TSTP Solution File: GRP377-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP377-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:47:06 EDT 2022
% Result : Unsatisfiable 0.18s 0.60s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP377-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 : Mon Jun 13 08:17:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.60
% 0.18/0.60 SPASS V 3.9
% 0.18/0.60 SPASS beiseite: Proof found.
% 0.18/0.60 % SZS status Theorem
% 0.18/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.60 SPASS derived 1911 clauses, backtracked 369 clauses, performed 9 splits and kept 924 clauses.
% 0.18/0.60 SPASS allocated 64867 KBytes.
% 0.18/0.60 SPASS spent 0:00:00.26 on the problem.
% 0.18/0.60 0:00:00.04 for the input.
% 0.18/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.60 0:00:00.02 for inferences.
% 0.18/0.60 0:00:00.00 for the backtracking.
% 0.18/0.60 0:00:00.18 for the reduction.
% 0.18/0.60
% 0.18/0.60
% 0.18/0.60 Here is a proof with depth 6, length 304 :
% 0.18/0.60 % SZS output start Refutation
% 0.18/0.60 1[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 2[0:Inp] || -> equal(inverse(sk_c2),sk_c10)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.60 5[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 6[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.60 7[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.18/0.60 8[0:Inp] || -> equal(inverse(sk_c6),sk_c5)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.60 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.60 10[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.60 11[0:Inp] || -> equal(multiply(sk_c2,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 12[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 21[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 22[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 23[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.60 24[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 25[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 26[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 31[0:Inp] || -> equal(multiply(sk_c2,sk_c10),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 32[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 33[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 34[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 35[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c10)** equal(multiply(sk_c8,sk_c9),sk_c10).
% 0.18/0.60 36[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 38[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 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_c9),sk_c10)** 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)* -> .
% 0.18/0.60 42[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.60 43[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.60 44[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.60 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_c9),sk_c10)** -> .
% 0.18/0.60 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)** -> .
% 0.18/0.60 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) -> .
% 0.18/0.60 48[2:Spt:9.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.18/0.60 53[3:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 55[4:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 62[2:SpR:48.0,43.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.18/0.60 63[3:SpR:53.0,43.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.18/0.60 74[2:SpR:62.0,44.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(identity,u))**.
% 0.18/0.60 76[0:SpR:43.0,44.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.60 79[2:Rew:42.0,74.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.18/0.60 81[0:Rew:42.0,76.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.60 85[3:SpR:63.0,79.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.18/0.60 89[3:SpR:85.0,44.0] || -> equal(multiply(sk_c9,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.18/0.60 92[3:Rew:42.0,89.0] || -> equal(multiply(sk_c1,u),multiply(sk_c9,u))**.
% 0.18/0.60 93[4:Rew:92.0,55.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.18/0.60 97[4:Rew:62.0,93.0] || -> equal(identity,sk_c9)**.
% 0.18/0.60 98[4:Rew:97.0,42.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.60 99[4:Rew:97.0,43.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.18/0.60 100[4:Rew:97.0,62.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.18/0.60 110[4:Rew:98.0,100.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 112[4:Rew:110.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 115[4:Rew:110.0,47.4] || 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) -> .
% 0.18/0.60 126[4:Rew:110.0,99.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.18/0.60 155[0:SpR:81.0,81.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.60 158[4:SpR:126.0,81.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.18/0.60 164[4:Rew:155.0,158.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.60 168[4:Rew:164.0,115.4] || 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) -> .
% 0.18/0.60 187[4:SpR:155.0,164.0] || -> equal(multiply(u,sk_c10),inverse(inverse(u)))**.
% 0.18/0.60 188[0:SpR:155.0,81.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.18/0.60 189[4:SpR:155.0,126.0] || -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.18/0.60 192[4:Rew:164.0,187.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.60 817[4:SpL:126.0,168.0] || 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) -> .
% 0.18/0.60 828[4:Rew:126.0,817.1,192.0,817.1,112.0,817.0] || equal(sk_c10,u) equal(sk_c10,u) equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.18/0.60 829[4:Obv:828.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)** equal(v,sk_c10) -> .
% 0.18/0.60 914[4:SpL:189.0,829.1] || equal(inverse(u),inverse(u))* equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) -> .
% 0.18/0.60 936[4:Obv:914.1] || equal(inverse(u),sk_c10)** -> .
% 0.18/0.60 937[4:UnC:936.0,192.0] || -> .
