TSTP Solution File: GRP293-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP293-1 : 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 11:46:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP293-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Tue Jun 14 07:11:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 757 clauses, backtracked 445 clauses, performed 14 splits and kept 760 clauses.
% 0.19/0.46 SPASS allocated 63553 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 291 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.46 4[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.46 5[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.46 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.46 8[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.46 9[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.46 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.46 15[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.46 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.46 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.46 19[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.46 20[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.46 21[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 22[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.46 23[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.19/0.46 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 25[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 26[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 28[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 29[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 31[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.46 32[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.46 33[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 34[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.46 35[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.46 36[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 37[0:Inp] || equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(v,sk_c8),sk_c6)** equal(inverse(v),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c8)** equal(inverse(w),sk_c7) equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.19/0.46 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 41[0:Con:37.9] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.46 42[1:Spt:41.1,41.4] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c6)** -> .
% 0.19/0.46 43[2:Spt:19.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.46 47[3:Spt:24.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.46 49[4:Spt:21.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 51[5:Spt:23.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.46 56[6:Spt:22.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.46 58[7:Spt:20.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.46 63[3:SpR:47.0,39.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.46 73[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 75[0:Rew:38.0,73.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 78[3:SpR:63.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.46 79[3:Rew:38.0,78.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.46 85[5:SpR:51.0,79.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.46 86[6:Rew:56.0,85.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.46 87[6:Rew:86.0,43.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.46 88[6:Rew:86.0,49.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.46 90[7:Rew:86.0,58.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.46 109[7:SpL:90.0,42.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c6,sk_c8) -> .
% 0.19/0.46 110[7:Rew:88.0,109.0] || equal(sk_c8,sk_c8) equal(sk_c6,sk_c8)** -> .
% 0.19/0.46 111[7:Obv:110.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.46 113[0:SpR:75.0,75.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 116[7:SpR:90.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.46 122[0:SpR:39.0,75.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 127[7:Rew:87.0,116.0,88.0,116.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.46 128[7:MRR:127.0,111.0] || -> .
% 0.19/0.46 144[7:Spt:128.0,20.0,58.0] || equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.19/0.46 145[7:Spt:128.0,20.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 147[7:Rew:86.0,144.0] || equal(multiply(sk_c3,sk_c8),sk_c8)** -> .
% 0.19/0.46 148[6:Rew:86.0,32.1] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.46 149[7:MRR:148.1,147.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 153[6:Rew:86.0,26.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 154[7:MRR:153.0,147.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 166[7:SpL:154.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 168[7:Obv:166.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 169[7:Rew:149.0,168.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 170[7:Obv:169.0] || -> .
% 0.19/0.46 171[6:Spt:170.0,22.0,56.0] || equal(multiply(sk_c8,sk_c5),sk_c7)** -> .
% 0.19/0.46 172[6:Spt:170.0,22.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 175[6:Rew:85.0,171.0] || equal(sk_c7,sk_c8)** -> .
% 0.19/0.46 176[0:Rew:113.0,122.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 177[5:Rew:85.0,34.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c8).
% 0.19/0.46 178[6:MRR:177.1,175.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 181[5:Rew:85.0,28.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 182[6:MRR:181.0,175.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 200[6:SpL:182.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 203[6:Obv:200.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 204[6:Rew:178.0,203.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 205[6:Obv:204.0] || -> .
% 0.19/0.46 206[5:Spt:205.0,23.0,51.0] || equal(multiply(sk_c4,sk_c8),sk_c5)** -> .
% 0.19/0.46 207[5:Spt:205.0,23.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 208[5:MRR:35.1,206.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 210[5:MRR:29.0,206.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 232[5:SpL:210.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 251[5:Obv:232.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 252[5:Rew:208.0,251.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 253[5:Obv:252.0] || -> .
% 0.19/0.46 256[4:Spt:253.0,21.0,49.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.46 257[4:Spt:253.0,21.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 258[4:MRR:33.0,256.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 260[4:MRR:27.0,256.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 290[4:SpL:260.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 304[4:Obv:290.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 305[4:Rew:258.0,304.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 306[4:Obv:305.0] || -> .
% 0.19/0.46 307[3:Spt:306.0,24.0,47.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.46 308[3:Spt:306.0,24.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 309[3:MRR:36.0,307.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 311[3:MRR:30.0,307.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 329[3:SpL:311.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 350[3:Obv:329.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 351[3:Rew:309.0,350.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 352[3:Obv:351.0] || -> .
% 0.19/0.46 356[2:Spt:352.0,19.0,43.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.46 357[2:Spt:352.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 358[2:MRR:31.1,356.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 360[2:MRR:25.0,356.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 373[2:SpL:360.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 391[2:Obv:373.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.46 392[2:Rew:358.0,391.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 393[2:Obv:392.0] || -> .
