TSTP Solution File: GRP326-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP326-1 : 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 11:46:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP326-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 08:57:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 802 clauses, backtracked 247 clauses, performed 9 splits and kept 563 clauses.
% 0.20/0.47 SPASS allocated 63572 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.01 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.05 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 4, length 317 :
% 0.20/0.47 % SZS output start Refutation
% 0.20/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 2[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 3[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c6),sk_c7).
% 0.20/0.47 6[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 7[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.47 8[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c6).
% 0.20/0.47 9[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.47 10[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 11[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 13[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c3),sk_c6).
% 0.20/0.47 14[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 15[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 17[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 18[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.47 20[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 21[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.47 22[0:Inp] || equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(multiply(sk_c7,v),sk_c6)** equal(multiply(w,sk_c7),v)* equal(inverse(w),sk_c7) equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)** equal(inverse(x),sk_c7) equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.20/0.47 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.47 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.47 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.47 26[0:Rew:1.0,22.0] || equal(sk_c5,sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(multiply(sk_c7,v),sk_c6)** equal(multiply(w,sk_c7),v)* equal(inverse(w),sk_c7) equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)** equal(inverse(x),sk_c7) equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.20/0.47 27[0:Obv:26.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(v,sk_c7),x)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.47 28[1:Spt:27.0,27.5] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.47 29[2:Spt:18.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 31[3:Spt:19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.47 34[4:Spt:8.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 36[5:Spt:21.1] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.47 38[5:SpL:36.0,28.1] || equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 39[5:Obv:38.1] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.47 40[5:Rew:34.0,39.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 41[5:Obv:40.0] || -> .
% 0.20/0.47 42[5:Spt:41.0,21.1,36.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.20/0.47 43[5:Spt:41.0,21.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 44[5:MRR:9.1,42.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 45[5:MRR:17.0,42.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 46[5:MRR:13.0,42.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 47[5:MRR:5.0,42.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 53[5:SpL:47.0,28.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 54[5:Obv:53.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.47 55[5:Rew:44.0,54.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.47 57[1:SpL:23.0,28.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c6) -> .
% 0.20/0.47 59[2:SpR:29.0,24.0] || -> equal(multiply(sk_c5,sk_c6),identity)**.
% 0.20/0.47 60[4:SpR:34.0,24.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.47 61[5:SpR:43.0,24.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.20/0.47 63[1:SpL:24.0,28.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 64[2:Rew:29.0,63.0] || equal(inverse(sk_c5),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 70[0:SpR:1.0,25.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.20/0.47 71[5:SpR:45.0,25.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c3,u))**.
% 0.20/0.47 73[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.47 75[0:Rew:23.0,73.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.47 78[2:SpR:59.0,25.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.20/0.47 80[2:Rew:23.0,78.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 91[0:SpR:75.0,75.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.47 93[5:SpR:47.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.20/0.47 94[2:SpR:59.0,75.0] || -> equal(multiply(inverse(sk_c5),identity),sk_c6)**.
% 0.20/0.47 95[3:SpR:31.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.20/0.47 96[5:SpR:46.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c3)**.
% 0.20/0.47 97[4:SpR:60.0,75.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.47 98[5:SpR:61.0,75.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.20/0.47 99[0:SpR:1.0,75.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.47 102[0:SpR:24.0,75.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.47 109[5:Rew:1.0,93.0,44.0,93.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 110[5:Rew:109.0,29.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 113[5:Rew:109.0,59.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.20/0.47 119[5:Rew:109.0,95.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c6)**.
% 0.20/0.47 120[5:Rew:119.0,96.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.47 124[5:Rew:120.0,71.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.47 125[5:Rew:97.0,98.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.47 130[5:Rew:113.0,99.0,110.0,99.0,109.0,99.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 131[5:Rew:130.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 133[5:Rew:130.0,60.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.20/0.47 135[5:Rew:130.0,113.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.20/0.47 140[5:Rew:131.0,133.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.47 143[5:Rew:140.0,125.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.47 170[5:Rew:131.0,124.0,143.0,124.0,131.0,124.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 172[5:Rew:170.0,135.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 173[5:MRR:172.0,55.0] || -> .
% 0.20/0.47 175[4:Spt:173.0,8.0,34.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.47 176[4:Spt:173.0,8.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 178[0:Rew:91.0,102.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.47 179[2:Rew:178.0,94.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.47 180[4:MRR:20.0,175.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 181[2:Rew:179.0,64.0] || equal(sk_c7,sk_c6) equal(identity,sk_c7)** -> .