% 0.18/0.60 943[4:Spt:937.0,19.1,55.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.18/0.60 944[4:Spt:937.0,19.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 945[4:Rew:92.0,943.0] || equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.18/0.60 946[4:Rew:62.0,945.0] || equal(identity,sk_c9)** -> .
% 0.18/0.60 949[3:Rew:62.0,16.1,92.0,16.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c9).
% 0.18/0.60 950[4:MRR:949.1,946.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 953[3:Rew:62.0,12.1,92.0,12.1] || -> equal(inverse(sk_c2),sk_c10)** equal(identity,sk_c9).
% 0.18/0.60 954[4:MRR:953.1,946.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 960[3:Rew:62.0,15.1,92.0,15.1] || -> equal(multiply(sk_c4,sk_c7),sk_c10)** equal(identity,sk_c9).
% 0.18/0.60 961[4:MRR:960.1,946.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 964[3:Rew:62.0,11.1,92.0,11.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)** equal(identity,sk_c9).
% 0.18/0.60 965[4:MRR:964.1,946.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 995[4:SpR:950.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 1000[4:SpR:954.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 1027[2:SpR:62.0,81.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.18/0.60 1045[4:SpR:961.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 1051[4:Rew:995.0,1045.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 1052[4:Rew:1051.0,63.0] || -> equal(identity,sk_c1)**.
% 0.18/0.60 1053[4:Rew:1051.0,1000.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 1062[4:Rew:1052.0,946.0] || equal(sk_c1,sk_c9)** -> .
% 0.18/0.60 1074[4:Rew:1052.0,1027.0] || -> equal(multiply(inverse(sk_c9),sk_c1),sk_c10)**.
% 0.18/0.60 1076[4:Rew:1053.0,965.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 1077[4:Rew:1076.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 1095[4:Rew:1076.0,1062.0] || equal(sk_c1,sk_c10)** -> .
% 0.18/0.60 1117[4:Rew:1051.0,1074.0,1077.0,1074.0,1076.0,1074.0] || -> equal(sk_c1,sk_c10)**.
% 0.18/0.60 1118[4:MRR:1117.0,1095.0] || -> .
% 0.18/0.60 1164[3:Spt:1118.0,29.1,53.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.18/0.60 1165[3:Spt:1118.0,29.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 1167[3:MRR:26.1,1164.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 1169[3:MRR:22.1,1164.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 1172[3:MRR:25.0,1164.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 1174[3:MRR:21.0,1164.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 1185[3:SpR:1167.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 1190[3:SpR:1169.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 1219[3:SpR:1172.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 1225[3:Rew:1185.0,1219.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 1227[3:Rew:1225.0,1190.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 1234[3:Rew:1227.0,1174.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 1235[3:Rew:1234.0,48.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 1237[3:Rew:1234.0,62.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.18/0.60 1253[3:Rew:1234.0,47.4] || 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) -> .
% 0.18/0.60 1259[3:Rew:1225.0,1237.0] || -> equal(identity,sk_c10)**.
% 0.18/0.60 1262[3:Rew:1259.0,43.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.18/0.60 1371[3:SpR:1262.0,81.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.18/0.60 1375[3:SpR:1262.0,188.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.60 1385[3:Rew:1375.0,1253.4] || 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) -> .
% 0.18/0.60 1400[3:Rew:1375.0,1371.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.60 1427[3:SpR:1375.0,188.0] || -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.18/0.60 1668[3:SpL:1262.0,1385.0] || 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) -> .
% 0.18/0.60 1677[3:Rew:1262.0,1668.1,1400.0,1668.1,1235.0,1668.0] || equal(sk_c10,u) equal(sk_c10,u) equal(inverse(v),u) equal(multiply(v,u),sk_c10)** equal(u,sk_c10) -> .
% 0.18/0.60 1678[3:Obv:1677.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)** equal(v,sk_c10) -> .
% 0.18/0.60 1975[3:SpL:1427.0,1678.1] || equal(inverse(u),inverse(u))* equal(sk_c10,sk_c10) equal(inverse(u),sk_c10) -> .
% 0.18/0.60 1997[3:Obv:1975.1] || equal(inverse(u),sk_c10)** -> .
% 0.18/0.60 1998[3:UnC:1997.0,1400.0] || -> .
