TSTP Solution File: GRP213-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:46:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 04:49:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 750 clauses, backtracked 215 clauses, performed 9 splits and kept 514 clauses.
% 0.20/0.48 SPASS allocated 63608 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.05 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 317 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.48 8[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 10[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 11[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.48 13[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 16[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 20[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 21[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 22[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 23[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 25[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(y),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),z)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(sk_c8,z),sk_c7)** -> .
% 0.20/0.48 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 29[1:Spt:25.0,25.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)** -> .
% 0.20/0.48 30[2:Spt:19.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 32[3:Spt:7.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 34[4:Spt:13.1] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 36[4:SpL:34.0,29.1] || equal(inverse(sk_c2),sk_c3)** equal(sk_c8,sk_c8) -> .
% 0.20/0.48 37[4:Obv:36.1] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.20/0.48 38[4:Rew:30.0,37.0] || equal(sk_c3,sk_c3)* -> .
% 0.20/0.48 39[4:Obv:38.0] || -> .
% 0.20/0.48 40[4:Spt:39.0,13.1,34.0] || equal(multiply(sk_c2,sk_c3),sk_c8)** -> .
% 0.20/0.48 41[4:Spt:39.0,13.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.48 42[4:MRR:18.1,40.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 43[4:MRR:14.1,40.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 44[4:MRR:17.1,40.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 45[4:MRR:16.1,40.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 46[4:MRR:15.1,40.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 64[2:SpR:30.0,27.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.20/0.48 65[3:SpR:32.0,27.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.20/0.48 66[4:SpR:41.0,27.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.20/0.48 67[4:SpR:42.0,27.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.20/0.48 68[4:SpR:43.0,27.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 83[4:SpR:66.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.20/0.48 84[4:SpR:45.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.48 87[4:SpR:46.0,28.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.48 89[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 90[2:SpR:64.0,28.0] || -> equal(multiply(sk_c3,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.48 92[4:Rew:26.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.48 95[2:Rew:26.0,90.0] || -> equal(multiply(sk_c3,multiply(sk_c2,u)),u)**.
% 0.20/0.48 96[0:Rew:26.0,89.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 105[4:SpR:45.0,92.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 106[4:SpR:65.0,92.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.20/0.48 107[4:SpR:67.0,92.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.20/0.48 108[4:SpR:68.0,92.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.48 109[4:SpL:92.0,29.1] || equal(multiply(sk_c8,u),inverse(sk_c7))** equal(u,sk_c8) -> .
% 0.20/0.48 110[4:Rew:106.0,107.0] || -> equal(sk_c5,sk_c1)**.
% 0.20/0.48 112[4:Rew:110.0,44.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.48 117[4:Rew:106.0,108.0] || -> equal(sk_c4,sk_c1)**.
% 0.20/0.48 121[4:Rew:117.0,87.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.48 130[4:SpR:105.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.48 133[4:SpR:106.0,28.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.20/0.48 136[4:Rew:26.0,133.0] || -> equal(multiply(sk_c7,u),multiply(sk_c1,u))**.
% 0.20/0.48 137[4:Rew:136.0,106.0] || -> equal(multiply(sk_c1,identity),sk_c1)**.
% 0.20/0.48 140[4:Rew:136.0,66.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.20/0.48 141[4:Rew:136.0,130.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.48 142[4:Rew:136.0,84.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c1,u))**.
% 0.20/0.48 143[4:Rew:136.0,121.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),multiply(sk_c8,u))**.
% 0.20/0.48 146[4:Rew:112.0,140.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 147[4:Rew:146.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 156[4:Rew:146.0,137.0] || -> equal(multiply(sk_c1,sk_c6),sk_c1)**.
% 0.20/0.48 159[4:Rew:136.0,141.0,147.0,141.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.20/0.48 160[4:Rew:147.0,142.0] || -> equal(multiply(sk_c8,u),multiply(sk_c1,u))**.
% 0.20/0.48 161[4:Rew:160.0,45.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.48 164[4:Rew:160.0,109.0] || equal(multiply(sk_c1,u),inverse(sk_c7))** equal(u,sk_c8) -> .
