TSTP Solution File: GRP375-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP375-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:47:05 EDT 2022
% Result : Unsatisfiable 0.38s 0.55s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP375-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 01:28:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.38/0.55
% 0.38/0.55 SPASS V 3.9
% 0.38/0.55 SPASS beiseite: Proof found.
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.55 SPASS derived 1573 clauses, backtracked 397 clauses, performed 9 splits and kept 910 clauses.
% 0.38/0.55 SPASS allocated 64625 KBytes.
% 0.38/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.38/0.55 0:00:00.04 for the input.
% 0.38/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.55 0:00:00.01 for inferences.
% 0.38/0.55 0:00:00.00 for the backtracking.
% 0.38/0.55 0:00:00.14 for the reduction.
% 0.38/0.55
% 0.38/0.55
% 0.38/0.55 Here is a proof with depth 5, length 334 :
% 0.38/0.55 % SZS output start Refutation
% 0.38/0.55 1[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 2[0:Inp] || -> equal(inverse(sk_c2),sk_c10)** equal(inverse(sk_c10),sk_c9).
% 0.38/0.55 5[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 6[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c10),sk_c9).
% 0.38/0.55 7[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.38/0.55 8[0:Inp] || -> equal(inverse(sk_c6),sk_c5)** equal(inverse(sk_c10),sk_c9).
% 0.38/0.55 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c10),sk_c9).
% 0.38/0.55 10[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.38/0.55 11[0:Inp] || -> equal(multiply(sk_c2,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 12[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 21[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 22[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 23[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.38/0.55 24[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 25[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 26[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 31[0:Inp] || -> equal(multiply(sk_c2,sk_c10),sk_c9) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 32[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 33[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 34[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 35[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c10)** equal(multiply(sk_c8,sk_c10),sk_c9).
% 0.38/0.55 36[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 38[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 39[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 41[0:Inp] || equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c10),sk_c9)** equal(inverse(u),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(inverse(v),sk_c10) equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(x,y),sk_c10)** equal(inverse(x),y) equal(multiply(y,sk_c9),sk_c10)** equal(inverse(z),x1) equal(inverse(x1),y)* equal(multiply(z,y),x1)* -> .
% 0.38/0.55 42[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.38/0.55 43[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.38/0.55 44[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.38/0.55 45[0:Con:41.4] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c9) equal(inverse(z),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(y,sk_c9),sk_c8)** equal(multiply(z,sk_c10),sk_c9)** equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 46[1:Spt:45.0,45.1,45.2,45.6,45.7,45.8] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.38/0.55 47[1:EqR:46.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c10)** equal(multiply(v,sk_c9),sk_c10) -> .
% 0.38/0.55 48[2:Spt:9.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.38/0.55 50[3:Spt:39.1] || -> equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 52[3:SpL:50.0,46.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c8),u)* equal(inverse(v),sk_c10) equal(sk_c9,u) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c10)** -> .
% 0.38/0.55 53[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 55[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 62[2:SpR:48.0,43.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.38/0.55 63[4:SpR:53.0,43.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.38/0.55 74[2:SpR:62.0,44.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(identity,u))**.
% 0.38/0.55 76[0:SpR:43.0,44.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.38/0.55 79[2:Rew:42.0,74.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.38/0.55 81[0:Rew:42.0,76.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.38/0.55 85[4:SpR:63.0,79.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.38/0.55 89[4:SpR:85.0,44.0] || -> equal(multiply(sk_c9,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.38/0.55 92[4:Rew:42.0,89.0] || -> equal(multiply(sk_c1,u),multiply(sk_c9,u))**.
% 0.38/0.55 93[5:Rew:92.0,55.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.38/0.55 97[5:Rew:62.0,93.0] || -> equal(identity,sk_c9)**.
% 0.38/0.55 98[5:Rew:97.0,42.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.38/0.55 99[5:Rew:97.0,43.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.38/0.55 100[5:Rew:97.0,62.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.38/0.55 109[5:Rew:98.0,100.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 111[5:Rew:109.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 114[5:Rew:109.0,47.4] || 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) -> .
% 0.38/0.55 126[5:Rew:109.0,99.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.38/0.55 153[0:SpR:81.0,81.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.38/0.55 156[5:SpR:126.0,81.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.38/0.55 162[5:Rew:153.0,156.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.38/0.55 166[5:Rew:162.0,114.4] || 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) -> .