% 0.18/0.60 2004[2:Spt:1998.0,9.1,48.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.18/0.60 2005[2:Spt:1998.0,9.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 2006[2:MRR:8.1,2004.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.18/0.60 2007[2:MRR:6.1,2004.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 2009[2:MRR:2.1,2004.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 2011[2:MRR:10.0,2004.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.60 2012[2:MRR:7.0,2004.0] || -> equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.18/0.60 2013[2:MRR:5.0,2004.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 2015[2:MRR:1.0,2004.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 2023[2:SpR:2005.0,81.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.60 2034[2:SpR:2007.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 2043[2:SpR:2009.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 2049[2:SpR:2011.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.18/0.60 2053[2:Rew:2006.0,2049.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.18/0.60 2061[2:SpR:2013.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 2062[2:SpR:2013.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c7)**.
% 0.18/0.60 2066[2:Rew:2007.0,2062.0] || -> equal(multiply(sk_c7,sk_c10),sk_c7)**.
% 0.18/0.60 2067[2:Rew:2034.0,2061.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 2069[2:Rew:2067.0,2043.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 2073[2:Rew:2069.0,2015.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 2075[2:Rew:2073.0,2004.0] || equal(inverse(sk_c10),sk_c10)** -> .
% 0.18/0.60 2076[2:Rew:2073.0,2012.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.18/0.60 2090[2:Rew:2066.0,2076.0] || -> equal(sk_c7,sk_c10)**.
% 0.18/0.60 2091[2:Rew:2090.0,2005.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.18/0.60 2095[2:Rew:2090.0,2023.0] || -> equal(multiply(sk_c10,multiply(sk_c5,u)),u)**.
% 0.18/0.60 2104[2:Rew:2090.0,2053.0] || -> equal(multiply(sk_c5,sk_c5),sk_c10)**.
% 0.18/0.60 2115[2:Rew:2067.0,2095.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.60 2116[2:Rew:2115.0,2104.0] || -> equal(sk_c5,sk_c10)**.
% 0.18/0.60 2122[2:Rew:2116.0,2091.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 2125[2:MRR:2122.0,2075.0] || -> .
% 0.18/0.60 2145[1:Spt:2125.0,45.3,45.4,45.5,45.9,45.10,45.11] || 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_c9),sk_c10)** -> .
% 0.18/0.60 2147[2:Spt:8.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.18/0.60 2148[2:Rew:2147.0,2145.2] || 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_c9),sk_c10)** -> .
% 0.18/0.60 2150[2:Obv:2148.2] || 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_c9),sk_c10)** -> .
% 0.18/0.60 2152[2:SpR:2147.0,81.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.18/0.60 2153[2:SpR:2147.0,188.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.18/0.60 2157[3:Spt:38.1] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.60 2159[3:Rew:2157.0,2150.4] || 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_c10,sk_c10) -> .
% 0.18/0.60 2160[3:Obv:2159.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.18/0.60 2162[3:SpR:2157.0,44.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.18/0.60 2168[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.60 2170[4:SpR:2168.0,188.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),u)**.
% 0.18/0.60 2174[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.60 2175[5:SpR:2174.0,44.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.18/0.60 2176[5:SpR:2174.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.18/0.60 2180[5:Rew:2168.0,2176.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.60 2181[5:Rew:2170.0,2175.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.60 2184[5:Rew:2181.0,2152.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 2187[5:Rew:2181.0,2162.0] || -> equal(multiply(sk_c8,u),multiply(sk_c10,u))**.
% 0.18/0.60 2190[5:Rew:2184.0,2180.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 2193[5:Rew:2190.0,2147.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 2196[5:Rew:2190.0,2160.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.18/0.60 2201[5:Rew:2184.0,2187.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.60 2208[5:Rew:2190.0,2196.3,2190.0,2196.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c8)** equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.18/0.60 2257[0:SpR:43.0,81.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.60 2263[0:SpR:43.0,188.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.60 2265[4:SpR:2168.0,43.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.18/0.60 2266[5:SpR:2193.0,43.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.18/0.60 2267[5:Rew:2184.0,2265.0] || -> equal(identity,sk_c1)**.
% 0.18/0.60 2271[5:Rew:2267.0,2263.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.60 2272[5:Rew:2184.0,2266.0] || -> equal(identity,sk_c10)**.
% 0.18/0.60 2273[5:Rew:2267.0,2272.0] || -> equal(sk_c1,sk_c10)**.