% 0.20/0.48 166[4:Rew:156.0,161.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.48 174[4:Rew:159.0,143.0,160.0,143.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 193[4:Rew:174.0,164.0,166.0,164.0] || equal(u,inverse(sk_c1))* equal(u,sk_c8) -> .
% 0.20/0.48 194[4:Rew:32.0,193.0] || equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.48 195[4:Obv:194.0] || equal(u,sk_c8)* -> .
% 0.20/0.48 196[4:UnC:195.0,32.0] || -> .
% 0.20/0.48 197[3:Spt:196.0,7.1,32.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.20/0.48 198[3:Spt:196.0,7.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.48 199[3:MRR:12.1,197.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 200[3:MRR:8.1,197.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 201[3:MRR:11.0,197.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 202[3:MRR:10.0,197.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 203[3:MRR:9.0,197.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 216[3:SpR:202.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.48 220[3:SpR:203.0,28.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.48 231[3:SpR:198.0,27.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.20/0.48 232[3:SpR:199.0,27.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.20/0.48 233[3:SpR:200.0,27.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 236[3:SpR:231.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.20/0.48 239[3:Rew:26.0,236.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.48 256[3:SpR:202.0,239.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 257[3:SpR:232.0,239.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.20/0.48 258[3:SpR:233.0,239.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.48 259[3:SpL:239.0,29.1] || equal(multiply(sk_c8,u),inverse(sk_c7))** equal(u,sk_c8) -> .
% 0.20/0.48 260[3:Rew:257.0,258.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 262[3:Rew:260.0,201.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.20/0.48 267[3:Rew:260.0,257.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.48 273[3:SpR:256.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.48 276[3:SpR:267.0,28.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c4,u))**.
% 0.20/0.48 279[3:Rew:26.0,276.0] || -> equal(multiply(sk_c4,u),multiply(sk_c7,u))**.
% 0.20/0.48 280[3:Rew:279.0,262.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 283[3:Rew:279.0,220.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.48 285[3:Rew:231.0,280.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 287[3:Rew:285.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 291[3:Rew:285.0,267.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.20/0.48 299[3:Rew:287.0,216.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.20/0.48 300[3:Rew:287.0,273.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.20/0.48 303[3:Rew:299.0,291.0] || -> equal(multiply(sk_c8,sk_c6),sk_c4)**.
% 0.20/0.48 307[3:Rew:202.0,303.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.48 308[3:Rew:307.0,200.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.48 311[3:Rew:308.0,259.0] || equal(multiply(sk_c8,u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 312[3:Rew:299.0,300.0,299.0,300.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.48 316[3:Rew:312.0,283.0,299.0,283.0,299.0,283.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 336[3:Rew:316.0,311.0] || equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.48 337[3:Obv:336.0] || equal(u,sk_c8)* -> .
% 0.20/0.48 338[3:UnC:337.0,95.0] || -> .
% 0.20/0.48 339[2:Spt:338.0,19.1,30.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.20/0.48 340[2:Spt:338.0,19.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.48 341[2:MRR:24.1,339.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 342[2:MRR:20.1,339.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 343[2:MRR:23.0,339.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 344[2:MRR:22.0,339.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 345[2:MRR:21.0,339.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 354[2:SpR:344.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.48 368[2:SpR:340.0,27.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.20/0.48 369[2:SpR:341.0,27.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.20/0.48 370[2:SpR:342.0,27.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 373[2:SpR:368.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.20/0.48 376[2:Rew:26.0,373.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.48 390[2:SpR:369.0,376.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.20/0.48 391[2:SpR:370.0,376.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.48 392[2:SpL:376.0,29.1] || equal(multiply(sk_c8,u),inverse(sk_c7))** equal(u,sk_c8) -> .
% 0.20/0.48 393[2:Rew:390.0,391.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 395[2:Rew:393.0,343.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.20/0.48 400[2:Rew:393.0,390.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.48 410[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 416[2:SpR:345.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.20/0.48 419[0:SpR:27.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 427[2:Rew:342.0,416.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.48 432[0:Rew:410.0,419.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 433[2:Rew:432.0,400.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.48 434[2:Rew:433.0,342.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.48 438[2:Rew:433.0,395.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 444[2:Rew:434.0,392.0] || equal(multiply(sk_c8,u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 448[2:Rew:368.0,438.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 449[2:Rew:448.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 451[2:Rew:448.0,368.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 457[2:Rew:449.0,354.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.20/0.48 464[2:Rew:457.0,451.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 465[2:Rew:427.0,464.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 468[2:Rew:465.0,449.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 473[2:Rew:457.0,468.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 490[2:Rew:473.0,444.0] || equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.48 491[2:Obv:490.0] || equal(u,sk_c8)* -> .
