TSTP Solution File: GRP280-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP280-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP280-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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 10:51:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 1192 clauses, backtracked 461 clauses, performed 12 splits and kept 978 clauses.
% 0.20/0.52 SPASS allocated 63769 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.52 0:00:00.04 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.09 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 4, length 431 :
% 0.20/0.52 % SZS output start Refutation
% 0.20/0.52 1[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.20/0.52 2[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 3[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 5[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 7[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.20/0.52 8[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 9[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 10[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 12[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 13[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.20/0.52 14[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c5),sk_c9)**.
% 0.20/0.52 15[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 16[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.52 18[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 19[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 21[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 22[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 23[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 24[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 25[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c2,sk_c9),sk_c3).
% 0.20/0.52 26[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 27[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 28[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 29[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 30[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 31[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.20/0.52 32[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c5),sk_c9)**.
% 0.20/0.52 33[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 34[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.52 35[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.20/0.52 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 37[0:Inp] || equal(multiply(sk_c9,sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(sk_c9,v),sk_c8)** equal(multiply(w,sk_c9),v)* equal(inverse(w),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(x,y),sk_c9)** equal(inverse(x),y) equal(multiply(y,sk_c8),sk_c9)** equal(multiply(z,sk_c9),sk_c7)** equal(inverse(z),sk_c9) -> .
% 0.20/0.52 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.52 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.52 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.52 41[0:Con:37.3] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(u,v),sk_c9)**+ equal(multiply(w,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7) -> .
% 0.20/0.52 42[1:Spt:41.0,41.3,41.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.20/0.52 43[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.20/0.52 45[2:SpL:43.0,42.1] || equal(inverse(sk_c9),sk_c7) equal(sk_c9,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 46[3:Spt:3.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.52 48[4:Spt:6.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.52 50[5:Spt:2.0] || -> equal(multiply(sk_c4,sk_c5),sk_c9)**.
% 0.20/0.52 52[5:SpL:50.0,42.1] || equal(inverse(sk_c4),sk_c5) equal(sk_c9,sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.20/0.52 53[5:Obv:52.1] || equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.20/0.52 54[5:Rew:46.0,53.0] || equal(sk_c5,sk_c5) equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.20/0.52 55[5:Obv:54.0] || equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.20/0.52 56[5:MRR:34.1,55.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 57[5:MRR:16.1,55.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 58[5:MRR:28.0,55.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 59[5:MRR:22.0,55.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 60[5:MRR:10.0,55.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 79[1:SpL:38.0,42.1] || equal(inverse(identity),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.52 82[4:SpR:48.0,39.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.52 83[5:SpR:56.0,39.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.20/0.52 84[5:SpR:57.0,39.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.20/0.52 95[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.52 97[0:Rew:38.0,95.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.52 116[0:SpR:97.0,97.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.52 118[2:SpR:43.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.20/0.52 119[5:SpR:59.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.20/0.52 121[4:SpR:82.0,97.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c6)**.
% 0.20/0.52 122[5:SpR:83.0,97.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.20/0.52 123[5:SpR:84.0,97.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.20/0.52 125[5:SpR:58.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 128[0:SpR:39.0,97.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.52 136[5:Rew:118.0,119.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.52 137[5:Rew:136.0,58.0] || -> equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.20/0.52 143[5:Rew:121.0,122.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.52 148[5:Rew:143.0,137.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.20/0.52 149[5:Rew:121.0,123.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.52 151[5:Rew:149.0,60.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.20/0.52 156[5:Rew:148.0,151.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 157[5:Rew:156.0,43.0] || -> equal(multiply(sk_c9,sk_c8),sk_c8)**.
% 0.20/0.52 164[5:Rew:156.0,118.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c8)**.
% 0.20/0.52 165[5:Rew:156.0,136.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.52 169[5:Rew:143.0,125.0,165.0,125.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c9)**.
