TSTP Solution File: GRP268-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP268-1 : 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 11:46:36 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP268-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 03:58:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.44
% 0.21/0.44 SPASS V 3.9
% 0.21/0.44 SPASS beiseite: Proof found.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.44 SPASS derived 393 clauses, backtracked 123 clauses, performed 7 splits and kept 277 clauses.
% 0.21/0.44 SPASS allocated 63396 KBytes.
% 0.21/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.44 0:00:00.04 for the input.
% 0.21/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.44 0:00:00.00 for inferences.
% 0.21/0.44 0:00:00.00 for the backtracking.
% 0.21/0.44 0:00:00.03 for the reduction.
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 Here is a proof with depth 4, length 160 :
% 0.21/0.44 % SZS output start Refutation
% 0.21/0.44 1[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.21/0.44 2[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.44 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.44 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.21/0.44 7[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.44 8[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.44 9[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.44 10[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.44 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.44 12[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.44 13[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.44 14[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.44 15[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.44 16[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.44 17[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.44 18[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.44 19[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.44 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.44 21[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.44 22[0:Inp] || equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(v,sk_c6),sk_c7)** equal(inverse(v),sk_c6) equal(multiply(sk_c6,w),sk_c7)** equal(multiply(x,sk_c6),w)* equal(inverse(x),sk_c6) equal(multiply(y,sk_c8),sk_c7)** equal(inverse(y),sk_c8) equal(inverse(sk_c6),sk_c7) -> .
% 0.21/0.44 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.44 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.44 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.44 26[0:Con:22.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(inverse(sk_c6),sk_c7) equal(multiply(u,sk_c6),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,x),sk_c7)** -> .
% 0.21/0.44 27[1:Spt:26.2,26.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.21/0.44 30[2:Spt:20.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.44 34[3:Spt:19.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.44 36[3:SpL:34.0,27.1] || equal(inverse(sk_c5),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.44 37[3:Obv:36.1] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.44 38[3:Rew:30.0,37.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.44 39[3:Obv:38.0] || -> .
% 0.21/0.44 40[3:Spt:39.0,19.1,34.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.21/0.44 41[3:Spt:39.0,19.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.44 43[3:MRR:4.1,40.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.44 47[3:MRR:1.0,40.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.44 55[3:SpL:47.0,27.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.44 56[3:Obv:55.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.21/0.44 57[3:Rew:43.0,56.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.44 58[3:Obv:57.0] || -> .
% 0.21/0.44 59[2:Spt:58.0,20.0,30.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.44 60[2:Spt:58.0,20.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.44 62[2:MRR:5.0,59.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.44 66[2:MRR:2.0,59.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.44 74[2:SpL:66.0,27.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.44 75[2:Obv:74.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.21/0.44 76[2:Rew:62.0,75.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.44 77[2:Obv:76.0] || -> .
% 0.21/0.44 78[1:Spt:77.0,26.0,26.1,26.3,26.4,26.5,26.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c7) equal(multiply(u,sk_c6),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,w),sk_c7)** -> .
% 0.21/0.44 79[1:EqR:78.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.21/0.44 81[2:Spt:21.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.44 84[2:Rew:81.0,79.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(sk_c7,sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.21/0.44 85[2:Obv:84.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.21/0.44 89[3:Spt:11.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.44 91[4:Spt:10.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.44 94[2:SpR:81.0,24.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.21/0.44 95[3:SpR:89.0,24.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.44 101[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.44 107[0:Rew:23.0,101.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.44 113[0:SpR:107.0,107.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.44 116[0:SpR:24.0,107.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.44 120[3:SpR:95.0,107.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.44 126[0:Rew:113.0,116.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.44 127[3:Rew:126.0,120.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.44 129[3:SpR:127.0,24.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.21/0.44 132[4:Rew:91.0,129.0] || -> equal(sk_c7,identity)**.
% 0.21/0.44 133[4:Rew:132.0,81.0] || -> equal(inverse(sk_c6),identity)**.
% 0.21/0.44 135[4:Rew:132.0,94.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.21/0.44 138[4:Rew:132.0,85.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),identity)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.21/0.44 143[4:Rew:23.0,135.0] || -> equal(identity,sk_c6)**.
% 0.21/0.44 144[4:Rew:143.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.44 148[4:Rew:143.0,126.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.44 149[4:Rew:143.0,132.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.44 150[4:Rew:143.0,133.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.44 157[4:Rew:148.0,138.3,144.0,138.3,149.0,138.3,148.0,138.2,143.0,138.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(v,sk_c6) equal(u,sk_c6) -> .
% 0.21/0.44 158[4:Con:157.0] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.44 261[4:SpL:150.0,158.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.21/0.44 263[4:Obv:261.1] || -> .
% 0.21/0.44 264[4:Spt:263.0,10.1,91.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.21/0.44 265[4:Spt:263.0,10.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.44 266[4:Rew:129.0,264.0] || equal(sk_c7,identity)** -> .