% 0.19/0.46 396[1:Spt:393.0,41.0,41.2,41.3,41.5,41.6,41.7,41.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.46 398[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.46 399[2:Rew:398.0,396.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c6) equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.46 401[2:Obv:399.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.46 404[2:SpR:398.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.19/0.46 406[3:Spt:21.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.46 408[3:Rew:406.0,401.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c7,sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.46 409[3:Obv:408.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.46 412[3:SpR:406.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.19/0.46 414[4:Spt:6.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.46 416[4:Rew:414.0,409.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 417[4:Obv:416.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.46 420[4:SpR:414.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.46 422[5:Spt:36.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.46 423[5:SpR:422.0,75.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.46 428[6:Spt:18.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.46 431[7:Spt:30.1] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.46 433[7:SpR:431.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.19/0.46 435[7:Rew:406.0,433.0,422.0,433.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.46 436[7:Rew:435.0,398.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.46 439[7:Rew:435.0,9.0] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.46 441[7:Rew:435.0,8.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.46 443[7:Rew:435.0,12.1] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.46 444[7:Rew:435.0,404.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.46 446[7:Rew:435.0,412.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.46 449[7:Rew:435.0,417.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.46 452[7:Rew:39.0,446.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 454[7:Rew:452.0,176.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.46 455[7:Rew:452.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.46 457[7:Rew:454.0,444.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.46 460[7:Rew:435.0,439.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.46 465[7:Rew:435.0,441.1] || -> equal(multiply(sk_c3,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.46 466[7:Rew:435.0,449.3,435.0,449.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.46 467[7:Con:466.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.46 482[7:SpR:455.0,75.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.46 485[7:SpR:428.0,455.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.19/0.46 487[7:Rew:454.0,482.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.46 504[7:SpR:485.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c1)**.
% 0.19/0.46 506[7:Rew:457.0,504.0] || -> equal(multiply(sk_c8,sk_c6),sk_c1)**.
% 0.19/0.46 507[7:Rew:454.0,506.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.46 512[7:Rew:507.0,465.1] || -> equal(multiply(sk_c3,sk_c8),sk_c8)** equal(multiply(sk_c8,sk_c8),sk_c8).
% 0.19/0.46 514[7:Rew:507.0,443.1] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.46 515[7:Rew:507.0,460.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.46 518[7:Rew:436.0,514.1] || -> equal(inverse(sk_c4),sk_c8)** equal(sk_c6,sk_c8).
% 0.19/0.46 519[7:Rew:436.0,515.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c6,sk_c8).
% 0.19/0.46 521[7:Rew:436.0,512.1] || -> equal(multiply(sk_c3,sk_c8),sk_c8)** equal(sk_c6,sk_c8).
% 0.19/0.46 524[8:Spt:518.1] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.46 529[8:Rew:524.0,454.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.46 532[8:Rew:529.0,467.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.46 584[8:SpL:457.0,532.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 586[8:Obv:584.1] || -> .
% 0.19/0.46 587[8:Spt:586.0,518.1,524.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.46 588[8:Spt:586.0,518.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.46 589[8:MRR:519.1,587.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.46 591[8:MRR:521.1,587.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.46 608[8:SpR:589.0,487.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.19/0.46 611[8:Rew:457.0,608.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.46 613[8:Rew:611.0,591.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.46 614[8:Rew:436.0,613.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.46 615[8:MRR:614.0,587.0] || -> .
% 0.19/0.46 618[7:Spt:615.0,30.1,431.0] || equal(multiply(sk_c2,sk_c8),sk_c6)** -> .
% 0.19/0.46 619[7:Spt:615.0,30.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.46 620[7:MRR:27.1,618.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 621[7:MRR:29.1,618.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.46 622[7:MRR:28.1,618.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.46 623[7:MRR:26.1,618.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.46 642[7:SpR:621.0,75.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.46 644[7:Rew:619.0,642.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.46 645[7:Rew:622.0,644.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.46 646[7:Rew:645.0,620.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.46 647[7:Rew:645.0,414.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.46 651[7:Rew:645.0,412.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.46 657[7:Rew:645.0,623.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.46 661[7:Rew:39.0,651.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 662[7:Rew:661.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 697[7:SpR:657.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.46 699[7:Rew:647.0,697.0,646.0,697.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.46 703[7:Rew:699.0,618.0] || equal(multiply(sk_c2,sk_c8),sk_c8)** -> .
% 0.19/0.46 704[7:Rew:699.0,662.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.46 714[7:Rew:704.0,423.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 723[7:Rew:714.0,703.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.46 724[7:Obv:723.0] || -> .