% 0.20/0.52 170[5:Rew:48.0,169.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.52 171[5:Rew:157.0,170.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 173[5:Rew:171.0,48.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.52 176[5:Rew:171.0,82.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.20/0.52 179[5:Rew:171.0,79.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.52 189[5:Rew:171.0,164.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.20/0.52 190[5:Rew:39.0,189.0] || -> equal(identity,sk_c8)**.
% 0.20/0.52 191[5:Rew:190.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.52 194[5:Rew:190.0,176.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.52 197[5:Rew:191.0,194.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.52 200[5:Rew:197.0,173.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 206[5:Rew:190.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.20/0.52 219[5:Rew:116.0,206.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 240[5:Rew:219.0,179.2,171.0,179.2,200.0,179.0,190.0,179.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.52 241[5:Obv:240.1] || equal(u,sk_c8)* -> .
% 0.20/0.52 242[5:UnC:241.0,97.0] || -> .
% 0.20/0.52 251[5:Spt:242.0,2.0,50.0] || equal(multiply(sk_c4,sk_c5),sk_c9)** -> .
% 0.20/0.52 252[5:Spt:242.0,2.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 253[0:Rew:116.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.52 255[4:Rew:253.0,121.0] || -> equal(inverse(sk_c9),sk_c6)**.
% 0.20/0.52 256[4:Rew:255.0,118.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.52 257[5:MRR:32.1,251.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 258[5:MRR:14.1,251.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 259[5:MRR:26.0,251.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 260[5:MRR:20.0,251.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 261[5:MRR:8.0,251.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 262[4:Rew:255.0,45.0] || equal(sk_c6,sk_c7) equal(sk_c9,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 269[5:SpR:252.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.20/0.52 271[5:Rew:255.0,269.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.52 276[4:SpR:255.0,97.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.20/0.52 296[4:SpR:256.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.20/0.52 301[5:SpR:259.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 303[5:Rew:257.0,301.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 304[5:Rew:260.0,303.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 305[5:Rew:304.0,252.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 307[5:Rew:304.0,255.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.52 309[5:Rew:304.0,258.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 311[5:Rew:304.0,82.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.20/0.52 317[5:Rew:304.0,261.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 318[5:Rew:304.0,262.1] || equal(sk_c6,sk_c7) equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 327[5:Rew:304.0,276.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.20/0.52 330[5:Rew:296.0,327.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.52 337[5:Obv:318.1] || equal(sk_c6,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 338[5:Rew:330.0,337.1,304.0,337.1] || equal(sk_c6,sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.20/0.52 339[5:Obv:338.1] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.52 354[5:SpR:271.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.52 358[5:Rew:330.0,354.0] || -> equal(multiply(sk_c6,u),multiply(sk_c8,u))**.
% 0.20/0.52 397[5:SpR:317.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 399[5:Rew:305.0,397.0,309.0,397.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 400[5:Rew:399.0,339.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.52 404[5:Rew:399.0,330.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.52 407[5:Rew:404.0,311.0] || -> equal(identity,sk_c6)**.
% 0.20/0.52 409[5:Rew:404.0,358.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.52 415[5:Rew:407.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.52 435[5:SpR:307.0,415.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.20/0.52 439[5:Rew:409.0,435.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.52 440[5:MRR:439.0,400.0] || -> .
% 0.20/0.52 451[4:Spt:440.0,6.0,48.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.20/0.52 452[4:Spt:440.0,6.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 453[4:MRR:36.0,451.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 454[4:MRR:18.0,451.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 455[4:MRR:30.0,451.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 456[4:MRR:24.0,451.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 457[4:MRR:12.0,451.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 459[4:SpR:452.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.20/0.52 474[4:SpR:455.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 476[4:Rew:453.0,474.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 477[4:Rew:456.0,476.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 478[4:Rew:477.0,452.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 480[4:Rew:477.0,454.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 484[4:Rew:477.0,118.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 485[4:Rew:477.0,45.0] || equal(inverse(sk_c8),sk_c7) equal(sk_c9,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 486[4:Rew:477.0,459.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 489[4:Rew:477.0,457.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 499[4:Rew:39.0,484.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 501[4:Rew:499.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 502[4:Rew:499.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.52 505[4:Rew:501.0,486.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 510[4:Rew:502.0,485.2,477.0,485.2,477.0,485.1,505.0,485.0] || equal(sk_c7,sk_c8)** equal(sk_c8,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.20/0.52 511[4:Obv:510.2] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.52 545[4:SpR:489.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 547[4:Rew:478.0,545.0,480.0,545.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 548[4:MRR:547.0,511.0] || -> .