% 0.20/0.48 492[2:UnC:491.0,96.0] || -> .
% 0.20/0.48 495[1:Spt:492.0,25.1,25.2,25.3,25.4,25.6,25.7,25.8,25.9] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.20/0.48 496[1:EqR:495.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.48 498[2:Spt:7.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.48 501[2:Rew:498.0,496.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(sk_c7,sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.48 502[2:Obv:501.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.48 505[2:SpR:498.0,96.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.48 507[3:Spt:24.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 508[3:SpR:507.0,96.0] || -> equal(multiply(sk_c3,multiply(sk_c2,u)),u)**.
% 0.20/0.48 510[4:Spt:12.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 511[4:SpR:510.0,96.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 516[5:Spt:18.1] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 518[5:SpR:516.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.48 520[5:Rew:507.0,518.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.48 521[6:Spt:6.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 523[6:SpR:521.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.48 525[6:Rew:510.0,523.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.48 527[5:SpR:520.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.20/0.48 529[5:Rew:27.0,527.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 530[5:Rew:529.0,26.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 531[5:Rew:529.0,432.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 534[6:Rew:530.0,525.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 540[5:Rew:530.0,511.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 541[5:Rew:530.0,502.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.48 548[5:Con:541.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.48 549[6:Rew:531.0,548.3,534.0,548.3,531.0,548.2,534.0,548.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.20/0.48 550[6:Con:549.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 573[5:SpR:540.0,531.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 575[5:Rew:573.0,510.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 583[6:Rew:573.0,550.0] || equal(inverse(u),sk_c1)** equal(u,sk_c8) -> .
% 0.20/0.48 585[6:Rew:573.0,583.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.48 637[6:SpL:575.0,585.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 639[6:Obv:637.1] || -> .
% 0.20/0.48 640[6:Spt:639.0,6.1,521.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.20/0.48 641[6:Spt:639.0,6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 642[5:Rew:575.0,498.0,573.0,498.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.48 647[6:Rew:540.0,640.0,573.0,640.0] || equal(sk_c7,sk_c1)** -> .
% 0.20/0.48 648[6:Rew:642.0,647.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 649[6:Obv:648.0] || -> .
% 0.20/0.48 665[5:Spt:649.0,18.1,516.0] || equal(multiply(sk_c2,sk_c3),sk_c8)** -> .
% 0.20/0.48 666[5:Spt:649.0,18.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 667[5:MRR:14.1,665.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 668[5:MRR:17.1,665.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 669[5:MRR:16.1,665.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 670[5:MRR:15.1,665.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 680[5:SpR:668.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.48 682[5:Rew:666.0,680.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 683[5:Rew:669.0,682.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 684[5:Rew:683.0,498.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 685[5:Rew:683.0,505.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.48 686[5:Rew:683.0,669.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 687[5:Rew:683.0,670.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 697[5:SpR:686.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.48 698[5:SpR:686.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 700[5:Rew:684.0,698.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 705[5:SpR:687.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c8)**.
% 0.20/0.48 707[5:Rew:667.0,705.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.48 708[5:Rew:700.0,707.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 712[5:Rew:708.0,697.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.20/0.48 714[5:Rew:685.0,712.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 733[3:SpR:432.0,508.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.20/0.48 738[3:SpR:733.0,96.0] || -> equal(multiply(inverse(sk_c3),identity),sk_c2)**.
% 0.20/0.48 740[3:Rew:432.0,738.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.20/0.48 747[5:SpR:714.0,432.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 753[5:Rew:747.0,27.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.48 776[5:SpR:510.0,753.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.20/0.48 779[5:SpR:740.0,753.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 783[5:Rew:714.0,776.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 790[5:Rew:783.0,665.0] || equal(multiply(sk_c2,sk_c3),sk_c1)** -> .
% 0.20/0.48 801[5:Rew:783.0,779.0] || -> equal(multiply(sk_c2,sk_c3),sk_c1)**.