% 0.21/0.44 269[3:Rew:129.0,19.1] || -> equal(inverse(sk_c3),sk_c6)** equal(sk_c7,identity).
% 0.21/0.44 270[4:MRR:269.1,266.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.44 271[3:Rew:129.0,16.0] || -> equal(sk_c7,identity) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.44 272[4:MRR:271.0,266.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.44 273[3:Rew:129.0,13.0] || -> equal(sk_c7,identity) equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.44 274[4:MRR:273.0,266.0] || -> equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.44 275[3:Rew:129.0,7.0] || -> equal(sk_c7,identity) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.44 276[4:MRR:275.0,266.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.44 288[4:SpR:272.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.21/0.44 290[4:Rew:270.0,288.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.44 291[4:Rew:274.0,290.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.44 292[4:Rew:291.0,81.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.44 293[4:Rew:291.0,266.0] || equal(identity,sk_c6)** -> .
% 0.21/0.44 294[4:Rew:291.0,94.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.21/0.44 297[4:Rew:291.0,274.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.44 298[4:Rew:291.0,276.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.21/0.44 317[4:SpR:297.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.21/0.44 319[4:Rew:292.0,317.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.45 320[4:Rew:294.0,319.0] || -> equal(identity,sk_c4)**.
% 0.21/0.45 321[4:Rew:320.0,293.0] || equal(sk_c4,sk_c6)** -> .
% 0.21/0.45 329[4:Rew:320.0,294.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.45 334[4:SpR:298.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.21/0.45 336[4:Rew:265.0,334.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.45 337[4:Rew:329.0,336.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.45 338[4:MRR:337.0,321.0] || -> .
% 0.21/0.45 339[3:Spt:338.0,11.0,89.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.45 340[3:Spt:338.0,11.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.45 342[3:MRR:20.0,339.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.45 343[3:MRR:17.0,339.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.45 344[3:MRR:14.0,339.0] || -> equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.45 345[3:MRR:8.0,339.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.45 361[3:SpR:343.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.21/0.45 363[3:Rew:342.0,361.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.45 364[3:Rew:344.0,363.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.45 365[3:Rew:364.0,81.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.45 366[3:Rew:364.0,94.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.21/0.45 369[3:Rew:364.0,344.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.45 370[3:Rew:364.0,345.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.21/0.45 373[3:Rew:364.0,85.2] || 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_c7)** -> .
% 0.21/0.45 376[3:Rew:364.0,373.3] || 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)** -> .
% 0.21/0.45 380[3:SpR:369.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.21/0.45 382[3:Rew:366.0,380.0,365.0,380.0] || -> equal(identity,sk_c4)**.
% 0.21/0.45 383[3:Rew:382.0,126.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.21/0.45 384[3:Rew:382.0,23.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.21/0.45 388[3:Rew:382.0,366.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.45 396[3:SpR:370.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.21/0.45 398[3:Rew:340.0,396.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.45 399[3:Rew:388.0,398.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.45 402[3:Rew:399.0,383.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.45 403[3:Rew:399.0,384.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.45 410[3:Rew:402.0,376.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.21/0.45 423[3:Rew:403.0,410.3,402.0,410.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(v,sk_c6) equal(u,sk_c6) -> .
% 0.21/0.45 424[3:Con:423.0] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.45 529[3:SpL:365.0,424.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.21/0.45 532[3:Obv:529.1] || -> .
% 0.21/0.45 533[2:Spt:532.0,21.0,81.0] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.21/0.45 534[2:Spt:532.0,21.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.45 535[2:MRR:12.0,533.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.45 537[2:MRR:18.0,533.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.21/0.45 538[2:MRR:15.0,533.0] || -> equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.21/0.45 539[2:MRR:9.0,533.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.45 548[2:SpR:537.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.21/0.45 550[2:Rew:534.0,548.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.45 551[2:Rew:538.0,550.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.45 552[2:Rew:551.0,533.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.21/0.45 553[2:Rew:551.0,538.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.45 554[2:Rew:551.0,539.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.21/0.45 558[2:SpR:553.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.21/0.45 560[2:Rew:24.0,558.0] || -> equal(identity,sk_c4)**.
% 0.21/0.45 562[2:Rew:560.0,126.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.21/0.45 563[2:Rew:560.0,24.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.21/0.45 569[2:SpR:554.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.21/0.45 571[2:Rew:535.0,569.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.45 577[2:SpR:571.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.45 579[2:Rew:563.0,577.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.45 580[2:Rew:579.0,537.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.45 583[2:Rew:579.0,562.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.45 592[2:Rew:583.0,580.0] || -> equal(sk_c3,sk_c6)**.
% 0.21/0.45 594[2:Rew:592.0,534.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.45 596[2:MRR:594.0,552.0] || -> .
% 0.21/0.45 % SZS output end Refutation
% 0.21/0.45 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 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
% 0.21/0.45
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