% 0.20/0.52 549[3:Spt:548.0,3.0,46.0] || equal(inverse(sk_c4),sk_c5)** -> .
% 0.20/0.52 550[3:Spt:548.0,3.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 551[3:MRR:33.0,549.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 552[3:MRR:15.0,549.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 553[3:MRR:27.0,549.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 554[3:MRR:21.0,549.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 555[3:MRR:9.0,549.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 557[3:SpR:550.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.20/0.52 567[3:SpR:553.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 569[3:Rew:551.0,567.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 570[3:Rew:554.0,569.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 571[3:Rew:570.0,550.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 573[3:Rew:570.0,552.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 576[3:Rew:570.0,118.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 577[3:Rew:570.0,45.0] || equal(inverse(sk_c8),sk_c7) equal(sk_c9,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.20/0.52 578[3:Rew:570.0,557.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 581[3:Rew:570.0,555.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 590[3:Rew:39.0,576.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 591[3:Rew:590.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.52 592[3:Rew:590.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 595[3:Rew:592.0,578.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 599[3:Rew:591.0,577.2,570.0,577.2,570.0,577.1,595.0,577.0] || equal(sk_c7,sk_c8)** equal(sk_c8,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.20/0.52 600[3:Obv:599.2] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.52 634[3:SpR:581.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 636[3:Rew:571.0,634.0,573.0,634.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 637[3:MRR:636.0,600.0] || -> .
% 0.20/0.52 638[2:Spt:637.0,1.0,43.0] || equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.20/0.52 639[2:Spt:637.0,1.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 640[2:MRR:31.1,638.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 641[2:MRR:13.1,638.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 642[2:MRR:25.0,638.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 643[2:MRR:19.0,638.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 644[2:MRR:7.0,638.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 646[2:SpR:639.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.20/0.52 653[2:SpR:642.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 655[2:Rew:640.0,653.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 656[2:Rew:643.0,655.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 657[2:Rew:656.0,639.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 659[2:Rew:656.0,641.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 662[2:Rew:656.0,643.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.20/0.52 663[2:Rew:656.0,644.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 664[2:Rew:656.0,79.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.52 669[2:Rew:656.0,646.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 674[2:Rew:656.0,664.2] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 692[2:SpR:662.0,97.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.20/0.52 694[2:Rew:39.0,692.0] || -> equal(identity,sk_c3)**.
% 0.20/0.52 695[2:Rew:694.0,253.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.52 698[2:Rew:694.0,674.0] || equal(inverse(sk_c3),u) equal(u,sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 699[2:Rew:694.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.20/0.52 705[2:SpR:663.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 707[2:Rew:657.0,705.0,659.0,705.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 710[2:Rew:707.0,669.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.20/0.52 714[2:Rew:699.0,710.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.52 717[2:Rew:714.0,695.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 720[2:Rew:714.0,698.0] || equal(inverse(sk_c8),u) equal(u,sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 723[2:Rew:717.0,663.0] || -> equal(sk_c1,sk_c8)**.
% 0.20/0.52 728[2:Rew:723.0,659.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 738[2:Rew:717.0,720.2,728.0,720.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.52 739[2:Obv:738.1] || equal(u,sk_c8)* -> .
% 0.20/0.52 740[2:UnC:739.0,656.0] || -> .
% 0.20/0.52 743[1:Spt:740.0,41.1,41.2,41.4,41.6,41.7,41.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)**+ equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7) -> .