% 0.19/0.46 727[6:Spt:724.0,18.1,428.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.46 728[6:Spt:724.0,18.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.46 729[6:MRR:15.1,727.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 730[6:MRR:17.0,727.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.46 731[6:MRR:16.0,727.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.46 732[6:MRR:14.0,727.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.46 747[6:SpR:730.0,75.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.46 749[6:Rew:728.0,747.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.46 750[6:Rew:731.0,749.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.46 751[6:Rew:750.0,729.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.46 752[6:Rew:750.0,398.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.46 755[6:Rew:750.0,404.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.47 756[6:Rew:750.0,412.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.47 762[6:Rew:750.0,732.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 763[6:Rew:750.0,417.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.47 766[6:Rew:39.0,756.0] || -> equal(identity,sk_c6)**.
% 0.19/0.47 767[6:Rew:766.0,176.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 771[6:Rew:767.0,755.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 776[6:Rew:750.0,763.3,750.0,763.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.47 777[6:Con:776.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.47 801[6:SpR:762.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 803[6:Rew:752.0,801.0,751.0,801.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 807[6:Rew:803.0,767.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 813[6:Rew:807.0,777.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 886[6:SpL:771.0,813.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 888[6:Obv:886.1] || -> .
% 0.19/0.47 889[5:Spt:888.0,36.1,422.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.47 890[5:Spt:888.0,36.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 891[5:MRR:33.1,889.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 892[5:MRR:35.0,889.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 893[5:MRR:34.0,889.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 894[5:MRR:32.0,889.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 909[5:SpR:892.0,75.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 911[5:Rew:890.0,909.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 912[5:Rew:893.0,911.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 913[5:Rew:912.0,891.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 914[5:Rew:912.0,414.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 917[5:Rew:912.0,420.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.47 918[5:Rew:912.0,412.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.47 924[5:Rew:912.0,894.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 925[5:Rew:912.0,417.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.47 928[5:Rew:39.0,918.0] || -> equal(identity,sk_c6)**.
% 0.19/0.47 930[5:Rew:928.0,176.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 933[5:Rew:930.0,917.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 938[5:Rew:912.0,925.3,912.0,925.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.47 939[5:Con:938.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.47 963[5:SpR:924.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 965[5:Rew:914.0,963.0,913.0,963.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 970[5:Rew:965.0,930.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 979[5:Rew:970.0,939.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 1025[5:SpL:933.0,979.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 1027[5:Obv:1025.1] || -> .
% 0.19/0.47 1028[4:Spt:1027.0,6.1,414.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.47 1029[4:Spt:1027.0,6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 1031[4:MRR:5.1,1028.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 1032[4:MRR:4.1,1028.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 1045[4:SpR:1031.0,75.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 1047[4:Rew:1029.0,1045.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 1048[4:Rew:1032.0,1047.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 1050[4:Rew:1048.0,398.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 1054[4:Rew:1048.0,1028.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.19/0.47 1066[4:Rew:1050.0,1054.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 1067[4:Obv:1066.0] || -> .
% 0.19/0.47 1070[3:Spt:1067.0,21.1,406.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.47 1071[3:Spt:1067.0,21.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 1072[3:MRR:24.1,1070.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 1073[3:MRR:20.1,1070.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 1074[3:MRR:22.1,1070.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 1075[3:MRR:23.1,1070.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 1078[3:SpR:1072.0,75.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.47 1084[3:SpR:1073.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.47 1086[3:Rew:398.0,1084.0,1071.0,1084.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1088[3:Rew:1086.0,404.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.47 1089[3:Rew:1086.0,1070.0] || equal(multiply(sk_c8,sk_c7),sk_c7)** -> .
% 0.19/0.47 1091[3:Rew:39.0,1088.0] || -> equal(identity,sk_c8)**.
% 0.19/0.47 1092[3:Rew:1091.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 1096[3:Rew:1092.0,1078.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.47 1097[3:Rew:1092.0,1074.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 1098[3:Rew:1097.0,1075.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.47 1099[3:Rew:1096.0,1098.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 1107[3:Rew:1092.0,1089.0,1099.0,1089.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 1108[3:Obv:1107.0] || -> .
% 0.19/0.47 1113[2:Spt:1108.0,1.0,398.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.47 1114[2:Spt:1108.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 1115[2:MRR:31.1,1113.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 1117[2:MRR:25.0,1113.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.47 1119[2:MRR:19.0,1113.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.47 1128[2:SpR:1117.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.19/0.47 1130[2:Rew:1115.0,1128.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.47 1131[2:Rew:1119.0,1130.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 1132[2:Rew:1131.0,1114.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 1133[2:Rew:1131.0,1113.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.19/0.47 1138[2:Rew:1132.0,1133.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 1139[2:Obv:1138.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 Formulae used in the proof : prove_this_1 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_12 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 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.19/0.47
%------------------------------------------------------------------------------