TSTP Solution File: GRP222-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP222-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:24 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP222-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n006.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 11:14:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 457 clauses, backtracked 170 clauses, performed 9 splits and kept 335 clauses.
% 0.21/0.45 SPASS allocated 63429 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.04 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.03 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 4, length 162 :
% 0.21/0.45 % SZS output start Refutation
% 0.21/0.45 2[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.21/0.45 3[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.21/0.45 4[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.21/0.45 6[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.21/0.45 7[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.21/0.45 8[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c6),sk_c7).
% 0.21/0.45 9[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 10[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 11[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 12[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 13[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.45 14[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 15[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 16[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.21/0.45 17[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 18[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 20[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 21[0:Inp] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,w),sk_c6)** equal(inverse(v),w) equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c7),sk_c6)** equal(inverse(x),sk_c7) equal(inverse(y),sk_c7) equal(multiply(y,sk_c6),sk_c7)** -> .
% 0.21/0.45 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.45 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.45 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.45 25[0:Con:21.7] || equal(inverse(u),v) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,v),sk_c6)**+ equal(multiply(w,sk_c7),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.21/0.45 26[1:Spt:25.0,25.3,25.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.21/0.45 27[2:Spt:15.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.45 29[3:Spt:14.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.45 33[4:Spt:16.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.21/0.45 38[5:Spt:13.1] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.45 40[5:SpL:38.0,26.1] || equal(inverse(sk_c4),sk_c7) equal(sk_c6,sk_c6) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.45 41[5:Obv:40.1] || equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.45 42[5:Rew:29.0,41.0] || equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.45 43[5:Obv:42.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.45 45[2:SpR:27.0,23.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.21/0.45 54[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.45 56[2:SpR:45.0,24.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.45 58[2:Rew:22.0,56.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.21/0.45 59[0:Rew:22.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.45 69[4:SpR:33.0,58.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.45 71[5:MRR:69.0,43.0] || -> .
% 0.21/0.45 74[5:Spt:71.0,13.1,38.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.45 75[5:Spt:71.0,13.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 77[5:MRR:17.0,74.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 78[5:MRR:9.0,74.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 98[5:SpL:78.0,26.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c6,sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 99[5:Obv:98.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 100[5:Rew:77.0,99.1,75.0,99.0] || equal(sk_c3,sk_c3)* equal(sk_c6,sk_c6) -> .
% 0.21/0.45 101[5:Obv:100.1] || -> .
% 0.21/0.45 102[4:Spt:101.0,16.1,33.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.21/0.45 103[4:Spt:101.0,16.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 105[4:MRR:20.0,102.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 106[4:MRR:12.0,102.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 118[4:SpL:106.0,26.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c6,sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 119[4:Obv:118.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 120[4:Rew:105.0,119.1,103.0,119.0] || equal(sk_c3,sk_c3)* equal(sk_c6,sk_c6) -> .
% 0.21/0.45 121[4:Obv:120.1] || -> .
% 0.21/0.45 122[3:Spt:121.0,14.0,29.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.21/0.45 123[3:Spt:121.0,14.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 125[3:MRR:18.0,122.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 126[3:MRR:10.0,122.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 138[3:SpL:126.0,26.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c6,sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 139[3:Obv:138.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 140[3:Rew:125.0,139.1,123.0,139.0] || equal(sk_c3,sk_c3)* equal(sk_c6,sk_c6) -> .
% 0.21/0.45 141[3:Obv:140.1] || -> .
% 0.21/0.45 142[2:Spt:141.0,15.0,27.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.21/0.45 143[2:Spt:141.0,15.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.45 145[2:MRR:19.0,142.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.45 146[2:MRR:11.0,142.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.45 158[2:SpL:146.0,26.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c6,sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 159[2:Obv:158.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.21/0.45 160[2:Rew:145.0,159.1,143.0,159.0] || equal(sk_c3,sk_c3)* equal(sk_c6,sk_c6) -> .
% 0.21/0.45 161[2:Obv:160.1] || -> .
% 0.21/0.45 162[1:Spt:161.0,25.1,25.2,25.4,25.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.21/0.45 164[1:SpL:23.0,162.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(inverse(u),sk_c7) equal(identity,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.45 166[2:Spt:14.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.45 167[2:SpR:166.0,23.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.45 169[3:Spt:3.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.45 170[3:SpR:169.0,23.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.21/0.45 172[4:Spt:13.1] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.45 175[4:SpL:172.0,162.2] || equal(inverse(sk_c4),sk_c7) equal(inverse(u),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.45 176[4:Obv:175.2] || equal(inverse(sk_c4),sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.45 177[4:Rew:166.0,176.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.45 178[4:Obv:177.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.45 182[5:Spt:4.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.21/0.45 189[0:SpR:59.0,59.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.45 192[0:SpR:23.0,59.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.45 195[2:SpR:167.0,59.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.21/0.45 196[3:SpR:170.0,59.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.21/0.45 201[3:Rew:195.0,196.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.45 203[5:Rew:201.0,182.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.21/0.45 210[0:Rew:189.0,192.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.45 211[2:Rew:210.0,195.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.45 214[2:SpR:211.0,23.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.21/0.45 217[4:Rew:172.0,214.0] || -> equal(identity,sk_c6)**.