% 0.18/0.60 2279[5:Rew:2273.0,2271.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.60 2281[5:Rew:2279.0,2208.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10)** equal(multiply(u,sk_c10),sk_c8)** equal(v,sk_c10) -> .
% 0.18/0.60 2298[5:Rew:2279.0,2281.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c8) equal(v,sk_c10) -> .
% 0.18/0.60 2311[5:SpR:2279.0,2201.0] || -> equal(sk_c8,sk_c10)**.
% 0.18/0.60 2314[5:Rew:2311.0,2298.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) -> .
% 0.18/0.60 2325[5:Con:2314.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.18/0.60 2327[5:SpL:2193.0,2325.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.18/0.60 2328[5:Obv:2327.1] || -> .
% 0.18/0.60 2329[5:Spt:2328.0,19.1,2174.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.18/0.60 2330[5:Spt:2328.0,19.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 2331[0:Rew:2263.0,2257.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.60 2333[5:MRR:16.1,2329.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 2335[5:MRR:12.1,2329.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 2339[5:MRR:15.1,2329.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 2341[5:MRR:11.1,2329.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 2368[5:SpR:2333.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 2377[5:SpR:2335.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 2389[4:SpR:2265.0,81.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.18/0.60 2393[4:Rew:2147.0,2389.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.18/0.60 2394[4:Rew:2263.0,2393.0] || -> equal(sk_c1,sk_c9)**.
% 0.18/0.60 2396[4:Rew:2394.0,2265.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.18/0.60 2397[5:Rew:2394.0,2329.0] || equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.18/0.60 2426[5:SpR:2339.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 2432[5:Rew:2368.0,2426.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 2433[5:Rew:2432.0,2377.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 2434[5:Rew:2432.0,2396.0] || -> equal(identity,sk_c9)**.
% 0.18/0.60 2448[5:Rew:2434.0,2263.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.60 2451[5:Rew:2433.0,2341.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 2469[5:Rew:2451.0,2397.0] || equal(multiply(sk_c10,sk_c10),sk_c10)** -> .
% 0.18/0.60 2475[5:Rew:2451.0,2448.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.60 2511[5:Rew:2475.0,2469.0] || equal(sk_c10,sk_c10)* -> .
% 0.18/0.60 2512[5:Obv:2511.0] || -> .
% 0.18/0.60 2549[4:Spt:2512.0,29.1,2168.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.18/0.60 2550[4:Spt:2512.0,29.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 2552[4:MRR:26.1,2549.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 2553[4:MRR:24.1,2549.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.60 2554[4:MRR:22.1,2549.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 2557[4:MRR:25.0,2549.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 2558[4:MRR:23.0,2549.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.60 2559[4:MRR:21.0,2549.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 2576[4:SpR:2552.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 2581[4:SpR:2553.0,188.0] || -> equal(multiply(sk_c3,multiply(sk_c9,u)),u)**.
% 0.18/0.60 2585[4:SpR:2554.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 2610[4:SpR:2557.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 2616[4:Rew:2576.0,2610.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 2619[4:Rew:2616.0,2585.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 2626[4:Rew:2619.0,2559.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 2627[4:Rew:2626.0,2147.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.60 2632[4:Rew:2626.0,2581.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),u)**.
% 0.18/0.60 2633[4:Rew:2626.0,2558.0] || -> equal(multiply(sk_c3,sk_c10),sk_c8)**.
% 0.18/0.60 2640[4:Rew:2626.0,2160.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.18/0.60 2667[4:Rew:2616.0,2632.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.18/0.60 2668[4:Rew:2667.0,2633.0] || -> equal(sk_c8,sk_c10)**.
% 0.18/0.60 2704[4:Rew:2626.0,2640.3,2626.0,2640.2,2668.0,2640.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c10),sk_c10)** -> .
% 0.18/0.60 2705[4:Con:2704.1] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.18/0.60 2806[4:SpR:2616.0,2263.0] || -> equal(identity,sk_c10)**.
% 0.18/0.60 2811[4:Rew:2806.0,2263.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.60 2816[4:Rew:2811.0,2705.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.18/0.60 2871[4:SpL:2627.0,2816.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.18/0.60 2873[4:Obv:2871.1] || -> .