% 0.20/0.52 745[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.20/0.52 746[2:Rew:745.0,743.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(sk_c8,sk_c8) equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.20/0.52 748[2:Obv:746.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.20/0.52 751[2:SpR:745.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.20/0.52 753[3:Spt:6.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 755[3:Rew:753.0,748.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.20/0.52 756[3:Obv:755.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.20/0.52 759[3:SpR:753.0,97.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.20/0.52 761[4:Spt:33.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.52 764[5:Spt:36.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.52 765[5:SpR:764.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.20/0.52 770[6:Spt:32.1] || -> equal(multiply(sk_c4,sk_c5),sk_c9)**.
% 0.20/0.52 772[6:SpR:770.0,97.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c5)**.
% 0.20/0.52 774[6:Rew:761.0,772.0] || -> equal(multiply(sk_c5,sk_c9),sk_c5)**.
% 0.20/0.52 775[7:Spt:34.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.52 777[7:SpR:775.0,97.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.52 779[8:Spt:35.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.20/0.52 781[8:SpR:779.0,97.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.20/0.52 783[8:Rew:745.0,781.0,764.0,781.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 785[8:Rew:783.0,753.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 786[8:Rew:783.0,764.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.52 788[8:Rew:783.0,775.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.20/0.52 789[8:Rew:783.0,779.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.52 790[8:Rew:783.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 793[8:Rew:783.0,756.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.20/0.52 797[8:Rew:783.0,774.0] || -> equal(multiply(sk_c5,sk_c8),sk_c5)**.
% 0.20/0.52 801[8:Rew:788.0,797.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.52 805[8:Rew:801.0,788.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.52 806[8:Rew:785.0,805.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 809[8:Rew:806.0,789.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.20/0.52 810[8:Rew:39.0,790.0,806.0,790.0] || -> equal(identity,sk_c8)**.
% 0.20/0.52 812[8:Rew:810.0,253.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 815[8:Rew:812.0,809.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.52 817[8:Rew:815.0,786.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 829[8:Rew:812.0,793.3,783.0,793.3,812.0,793.2,783.0,793.2,806.0,793.2,783.0,793.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.20/0.52 830[8:Con:829.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.52 860[8:SpL:817.0,830.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.52 861[8:Obv:860.1] || -> .
% 0.20/0.52 862[8:Spt:861.0,35.1,779.0] || equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.20/0.52 863[8:Spt:861.0,35.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 865[8:MRR:29.0,862.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 866[8:MRR:23.0,862.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 890[8:SpR:865.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 892[8:Rew:863.0,890.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 893[8:Rew:866.0,892.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 897[8:Rew:893.0,775.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.20/0.52 899[8:Rew:893.0,753.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 902[8:Rew:893.0,774.0] || -> equal(multiply(sk_c5,sk_c8),sk_c5)**.
% 0.20/0.52 903[8:Rew:893.0,777.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c8)**.
% 0.20/0.52 906[8:Rew:893.0,862.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.52 907[8:Rew:893.0,765.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.20/0.52 918[8:Rew:897.0,902.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.52 921[8:Rew:918.0,897.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.52 923[8:Rew:899.0,921.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 926[8:Rew:39.0,903.0,918.0,903.0] || -> equal(identity,sk_c8)**.
% 0.20/0.52 927[8:Rew:926.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.52 928[8:Rew:926.0,253.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 941[8:Rew:928.0,906.0,923.0,906.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.52 943[8:Rew:927.0,907.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.52 983[8:SpR:943.0,928.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.52 985[8:MRR:983.0,941.0] || -> .
% 0.20/0.52 987[7:Spt:985.0,34.1,775.0] || equal(multiply(sk_c5,sk_c8),sk_c9)** -> .
% 0.20/0.52 988[7:Spt:985.0,34.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 990[7:MRR:28.0,987.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 991[7:MRR:22.0,987.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 1008[7:SpR:990.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 1010[7:Rew:988.0,1008.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 1011[7:Rew:991.0,1010.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1019[7:Rew:1011.0,774.0] || -> equal(multiply(sk_c5,sk_c8),sk_c5)**.