% 0.38/0.55 185[5:SpR:153.0,162.0] || -> equal(multiply(u,sk_c10),inverse(inverse(u)))**.
% 0.38/0.55 186[0:SpR:153.0,81.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.38/0.55 187[5:SpR:153.0,126.0] || -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.38/0.55 190[5:Rew:162.0,185.0] || -> equal(inverse(inverse(u)),u)**.
% 0.38/0.55 815[5:SpL:126.0,166.0] || 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) -> .
% 0.38/0.55 826[5:Rew:126.0,815.1,190.0,815.1,111.0,815.0] || equal(sk_c10,u) equal(sk_c10,u) equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.38/0.55 827[5:Obv:826.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)** equal(v,sk_c10) -> .
% 0.38/0.55 912[5:SpL:187.0,827.1] || equal(inverse(u),inverse(u))* equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) -> .
% 0.38/0.55 934[5:Obv:912.1] || equal(inverse(u),sk_c10)** -> .
% 0.38/0.55 935[5:UnC:934.0,190.0] || -> .
% 0.38/0.55 941[5:Spt:935.0,19.1,55.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.38/0.55 942[5:Spt:935.0,19.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 943[5:Rew:92.0,941.0] || equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.38/0.55 944[5:Rew:62.0,943.0] || equal(identity,sk_c9)** -> .
% 0.38/0.55 947[4:Rew:62.0,16.1,92.0,16.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c9).
% 0.38/0.55 948[5:MRR:947.1,944.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 951[4:Rew:62.0,12.1,92.0,12.1] || -> equal(inverse(sk_c2),sk_c10)** equal(identity,sk_c9).
% 0.38/0.55 952[5:MRR:951.1,944.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 958[4:Rew:62.0,15.1,92.0,15.1] || -> equal(multiply(sk_c4,sk_c7),sk_c10)** equal(identity,sk_c9).
% 0.38/0.55 959[5:MRR:958.1,944.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 962[4:Rew:62.0,11.1,92.0,11.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)** equal(identity,sk_c9).
% 0.38/0.55 963[5:MRR:962.1,944.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 993[5:SpR:948.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 998[5:SpR:952.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 1025[2:SpR:62.0,81.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.38/0.55 1043[5:SpR:959.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 1049[5:Rew:993.0,1043.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1050[5:Rew:1049.0,63.0] || -> equal(identity,sk_c1)**.
% 0.38/0.55 1051[5:Rew:1049.0,998.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 1061[5:Rew:1050.0,944.0] || equal(sk_c1,sk_c9)** -> .
% 0.38/0.55 1073[5:Rew:1050.0,1025.0] || -> equal(multiply(inverse(sk_c9),sk_c1),sk_c10)**.
% 0.38/0.55 1075[5:Rew:1051.0,963.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 1076[5:Rew:1075.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 1093[5:Rew:1075.0,1061.0] || equal(sk_c1,sk_c10)** -> .
% 0.38/0.55 1115[5:Rew:1049.0,1073.0,1076.0,1073.0,1075.0,1073.0] || -> equal(sk_c1,sk_c10)**.
% 0.38/0.55 1116[5:MRR:1115.0,1093.0] || -> .
% 0.38/0.55 1162[4:Spt:1116.0,29.1,53.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.38/0.55 1163[4:Spt:1116.0,29.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 1165[4:MRR:26.1,1162.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 1166[4:MRR:24.1,1162.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.38/0.55 1167[4:MRR:22.1,1162.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 1170[4:MRR:25.0,1162.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 1171[4:MRR:23.0,1162.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.38/0.55 1172[4:MRR:21.0,1162.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 1183[4:SpR:1165.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 1186[4:SpR:1166.0,186.0] || -> equal(multiply(sk_c3,multiply(sk_c9,u)),u)**.
% 0.38/0.55 1188[4:SpR:1167.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 1217[4:SpR:1170.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 1223[4:Rew:1183.0,1217.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1224[4:Rew:1223.0,52.5] || equal(inverse(u),sk_c10)** equal(inverse(sk_c8),u)* equal(inverse(v),sk_c10) equal(sk_c9,u) equal(multiply(v,sk_c10),sk_c10)** equal(sk_c9,sk_c10) -> .