% 0.21/0.45 222[4:Rew:217.0,210.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.45 225[5:Rew:222.0,203.0] || -> equal(sk_c7,sk_c4)**.
% 0.21/0.45 226[4:Rew:222.0,178.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.45 227[5:Rew:225.0,166.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.21/0.46 236[5:Rew:225.0,226.1,225.0,226.0] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.21/0.46 314[5:SpL:227.0,236.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.21/0.46 317[5:Obv:314.1] || -> .
% 0.21/0.46 319[5:Spt:317.0,4.1,182.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.21/0.46 320[5:Spt:317.0,4.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.46 321[5:Rew:222.0,319.0,201.0,319.0] || equal(sk_c7,sk_c4)** -> .
% 0.21/0.46 328[4:Rew:222.0,8.1,201.0,8.0,222.0,8.0] || -> equal(sk_c7,sk_c4)** equal(sk_c7,sk_c1).
% 0.21/0.46 329[5:MRR:328.0,321.0] || -> equal(sk_c7,sk_c1)**.
% 0.21/0.46 330[5:Rew:329.0,211.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.21/0.46 332[5:Rew:329.0,320.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.46 335[5:Rew:329.0,321.0] || equal(sk_c4,sk_c1)** -> .
% 0.21/0.46 340[5:Rew:330.0,332.0] || -> equal(sk_c4,sk_c1)**.
% 0.21/0.46 344[5:Rew:340.0,335.0] || equal(sk_c1,sk_c1)* -> .
% 0.21/0.46 345[5:Obv:344.0] || -> .
% 0.21/0.46 351[4:Spt:345.0,13.1,172.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.46 352[4:Spt:345.0,13.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.46 353[4:Rew:214.0,351.0] || equal(identity,sk_c6)** -> .
% 0.21/0.46 362[2:Rew:214.0,9.0] || -> equal(identity,sk_c6) equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.46 363[4:MRR:362.0,353.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.46 389[4:SpR:363.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c3)**.
% 0.21/0.46 391[4:Rew:352.0,389.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.21/0.46 397[4:SpR:391.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c6)**.
% 0.21/0.46 399[4:Rew:23.0,397.0] || -> equal(identity,sk_c6)**.
% 0.21/0.46 400[4:MRR:399.0,353.0] || -> .
% 0.21/0.46 401[3:Spt:400.0,3.0,169.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.21/0.46 402[3:Spt:400.0,3.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.46 403[3:MRR:15.0,401.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.46 405[3:MRR:11.0,401.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.46 406[3:MRR:7.0,401.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.21/0.46 407[2:Rew:166.0,164.0,211.0,164.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c7) equal(identity,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 408[2:Obv:407.0] || equal(inverse(u),sk_c7) equal(identity,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 417[3:SpR:405.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c3)**.
% 0.21/0.46 419[3:Rew:403.0,417.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.21/0.46 425[3:SpR:419.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c6)**.
% 0.21/0.46 427[3:Rew:23.0,425.0] || -> equal(identity,sk_c6)**.
% 0.21/0.46 431[3:Rew:427.0,210.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.46 435[3:Rew:427.0,408.1] || equal(inverse(u),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 439[3:Rew:431.0,406.0] || -> equal(sk_c7,sk_c1)**.
% 0.21/0.46 443[3:Rew:439.0,166.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.21/0.46 444[3:Rew:439.0,211.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.21/0.46 445[3:Rew:439.0,402.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.46 455[3:Rew:444.0,445.0] || -> equal(sk_c4,sk_c1)**.
% 0.21/0.46 456[3:Rew:455.0,443.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.46 465[3:Obv:435.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 466[3:Rew:431.0,465.1,439.0,465.1,439.0,465.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.46 551[3:SpL:456.0,466.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.46 554[3:Obv:551.1] || -> .
% 0.21/0.46 556[2:Spt:554.0,14.0,166.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.21/0.46 557[2:Spt:554.0,14.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.46 558[2:MRR:2.0,556.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.46 560[2:MRR:10.0,556.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.46 561[2:MRR:6.0,556.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.21/0.46 570[2:SpR:560.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c3)**.
% 0.21/0.46 572[2:Rew:557.0,570.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.21/0.46 578[2:SpR:572.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c6)**.
% 0.21/0.46 580[2:Rew:23.0,578.0] || -> equal(identity,sk_c6)**.
% 0.21/0.46 581[2:Rew:580.0,210.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.46 586[2:Rew:580.0,164.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(inverse(u),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 587[2:Rew:581.0,561.0] || -> equal(sk_c7,sk_c1)**.
% 0.21/0.46 591[2:Rew:587.0,558.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.46 606[2:Obv:586.2] || equal(inverse(inverse(sk_c7)),sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.46 607[2:Rew:581.0,606.2,587.0,606.2,587.0,606.1,591.0,606.0,591.0,606.0,587.0,606.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.46 608[2:Obv:607.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.46 706[2:SpL:591.0,608.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.46 709[2:Obv:706.1] || -> .
% 0.21/0.46 % SZS output end Refutation
% 0.21/0.46 Formulae used in the proof : prove_this_2 prove_this_3 prove_this_4 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 left_identity left_inverse associativity
% 0.21/0.46
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