% 0.20/0.48 803[5:Rew:801.0,790.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 804[5:Obv:803.0] || -> .
% 0.20/0.48 809[4:Spt:804.0,12.1,510.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.20/0.48 810[4:Spt:804.0,12.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 811[4:MRR:8.1,809.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 812[4:MRR:11.0,809.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 813[4:MRR:10.0,809.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 814[4:MRR:9.0,809.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 827[4:SpR:812.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.48 829[4:Rew:810.0,827.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 830[4:Rew:813.0,829.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 831[4:Rew:830.0,498.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 832[4:Rew:830.0,505.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.48 833[4:Rew:830.0,813.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 834[4:Rew:830.0,814.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 836[4:Rew:830.0,502.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.48 838[4:Rew:830.0,836.5,830.0,836.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 839[4:Con:838.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 847[4:SpR:833.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.48 848[4:SpR:833.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 850[4:Rew:831.0,848.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 852[4:SpR:834.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c8)**.
% 0.20/0.48 854[4:Rew:811.0,852.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.48 855[4:Rew:850.0,854.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 859[4:Rew:855.0,847.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.20/0.48 861[4:Rew:832.0,859.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 867[4:Rew:861.0,839.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 870[4:Con:867.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 885[4:SpR:861.0,432.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 889[4:Rew:885.0,432.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 892[4:Rew:889.0,870.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 945[4:SpL:831.0,892.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 946[4:Obv:945.1] || -> .
% 0.20/0.48 947[3:Spt:946.0,24.1,507.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.20/0.48 948[3:Spt:946.0,24.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 949[3:MRR:20.1,947.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 950[3:MRR:23.0,947.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 951[3:MRR:22.0,947.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.48 952[3:MRR:21.0,947.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 960[3:SpR:950.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.48 962[3:Rew:948.0,960.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 963[3:Rew:951.0,962.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 964[3:Rew:963.0,498.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 965[3:Rew:963.0,505.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.48 966[3:Rew:963.0,951.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 967[3:Rew:963.0,952.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 969[3:Rew:963.0,502.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.48 971[3:Rew:963.0,969.5,963.0,969.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 972[3:Con:971.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 980[3:SpR:966.0,28.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.48 981[3:SpR:966.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 983[3:Rew:964.0,981.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 985[3:SpR:967.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c8)**.
% 0.20/0.48 987[3:Rew:949.0,985.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.48 988[3:Rew:983.0,987.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 992[3:Rew:988.0,980.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.20/0.48 994[3:Rew:965.0,992.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 1000[3:Rew:994.0,972.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 1003[3:Con:1000.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 1017[3:SpR:994.0,432.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 1019[3:Rew:1017.0,432.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 1023[3:Rew:1019.0,1003.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 1051[3:SpL:964.0,1023.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 1052[3:Obv:1051.1] || -> .
% 0.20/0.48 1053[2:Spt:1052.0,7.0,498.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.20/0.48 1054[2:Spt:1052.0,7.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 1055[2:MRR:19.0,1053.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.48 1056[2:MRR:1.0,1053.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 1057[2:MRR:13.0,1053.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.48 1063[2:SpR:1056.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.48 1065[2:Rew:1054.0,1063.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.48 1067[2:SpR:1057.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.48 1069[2:Rew:1055.0,1067.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.48 1074[2:SpR:1065.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.48 1076[2:Rew:27.0,1074.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 1078[2:Rew:1076.0,432.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 1079[2:Rew:1076.0,27.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.48 1085[2:SpR:1069.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.20/0.48 1087[2:Rew:1079.0,1085.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 1088[2:Rew:1087.0,1053.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.20/0.48 1089[2:Rew:1087.0,1056.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.48 1092[2:Rew:1087.0,1078.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 1098[2:Rew:1092.0,1089.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 1099[2:Rew:1098.0,1054.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 1103[2:Rew:1098.0,1088.0] || equal(inverse(sk_c1),sk_c1)** -> .
% 0.20/0.48 1106[2:Rew:1099.0,1103.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 1107[2:Obv:1106.0] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 Formulae used in the proof : prove_this_1 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 prove_this_23 prove_this_24 prove_this_25 left_identity left_inverse associativity
% 0.20/0.48
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