% 0.38/0.55 1226[4:Rew:1223.0,1188.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 1233[4:Rew:1226.0,1172.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 1234[4:Rew:1233.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 1236[4:Rew:1233.0,62.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.38/0.55 1243[4:Rew:1233.0,1186.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),u)**.
% 0.38/0.55 1244[4:Rew:1233.0,1171.0] || -> equal(multiply(sk_c3,sk_c10),sk_c8)**.
% 0.38/0.55 1257[4:Rew:1223.0,1236.0] || -> equal(identity,sk_c10)**.
% 0.38/0.55 1260[4:Rew:1257.0,43.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.38/0.55 1280[4:Rew:1223.0,1243.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.38/0.55 1281[4:Rew:1280.0,1244.0] || -> equal(sk_c8,sk_c10)**.
% 0.38/0.55 1306[4:Rew:1233.0,1224.5,1233.0,1224.3,1234.0,1224.1,1281.0,1224.1] || 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) -> .
% 0.38/0.55 1307[4:Obv:1306.5] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.38/0.55 1373[4:SpR:1260.0,186.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.38/0.55 1385[4:Rew:1373.0,1307.3] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.38/0.55 1495[4:SpL:1234.0,1385.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.38/0.55 1497[4:Obv:1495.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.38/0.55 1499[4:SpL:1234.0,1497.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 1501[4:Obv:1499.1] || -> .
% 0.38/0.55 1502[3:Spt:1501.0,39.1,50.0] || equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 1503[3:Spt:1501.0,39.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 1505[3:MRR:36.1,1502.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 1506[3:MRR:34.1,1502.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.38/0.55 1507[3:MRR:32.1,1502.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 1510[3:MRR:35.1,1502.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 1511[3:MRR:33.1,1502.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.38/0.55 1512[3:MRR:31.1,1502.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 1523[3:SpR:1505.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 1526[3:SpR:1506.0,186.0] || -> equal(multiply(sk_c3,multiply(sk_c9,u)),u)**.
% 0.38/0.55 1528[3:SpR:1507.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 1551[3:SpR:1510.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 1557[3:Rew:1523.0,1551.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1560[3:Rew:1557.0,1528.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 1565[3:Rew:1560.0,1512.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 1571[3:Rew:1565.0,1502.0] || equal(multiply(sk_c8,sk_c10),sk_c10)** -> .
% 0.38/0.55 1573[3:Rew:1565.0,1526.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),u)**.
% 0.38/0.55 1574[3:Rew:1565.0,1511.0] || -> equal(multiply(sk_c3,sk_c10),sk_c8)**.
% 0.38/0.55 1608[3:Rew:1557.0,1573.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.38/0.55 1609[3:Rew:1608.0,1574.0] || -> equal(sk_c8,sk_c10)**.
% 0.38/0.55 1610[3:Rew:1609.0,1571.0] || equal(multiply(sk_c10,sk_c10),sk_c10)** -> .
% 0.38/0.55 1611[3:Rew:1557.0,1610.0] || equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 1612[3:Obv:1611.0] || -> .
% 0.38/0.55 1638[2:Spt:1612.0,9.1,48.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.38/0.55 1639[2:Spt:1612.0,9.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 1640[2:MRR:8.1,1638.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.38/0.55 1641[2:MRR:6.1,1638.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 1643[2:MRR:2.1,1638.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 1644[2:MRR:10.0,1638.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.38/0.55 1645[2:MRR:7.0,1638.0] || -> equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.38/0.55 1646[2:MRR:5.0,1638.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 1648[2:MRR:1.0,1638.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 1649[2:SpR:1639.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.38/0.55 1656[2:SpR:1641.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 1661[2:SpR:1643.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 1665[2:SpR:1644.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.38/0.55 1669[2:Rew:1640.0,1665.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.38/0.55 1676[2:SpR:1646.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 1677[2:SpR:1646.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c7)**.
% 0.38/0.55 1681[2:Rew:1641.0,1677.0] || -> equal(multiply(sk_c7,sk_c10),sk_c7)**.