% 0.20/0.47 182[4:MRR:16.0,175.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 183[4:MRR:12.0,175.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 212[4:SpR:182.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.47 214[4:Rew:180.0,212.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.47 215[4:Rew:183.0,214.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 224[4:Rew:215.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.47 225[4:Rew:215.0,57.0] || equal(inverse(identity),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.20/0.47 233[4:Rew:59.0,224.0,29.0,224.0] || -> equal(identity,sk_c5)**.
% 0.20/0.47 234[4:Rew:233.0,59.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.47 235[4:Rew:233.0,23.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.47 239[4:Rew:235.0,234.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 243[4:Rew:239.0,29.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 247[4:Rew:239.0,233.0] || -> equal(identity,sk_c6)**.
% 0.20/0.47 266[4:Rew:215.0,225.1,243.0,225.0,247.0,225.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 267[4:Obv:266.1] || -> .
% 0.20/0.47 273[3:Spt:267.0,19.1,31.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.47 274[3:Spt:267.0,19.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 275[3:MRR:7.1,273.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 276[3:MRR:15.0,273.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 277[3:MRR:11.0,273.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 278[3:MRR:3.0,273.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 295[3:SpR:276.0,25.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c3,u))**.
% 0.20/0.47 296[3:SpR:276.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.47 298[3:Rew:274.0,296.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.47 299[3:Rew:277.0,298.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 302[3:Rew:299.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 303[3:Rew:299.0,276.0] || -> equal(multiply(sk_c2,sk_c6),sk_c3)**.
% 0.20/0.47 306[3:Rew:299.0,181.0] || equal(sk_c6,sk_c6) equal(identity,sk_c7)** -> .
% 0.20/0.47 308[3:Rew:299.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.47 309[3:Rew:299.0,277.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.20/0.47 310[3:Rew:299.0,278.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.47 314[3:Obv:306.0] || equal(identity,sk_c7)** -> .
% 0.20/0.47 315[3:Rew:299.0,314.0] || equal(identity,sk_c6)** -> .
% 0.20/0.47 316[3:Rew:299.0,295.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c3,u))**.
% 0.20/0.47 342[3:SpR:309.0,75.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c3)**.
% 0.20/0.47 344[3:Rew:59.0,342.0,29.0,342.0] || -> equal(identity,sk_c3)**.
% 0.20/0.47 345[3:Rew:344.0,315.0] || equal(sk_c3,sk_c6)** -> .
% 0.20/0.47 348[3:Rew:344.0,23.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.47 352[3:Rew:348.0,316.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.20/0.47 356[3:SpR:310.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.47 358[3:Rew:302.0,356.0,275.0,356.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 363[3:Rew:358.0,80.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.47 365[3:Rew:358.0,308.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.47 373[3:Rew:363.0,365.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 374[3:Rew:373.0,352.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.47 379[3:Rew:374.0,303.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.47 380[3:MRR:379.0,345.0] || -> .
% 0.20/0.47 381[2:Spt:380.0,18.0,29.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.20/0.47 382[2:Spt:380.0,18.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 383[2:MRR:6.0,381.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 384[2:MRR:14.0,381.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.47 385[2:MRR:10.0,381.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.47 386[2:MRR:2.0,381.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 395[2:SpR:384.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.47 397[2:Rew:382.0,395.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.47 398[2:Rew:385.0,397.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 399[2:Rew:398.0,382.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 400[2:Rew:398.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 401[2:Rew:398.0,384.0] || -> equal(multiply(sk_c2,sk_c6),sk_c3)**.
% 0.20/0.47 402[2:Rew:398.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.47 405[2:Rew:398.0,385.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.20/0.47 406[2:Rew:398.0,386.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.47 428[2:SpR:405.0,75.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c3)**.
% 0.20/0.47 430[2:Rew:24.0,428.0] || -> equal(identity,sk_c3)**.
% 0.20/0.47 432[2:Rew:430.0,178.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.47 433[2:Rew:430.0,24.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.20/0.47 440[2:SpR:406.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.47 442[2:Rew:400.0,440.0,383.0,440.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 443[2:Rew:442.0,381.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.47 445[2:Rew:442.0,402.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.47 447[2:Rew:433.0,445.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.47 448[2:Rew:447.0,401.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.47 451[2:Rew:447.0,432.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 460[2:Rew:451.0,448.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.47 464[2:Rew:460.0,399.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 466[2:MRR:464.0,443.0] || -> .