% 0.20/0.52 1020[7:Rew:1011.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 1021[7:Rew:1011.0,759.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 1029[7:Rew:1011.0,756.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.20/0.52 1033[7:Rew:39.0,1020.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 1034[7:Rew:1033.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 1036[7:Rew:1033.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.52 1038[7:Rew:1034.0,1021.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 1043[7:Rew:1011.0,1029.3,1011.0,1029.2,1011.0,1029.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1079[7:SpR:1019.0,97.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c8)**.
% 0.20/0.52 1081[7:Rew:1036.0,1079.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1085[7:Rew:1081.0,1034.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 1089[7:Rew:1081.0,1043.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1107[7:Con:1089.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 1108[7:Rew:1085.0,1107.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.52 1152[7:SpL:1038.0,1108.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.52 1153[7:Obv:1152.1] || -> .
% 0.20/0.52 1154[6:Spt:1153.0,32.1,770.0] || equal(multiply(sk_c4,sk_c5),sk_c9)** -> .
% 0.20/0.52 1155[6:Spt:1153.0,32.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 1156[6:MRR:14.1,1154.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 1157[6:MRR:26.0,1154.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 1158[6:MRR:20.0,1154.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 1159[6:MRR:8.0,1154.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 1173[6:SpR:1157.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 1175[6:Rew:1155.0,1173.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 1176[6:Rew:1158.0,1175.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1179[6:Rew:1176.0,1156.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 1180[6:Rew:1176.0,753.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 1184[6:Rew:1176.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 1185[6:Rew:1176.0,1154.0] || equal(multiply(sk_c4,sk_c5),sk_c8)** -> .
% 0.20/0.52 1190[6:Rew:1176.0,1159.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 1195[6:Rew:39.0,1184.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 1197[6:Rew:1195.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 1199[6:Rew:1195.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.52 1235[6:SpR:1190.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 1237[6:Rew:1180.0,1235.0,1179.0,1235.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1241[6:Rew:1237.0,1197.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 1243[6:Rew:1237.0,1199.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.52 1296[6:SpR:761.0,1243.0] || -> equal(multiply(sk_c5,sk_c4),sk_c8)**.
% 0.20/0.52 1302[6:SpR:1296.0,97.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c4)**.
% 0.20/0.52 1304[6:Rew:1241.0,1302.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.20/0.52 1307[6:SpR:1304.0,1243.0] || -> equal(multiply(sk_c4,sk_c5),sk_c8)**.
% 0.20/0.52 1309[6:MRR:1307.0,1185.0] || -> .
% 0.20/0.52 1310[5:Spt:1309.0,36.0,764.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.20/0.52 1311[5:Spt:1309.0,36.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 1312[5:MRR:18.0,1310.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 1313[5:MRR:30.0,1310.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 1314[5:MRR:24.0,1310.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 1315[5:MRR:12.0,1310.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 1327[5:SpR:1313.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 1329[5:Rew:1311.0,1327.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 1330[5:Rew:1314.0,1329.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1332[5:Rew:1330.0,1312.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 1335[5:Rew:1330.0,753.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 1337[5:Rew:1330.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 1338[5:Rew:1330.0,759.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 1342[5:Rew:1330.0,1315.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 1343[5:Rew:1330.0,756.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.20/0.52 1347[5:Rew:39.0,1337.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 1348[5:Rew:1347.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 1352[5:Rew:1348.0,1338.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 1356[5:Rew:1330.0,1343.3,1330.0,1343.2,1330.0,1343.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1386[5:SpR:1342.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 1388[5:Rew:1335.0,1386.0,1332.0,1386.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1392[5:Rew:1388.0,1348.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 1396[5:Rew:1388.0,1356.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1412[5:Con:1396.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 1413[5:Rew:1392.0,1412.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.52 1450[5:SpL:1352.0,1413.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.52 1452[5:Obv:1450.1] || -> .
% 0.20/0.52 1453[4:Spt:1452.0,33.0,761.0] || equal(inverse(sk_c4),sk_c5)** -> .