% 0.38/0.55 1682[2:Rew:1656.0,1676.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1683[2:Rew:1682.0,1661.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 1686[2:Rew:1683.0,1648.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 1688[2:Rew:1686.0,1638.0] || equal(inverse(sk_c10),sk_c10)** -> .
% 0.38/0.55 1689[2:Rew:1686.0,1645.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.38/0.55 1701[2:Rew:1681.0,1689.0] || -> equal(sk_c7,sk_c10)**.
% 0.38/0.55 1702[2:Rew:1701.0,1639.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.38/0.55 1706[2:Rew:1701.0,1649.0] || -> equal(multiply(sk_c10,multiply(sk_c5,u)),u)**.
% 0.38/0.55 1711[2:Rew:1701.0,1669.0] || -> equal(multiply(sk_c5,sk_c5),sk_c10)**.
% 0.38/0.55 1723[2:Rew:1682.0,1706.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.38/0.55 1724[2:Rew:1723.0,1711.0] || -> equal(sk_c5,sk_c10)**.
% 0.38/0.55 1728[2:Rew:1724.0,1702.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 1731[2:MRR:1728.0,1688.0] || -> .
% 0.38/0.55 1744[1:Spt:1731.0,45.3,45.4,45.5,45.9,45.10,45.11] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c10),sk_c9)** equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 1746[2:Spt:8.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.38/0.55 1747[2:Rew:1746.0,1744.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 1749[2:Obv:1747.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 1751[2:SpR:1746.0,81.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.38/0.55 1752[2:SpR:1746.0,186.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.38/0.55 1754[3:Spt:38.1] || -> equal(multiply(sk_c8,sk_c10),sk_c9)**.
% 0.38/0.55 1756[3:Rew:1754.0,1749.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.38/0.55 1757[3:Obv:1756.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.38/0.55 1759[3:SpR:1754.0,44.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.38/0.55 1765[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.38/0.55 1767[4:SpR:1765.0,186.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),u)**.
% 0.38/0.55 1769[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 1770[5:SpR:1769.0,44.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.38/0.55 1771[5:SpR:1769.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.38/0.55 1775[5:Rew:1765.0,1771.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.38/0.55 1776[5:Rew:1767.0,1770.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.38/0.55 1777[5:Rew:1776.0,1751.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1779[5:Rew:1776.0,1759.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),u)**.
% 0.38/0.55 1781[5:Rew:1777.0,1775.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 1784[5:Rew:1781.0,1746.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 1787[5:Rew:1781.0,1757.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.38/0.55 1792[5:Rew:1777.0,1779.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.38/0.55 1797[5:Rew:1781.0,1787.3,1781.0,1787.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c8)** equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.38/0.55 1842[0:SpR:43.0,81.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.38/0.55 1846[0:SpR:43.0,186.0] || -> equal(multiply(u,identity),u)**.
% 0.38/0.55 1848[4:SpR:1765.0,43.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.38/0.55 1849[5:SpR:1784.0,43.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.38/0.55 1850[5:Rew:1777.0,1848.0] || -> equal(identity,sk_c1)**.
% 0.38/0.55 1854[5:Rew:1850.0,1846.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.38/0.55 1855[5:Rew:1777.0,1849.0] || -> equal(identity,sk_c10)**.
% 0.38/0.55 1856[5:Rew:1850.0,1855.0] || -> equal(sk_c1,sk_c10)**.
% 0.38/0.55 1861[5:Rew:1856.0,1854.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.38/0.55 1863[5:Rew:1861.0,1797.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10)** equal(multiply(u,sk_c10),sk_c8)** equal(v,sk_c10) -> .
% 0.38/0.55 1875[5:Rew:1861.0,1863.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c8) equal(v,sk_c10) -> .
% 0.38/0.55 1887[5:SpR:1861.0,1792.0] || -> equal(sk_c8,sk_c10)**.
% 0.38/0.55 1890[5:Rew:1887.0,1875.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) -> .
% 0.38/0.55 1898[5:Con:1890.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.38/0.55 1900[5:SpL:1784.0,1898.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 1901[5:Obv:1900.1] || -> .
% 0.38/0.55 1902[5:Spt:1901.0,19.1,1769.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.38/0.55 1903[5:Spt:1901.0,19.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 1904[0:Rew:1846.0,1842.0] || -> equal(inverse(inverse(u)),u)**.