% 0.20/0.47 472[1:Spt:466.0,27.1,27.2,27.3,27.4,27.6,27.7,27.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c7),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,w),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.47 473[1:EqR:472.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.20/0.47 475[2:Spt:6.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 477[2:Rew:475.0,99.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.20/0.47 479[2:Rew:475.0,473.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(sk_c5,sk_c5) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.20/0.47 480[2:Obv:479.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.20/0.47 483[2:SpR:475.0,75.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 485[3:Spt:7.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.47 488[3:Rew:485.0,480.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.20/0.47 489[3:Obv:488.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.20/0.47 492[3:SpR:485.0,25.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.47 493[3:SpR:485.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.20/0.47 495[4:Spt:20.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 496[4:SpR:495.0,75.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.20/0.47 502[5:Spt:21.1] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.47 504[5:SpR:502.0,75.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c6)**.
% 0.20/0.47 506[5:Rew:495.0,504.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 510[5:SpR:506.0,25.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.47 511[5:SpR:506.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.47 513[5:Rew:493.0,511.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 514[5:Rew:513.0,475.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.47 517[5:Rew:513.0,477.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.47 520[5:Rew:513.0,483.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.20/0.47 524[5:Rew:506.0,517.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 525[5:Rew:524.0,495.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.47 530[5:Rew:524.0,489.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.20/0.47 534[5:Rew:524.0,514.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 538[5:Rew:524.0,520.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.47 539[5:Rew:538.0,510.0,524.0,510.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 544[5:Rew:539.0,530.3,524.0,530.3,524.0,530.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.47 545[5:Con:544.0] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.47 567[0:SpR:24.0,75.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.47 568[0:SpR:24.0,178.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.47 570[5:SpR:525.0,24.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.47 573[5:Rew:539.0,570.0] || -> equal(identity,sk_c4)**.
% 0.20/0.47 575[5:Rew:573.0,178.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.20/0.47 577[5:Rew:573.0,568.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.20/0.47 578[5:Rew:525.0,577.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.47 585[5:Rew:578.0,575.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 586[5:Rew:585.0,545.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.47 642[5:SpL:534.0,586.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 644[5:Obv:642.1] || -> .
% 0.20/0.47 645[5:Spt:644.0,21.1,502.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.20/0.47 646[5:Spt:644.0,21.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.47 647[0:Rew:178.0,567.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.48 648[5:MRR:9.1,645.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 650[5:MRR:17.0,645.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.48 651[5:MRR:13.0,645.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.48 652[5:MRR:5.0,645.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.48 676[5:SpR:650.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.48 678[5:Rew:646.0,676.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.48 679[5:Rew:651.0,678.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 683[5:Rew:679.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 688[5:Rew:679.0,645.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.20/0.48 689[5:Rew:679.0,496.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.48 691[5:Rew:679.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.48 694[5:Rew:679.0,652.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.48 735[5:SpR:694.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.48 737[5:Rew:683.0,735.0,648.0,735.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 743[5:Rew:737.0,483.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.48 746[5:Rew:737.0,691.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.48 752[5:Rew:743.0,746.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 759[5:Rew:752.0,689.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.48 761[5:UnC:759.0,688.0] || -> .
% 0.20/0.48 763[4:Spt:761.0,20.0,495.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.48 764[4:Spt:761.0,20.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 765[4:MRR:8.0,763.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 766[4:MRR:16.0,763.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.48 767[4:MRR:12.0,763.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.48 768[4:MRR:4.0,763.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.48 786[4:SpR:766.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.48 788[4:Rew:764.0,786.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.48 789[4:Rew:767.0,788.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 791[4:Rew:789.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 798[4:Rew:789.0,492.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.48 802[4:Rew:789.0,768.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.48 804[4:Rew:789.0,489.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.20/0.48 809[4:Rew:789.0,804.3,789.0,804.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.20/0.48 841[4:SpR:802.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.48 843[4:Rew:791.0,841.0,765.0,841.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 844[4:Rew:843.0,475.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 849[4:Rew:843.0,483.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.48 852[4:Rew:843.0,798.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.48 858[4:Rew:849.0,852.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 863[4:Rew:858.0,809.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.48 866[4:Con:863.0] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.48 888[4:SpR:765.0,24.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.20/0.48 891[4:Rew:858.0,888.0] || -> equal(identity,sk_c1)**.