% 0.18/0.60 2874[3:Spt:2873.0,38.1,2157.0] || equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.60 2875[3:Spt:2873.0,38.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.18/0.60 2876[3:MRR:36.1,2874.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 2877[3:MRR:34.1,2874.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.60 2878[3:MRR:32.1,2874.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 2882[3:MRR:35.1,2874.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 2883[3:MRR:33.1,2874.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.60 2884[3:MRR:31.1,2874.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 2899[3:SpR:2876.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 2917[2:SpR:2147.0,2331.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.18/0.60 2923[3:SpR:2877.0,2331.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.18/0.60 2926[3:Rew:2917.0,2923.0] || -> equal(sk_c3,sk_c10)**.
% 0.18/0.60 2928[3:Rew:2926.0,2883.0] || -> equal(multiply(sk_c10,sk_c9),sk_c8)**.
% 0.18/0.60 2936[3:SpR:2878.0,2331.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.18/0.60 2939[3:Rew:2147.0,2936.0] || -> equal(sk_c2,sk_c9)**.
% 0.18/0.60 2941[3:Rew:2939.0,2884.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.18/0.60 2968[3:SpR:2882.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 2974[3:Rew:2899.0,2968.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 2976[3:Rew:2974.0,2928.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.60 2978[3:Rew:2974.0,2153.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.60 2983[3:Rew:2976.0,2874.0] || equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.18/0.60 2984[3:Rew:2978.0,2941.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 3013[3:Rew:2974.0,2983.0,2984.0,2983.0] || equal(sk_c10,sk_c10)* -> .
% 0.18/0.60 3014[3:Obv:3013.0] || -> .
% 0.18/0.60 3028[2:Spt:3014.0,8.1,2147.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.18/0.60 3029[2:Spt:3014.0,8.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.18/0.60 3030[2:MRR:6.1,3028.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.60 3032[2:MRR:2.1,3028.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.18/0.60 3033[2:MRR:9.1,3028.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.60 3034[2:MRR:10.0,3028.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.60 3035[2:MRR:7.0,3028.0] || -> equal(multiply(sk_c7,sk_c9),sk_c10)**.
% 0.18/0.60 3036[2:MRR:5.0,3028.0] || -> equal(multiply(sk_c4,sk_c7),sk_c10)**.
% 0.18/0.60 3038[2:MRR:1.0,3028.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.18/0.60 3042[2:SpR:3029.0,2331.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.60 3045[2:Rew:3033.0,3042.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.60 3046[2:Rew:3045.0,3029.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.60 3047[2:Rew:3045.0,3034.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.18/0.60 3054[2:SpR:3030.0,188.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.18/0.60 3056[2:SpR:3030.0,2331.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.60 3059[2:Rew:3046.0,3056.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.60 3061[2:Rew:3059.0,3046.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.60 3062[2:Rew:3059.0,3047.0] || -> equal(multiply(sk_c7,sk_c7),sk_c4)**.
% 0.18/0.60 3074[2:SpR:3032.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.18/0.60 3077[2:SpR:3032.0,2331.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.18/0.60 3080[2:Rew:3077.0,3028.0] || equal(sk_c2,sk_c9)** -> .
% 0.18/0.60 3107[2:SpR:3036.0,44.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c10,u))**.
% 0.18/0.60 3108[2:SpR:3036.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c7)**.
% 0.18/0.60 3112[2:Rew:3030.0,3108.0] || -> equal(multiply(sk_c7,sk_c10),sk_c7)**.
% 0.18/0.60 3113[2:Rew:3054.0,3107.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.60 3115[2:Rew:3113.0,3074.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.60 3120[2:Rew:3115.0,3038.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.60 3125[2:Rew:3120.0,3080.0] || equal(sk_c2,sk_c10)** -> .
% 0.18/0.60 3126[2:Rew:3120.0,3035.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.18/0.60 3137[2:Rew:3112.0,3126.0] || -> equal(sk_c7,sk_c10)**.
% 0.18/0.60 3140[2:Rew:3137.0,3061.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.18/0.60 3142[2:Rew:3137.0,3062.0] || -> equal(multiply(sk_c10,sk_c10),sk_c4)**.
% 0.18/0.60 3150[2:Rew:3077.0,3140.0] || -> equal(sk_c4,sk_c2)**.
% 0.18/0.60 3156[2:Rew:3113.0,3142.0,3150.0,3142.0] || -> equal(sk_c2,sk_c10)**.
% 0.18/0.60 3157[2:MRR:3156.0,3125.0] || -> .
% 0.18/0.60 % SZS output end Refutation
% 0.18/0.60 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_41 left_identity left_inverse associativity
% 0.44/0.61
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