% 0.38/0.55 1906[5:MRR:16.1,1902.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 1908[5:MRR:12.1,1902.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 1912[5:MRR:15.1,1902.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 1914[5:MRR:11.1,1902.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 1931[5:SpR:1906.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 1936[5:SpR:1908.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 1946[4:SpR:1848.0,81.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.38/0.55 1950[4:Rew:1746.0,1946.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.38/0.55 1951[4:Rew:1846.0,1950.0] || -> equal(sk_c1,sk_c9)**.
% 0.38/0.55 1953[4:Rew:1951.0,1848.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.38/0.55 1954[5:Rew:1951.0,1902.0] || equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.38/0.55 1983[5:SpR:1912.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 1989[5:Rew:1931.0,1983.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 1991[5:Rew:1989.0,1953.0] || -> equal(identity,sk_c9)**.
% 0.38/0.55 1993[5:Rew:1989.0,1936.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 2002[5:Rew:1991.0,1846.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.38/0.55 2005[5:Rew:1993.0,1914.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 2018[5:Rew:2005.0,1954.0] || equal(multiply(sk_c10,sk_c10),sk_c10)** -> .
% 0.38/0.55 2024[5:Rew:2005.0,2002.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.38/0.55 2055[5:Rew:2024.0,2018.0] || equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 2056[5:Obv:2055.0] || -> .
% 0.38/0.55 2081[4:Spt:2056.0,29.1,1765.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.38/0.55 2082[4:Spt:2056.0,29.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 2084[4:MRR:26.1,2081.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 2085[4:MRR:24.1,2081.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.38/0.55 2086[4:MRR:22.1,2081.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 2089[4:MRR:25.0,2081.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 2090[4:MRR:23.0,2081.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.38/0.55 2091[4:MRR:21.0,2081.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 2102[4:SpR:2084.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 2105[4:SpR:2085.0,186.0] || -> equal(multiply(sk_c3,multiply(sk_c9,u)),u)**.
% 0.38/0.55 2107[4:SpR:2086.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.55 2129[4:SpR:2089.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 2135[4:Rew:2102.0,2129.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 2136[4:Rew:2135.0,2107.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.55 2142[4:Rew:2136.0,2091.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 2143[4:Rew:2142.0,1746.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.38/0.55 2148[4:Rew:2142.0,2105.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),u)**.
% 0.38/0.55 2149[4:Rew:2142.0,2090.0] || -> equal(multiply(sk_c3,sk_c10),sk_c8)**.
% 0.38/0.55 2152[4:Rew:2142.0,1757.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.38/0.55 2177[4:Rew:2135.0,2148.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.38/0.55 2178[4:Rew:2177.0,2149.0] || -> equal(sk_c8,sk_c10)**.
% 0.38/0.55 2203[4:Rew:2142.0,2152.3,2142.0,2152.2,2178.0,2152.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.38/0.55 2204[4:Con:2203.1] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.38/0.55 2279[4:SpR:2135.0,1846.0] || -> equal(identity,sk_c10)**.
% 0.38/0.55 2284[4:Rew:2279.0,1846.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.38/0.55 2288[4:Rew:2284.0,2204.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.38/0.55 2335[4:SpL:2143.0,2288.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 2337[4:Obv:2335.1] || -> .
% 0.38/0.55 2338[3:Spt:2337.0,38.1,1754.0] || equal(multiply(sk_c8,sk_c10),sk_c9)** -> .
% 0.38/0.55 2339[3:Spt:2337.0,38.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.38/0.55 2340[3:MRR:36.1,2338.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 2341[3:MRR:34.1,2338.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.38/0.55 2342[3:MRR:32.1,2338.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 2346[3:MRR:35.1,2338.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.55 2347[3:MRR:33.1,2338.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.38/0.55 2348[3:MRR:31.1,2338.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.55 2359[3:SpR:2340.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.55 2372[2:SpR:1746.0,1904.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.38/0.55 2376[3:SpR:2341.0,1904.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.38/0.55 2378[3:Rew:2372.0,2376.0] || -> equal(sk_c3,sk_c10)**.
% 0.38/0.55 2380[3:Rew:2378.0,2347.0] || -> equal(multiply(sk_c10,sk_c9),sk_c8)**.