% 0.20/0.48 892[4:Rew:891.0,568.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 894[4:Rew:891.0,178.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.48 896[4:Rew:765.0,892.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.48 905[4:Rew:896.0,894.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 906[4:Rew:905.0,866.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.48 914[0:SpR:647.0,75.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.48 962[4:SpL:844.0,906.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 964[4:Obv:962.1] || -> .
% 0.20/0.48 965[3:Spt:964.0,7.1,485.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.48 966[3:Spt:964.0,7.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 968[3:MRR:19.1,965.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 970[3:MRR:15.0,965.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.48 971[3:MRR:11.0,965.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.48 972[3:MRR:3.0,965.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.48 974[3:SpR:966.0,647.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.20/0.48 977[3:Rew:475.0,974.0] || -> equal(sk_c1,sk_c5)**.
% 0.20/0.48 979[3:Rew:977.0,972.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 995[3:SpR:968.0,647.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.20/0.48 1015[3:SpR:970.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.48 1017[3:Rew:968.0,1015.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.48 1018[3:Rew:971.0,1017.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 1020[3:Rew:1018.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 1021[3:Rew:1018.0,995.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.48 1023[3:Rew:1018.0,970.0] || -> equal(multiply(sk_c2,sk_c6),sk_c3)**.
% 0.20/0.48 1024[3:Rew:1018.0,965.0] || equal(multiply(sk_c6,sk_c5),sk_c6)** -> .
% 0.20/0.48 1028[3:Rew:1018.0,971.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.20/0.48 1029[3:Rew:1018.0,979.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.20/0.48 1031[3:Rew:475.0,1021.0] || -> equal(sk_c2,sk_c5)**.
% 0.20/0.48 1033[3:Rew:1031.0,1023.0] || -> equal(multiply(sk_c5,sk_c6),sk_c3)**.
% 0.20/0.48 1034[3:Rew:1033.0,1029.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.48 1036[3:Rew:1034.0,1028.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 1037[3:Rew:1020.0,1036.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 1044[3:Rew:1037.0,1020.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 1047[3:Rew:1044.0,1024.0,1037.0,1024.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 1048[3:Obv:1047.0] || -> .
% 0.20/0.48 1055[2:Spt:1048.0,6.0,475.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.20/0.48 1056[2:Spt:1048.0,6.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 1057[2:MRR:18.0,1055.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 1058[2:MRR:14.0,1055.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.48 1059[2:MRR:10.0,1055.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.20/0.48 1060[2:MRR:2.0,1055.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.48 1062[2:SpR:1056.0,647.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.20/0.48 1063[2:SpR:1056.0,914.0] || -> equal(multiply(sk_c1,multiply(sk_c6,u)),u)**.
% 0.20/0.48 1065[2:Rew:1062.0,1055.0] || equal(sk_c1,sk_c5)** -> .
% 0.20/0.48 1068[2:SpR:1057.0,647.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.20/0.48 1083[2:SpR:1058.0,25.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c3,u))**.
% 0.20/0.48 1084[2:SpR:1058.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.20/0.48 1086[2:Rew:1057.0,1084.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.20/0.48 1087[2:Rew:1059.0,1086.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 1089[2:Rew:1087.0,1068.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.48 1090[2:Rew:1087.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 1091[2:Rew:1087.0,1058.0] || -> equal(multiply(sk_c2,sk_c6),sk_c3)**.
% 0.20/0.48 1094[2:Rew:1087.0,1059.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.20/0.48 1095[2:Rew:1087.0,1060.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.48 1098[2:Rew:1062.0,1089.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.48 1100[2:Rew:1098.0,1091.0] || -> equal(multiply(sk_c1,sk_c6),sk_c3)**.
% 0.20/0.48 1101[2:Rew:1100.0,1095.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.48 1103[2:Rew:1101.0,1094.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 1104[2:Rew:1090.0,1103.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 1105[2:Rew:1104.0,1065.0] || equal(sk_c1,sk_c6)** -> .
% 0.20/0.48 1110[2:Rew:1063.0,1083.0,1098.0,1083.0,1087.0,1083.0,1101.0,1083.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 1135[2:SpR:1110.0,178.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 1137[2:Rew:1135.0,568.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 1142[2:Rew:1062.0,1137.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.48 1143[2:MRR:1142.0,1105.0] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 left_identity left_inverse associativity
% 0.20/0.48
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