.59 2668[3:MRR:11.0,2658.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.59 2690[3:SpR:2666.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.59 2692[3:Rew:2661.0,2690.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.59 2698[3:SpR:2668.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.59 2700[3:Rew:2663.0,2698.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.59 2706[3:SpR:2692.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.59 2708[3:Rew:53.0,2706.0] || -> equal(identity,sk_c11)**.
% 0.19/0.59 2709[3:Rew:2708.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.59 2710[3:Rew:2708.0,1043.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.59 2714[3:Rew:2709.0,2700.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.59 2720[3:Rew:2714.0,2071.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.59 2727[3:Rew:2714.0,2074.1] || 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_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.19/0.59 2732[3:Rew:2714.0,2710.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.59 2733[3:Rew:2732.0,2667.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.59 2734[3:Rew:2733.0,2662.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.59 2737[3:Rew:2732.0,2720.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.59 2740[3:Rew:2737.0,2734.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.59 2778[3:Rew:2732.0,2727.7,2714.0,2727.7,2732.0,2727.6,2714.0,2727.6,2732.0,2727.5,2714.0,2727.5,2732.0,2727.4,2737.0,2727.4,2714.0,2727.3] || 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) -> .
% 0.19/0.59 2779[3:Con:2778.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.59 2830[3:SpL:2740.0,2779.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.59 2832[3:Obv:2830.1] || -> .
% 0.19/0.59 2833[2:Spt:2832.0,8.1,2071.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.19/0.59 2834[2:Spt:2832.0,8.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.59 2835[2:MRR:6.1,2833.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.59 2836[2:MRR:4.1,2833.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.59 2837[2:MRR:2.1,2833.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.59 2841[2:MRR:5.1,2833.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.59 2842[2:MRR:3.1,2833.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.59 2843[2:MRR:1.1,2833.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.59 2862[2:SpR:2841.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.59 2864[2:Rew:2835.0,2862.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.59 2866[2:SpR:2842.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.19/0.59 2868[2:Rew:2836.0,2866.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.19/0.59 2870[2:SpR:2843.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.59 2872[2:Rew:2837.0,2870.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.59 2881[2:SpR:2864.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.59 2883[2:Rew:53.0,2881.0] || -> equal(identity,sk_c11)**.
% 0.19/0.59 2884[2:Rew:2883.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.59 2888[2:Rew:2884.0,2872.0] || -> equal(sk_c11,sk_c10)**.
% 0.19/0.59 2898[2:Rew:2888.0,2833.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.59 2901[2:Rew:2888.0,2884.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.59 2919[2:Rew:2901.0,2868.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.59 2933[2:Rew:2901.0,2898.0,2919.0,2898.0] || equal(sk_c10,sk_c10)* -> .
% 0.19/0.59 2934[2:Obv:2933.0] || -> .
% 0.19/0.59 % SZS output end Refutation
% 0.19/0.59 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_8 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_25 prove_this_26 prove_this_29 prove_this_31 prove_this_32 prove_this_35 prove_this_36 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_49 prove_this_51 left_identity left_inverse associativity
% 0.19/0.59
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