% 0.38/0.55 2385[3:SpR:2342.0,1904.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.38/0.55 2387[3:Rew:1746.0,2385.0] || -> equal(sk_c2,sk_c9)**.
% 0.38/0.55 2389[3:Rew:2387.0,2348.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.38/0.55 2409[3:SpR:2346.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.55 2415[3:Rew:2359.0,2409.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.55 2416[3:Rew:2415.0,2380.0] || -> equal(sk_c8,sk_c9)**.
% 0.38/0.55 2417[3:Rew:2415.0,1752.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.38/0.55 2421[3:Rew:2416.0,2338.0] || equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.38/0.55 2422[3:Rew:2417.0,2389.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.55 2447[3:Rew:2415.0,2421.0,2422.0,2421.0] || equal(sk_c10,sk_c10)* -> .
% 0.38/0.55 2448[3:Obv:2447.0] || -> .
% 0.38/0.55 2456[2:Spt:2448.0,8.1,1746.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.38/0.55 2457[2:Spt:2448.0,8.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.38/0.55 2458[2:MRR:6.1,2456.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.38/0.55 2460[2:MRR:2.1,2456.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.38/0.55 2461[2:MRR:9.1,2456.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.38/0.55 2462[2:MRR:10.0,2456.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.38/0.56 2463[2:MRR:7.0,2456.0] || -> equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.38/0.56 2464[2:MRR:5.0,2456.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.38/0.56 2466[2:MRR:1.0,2456.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.38/0.56 2469[2:SpR:2457.0,1904.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.38/0.56 2471[2:Rew:2461.0,2469.0] || -> equal(sk_c6,sk_c7)**.
% 0.38/0.56 2472[2:Rew:2471.0,2457.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.38/0.56 2473[2:Rew:2471.0,2462.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.38/0.56 2478[2:SpR:2458.0,186.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.38/0.56 2479[2:SpR:2458.0,1904.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.38/0.56 2481[2:Rew:2472.0,2479.0] || -> equal(sk_c5,sk_c4)**.
% 0.38/0.56 2483[2:Rew:2481.0,2472.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.38/0.56 2484[2:Rew:2481.0,2473.0] || -> equal(multiply(sk_c7,sk_c7),sk_c4)**.
% 0.38/0.56 2492[2:SpR:2460.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.38/0.56 2494[2:SpR:2460.0,1904.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.38/0.56 2496[2:Rew:2494.0,2456.0] || equal(sk_c2,sk_c9)** -> .
% 0.38/0.56 2516[2:SpR:2464.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.38/0.56 2517[2:SpR:2464.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c7)**.
% 0.38/0.56 2521[2:Rew:2458.0,2517.0] || -> equal(multiply(sk_c7,sk_c10),sk_c7)**.
% 0.38/0.56 2522[2:Rew:2478.0,2516.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.38/0.56 2523[2:Rew:2522.0,2492.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.38/0.56 2526[2:Rew:2523.0,2466.0] || -> equal(sk_c9,sk_c10)**.
% 0.38/0.56 2530[2:Rew:2526.0,2496.0] || equal(sk_c2,sk_c10)** -> .
% 0.38/0.56 2531[2:Rew:2526.0,2463.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.38/0.56 2539[2:Rew:2521.0,2531.0] || -> equal(sk_c7,sk_c10)**.
% 0.38/0.56 2542[2:Rew:2539.0,2483.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.38/0.56 2544[2:Rew:2539.0,2484.0] || -> equal(multiply(sk_c10,sk_c10),sk_c4)**.
% 0.38/0.56 2548[2:Rew:2494.0,2542.0] || -> equal(sk_c4,sk_c2)**.
% 0.38/0.56 2554[2:Rew:2522.0,2544.0,2548.0,2544.0] || -> equal(sk_c2,sk_c10)**.
% 0.38/0.56 2555[2:MRR:2554.0,2530.0] || -> .
% 0.38/0.56 % SZS output end Refutation
% 0.38/0.56 Formulae used in the proof : prove_this_1 prove_this_2 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_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_29 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_38 prove_this_39 prove_this_41 left_identity left_inverse associativity
% 0.38/0.56
%------------------------------------------------------------------------------