% 0.20/0.52 1454[4:Spt:1452.0,33.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 1455[4:MRR:15.0,1453.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 1456[4:MRR:27.0,1453.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 1457[4:MRR:21.0,1453.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 1458[4:MRR:9.0,1453.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 1470[4:SpR:1456.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 1472[4:Rew:1454.0,1470.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 1473[4:Rew:1457.0,1472.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1475[4:Rew:1473.0,1455.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 1476[4:Rew:1473.0,753.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 1479[4:Rew:1473.0,759.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.52 1480[4:Rew:1473.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 1484[4:Rew:1473.0,1458.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 1485[4:Rew:1473.0,756.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.20/0.52 1489[4:Rew:39.0,1480.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 1491[4:Rew:1489.0,253.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 1494[4:Rew:1491.0,1479.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.52 1498[4:Rew:1473.0,1485.3,1473.0,1485.2,1473.0,1485.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1528[4:SpR:1484.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 1530[4:Rew:1476.0,1528.0,1475.0,1528.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1535[4:Rew:1530.0,1491.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.52 1538[4:Rew:1530.0,1498.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.52 1554[4:Con:1538.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.52 1555[4:Rew:1535.0,1554.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.52 1587[4:SpL:1494.0,1555.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.52 1589[4:Obv:1587.1] || -> .
% 0.20/0.52 1590[3:Spt:1589.0,6.1,753.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.20/0.52 1591[3:Spt:1589.0,6.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.52 1592[3:MRR:3.1,1590.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.52 1593[3:MRR:4.1,1590.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.52 1594[3:MRR:5.1,1590.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.20/0.52 1595[3:MRR:2.1,1590.0] || -> equal(multiply(sk_c4,sk_c5),sk_c9)**.
% 0.20/0.52 1604[3:SpR:1593.0,97.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.52 1607[3:SpR:1594.0,97.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.20/0.52 1609[3:Rew:745.0,1607.0,1591.0,1607.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1612[3:Rew:1609.0,1593.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.20/0.52 1614[3:Rew:1609.0,751.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.52 1615[3:Rew:1609.0,1590.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.20/0.52 1617[3:Rew:1609.0,1595.0] || -> equal(multiply(sk_c4,sk_c5),sk_c8)**.
% 0.20/0.52 1619[3:Rew:1609.0,1604.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c8)**.
% 0.20/0.52 1621[3:Rew:39.0,1614.0] || -> equal(identity,sk_c7)**.
% 0.20/0.52 1624[3:Rew:1621.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.52 1641[3:SpR:1617.0,97.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c5)**.
% 0.20/0.52 1643[3:Rew:1612.0,1641.0,1592.0,1641.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.52 1645[3:Rew:1643.0,1612.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.52 1648[3:Rew:1643.0,1619.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.20/0.52 1650[3:Rew:1645.0,1615.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.52 1651[3:Rew:1624.0,1648.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1652[3:MRR:1651.0,1650.0] || -> .
% 0.20/0.52 1654[2:Spt:1652.0,1.0,745.0] || equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.20/0.52 1655[2:Spt:1652.0,1.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.20/0.52 1656[2:MRR:31.1,1654.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.52 1657[2:MRR:13.1,1654.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.52 1658[2:MRR:25.0,1654.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.52 1659[2:MRR:19.0,1654.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.52 1660[2:MRR:7.0,1654.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.52 1669[2:SpR:1658.0,97.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.20/0.52 1671[2:Rew:1656.0,1669.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.52 1672[2:Rew:1659.0,1671.0] || -> equal(sk_c9,sk_c8)**.
% 0.20/0.52 1673[2:Rew:1672.0,1655.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.52 1675[2:Rew:1672.0,1657.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 1677[2:Rew:1672.0,1654.0] || equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.20/0.52 1679[2:Rew:1672.0,1660.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.52 1708[2:SpR:1679.0,97.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.52 1710[2:Rew:1673.0,1708.0,1675.0,1708.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.52 1711[2:Rew:1710.0,1673.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.52 1712[2:Rew:1710.0,1677.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.20/0.52 1715[2:Rew:1711.0,1712.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.52 1716[2:Obv:1715.0] || -> .
% 0.20/0.52 % SZS output end Refutation
% 0.20/0.52 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_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 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
% 0.20/0.53
%------------------------------------------------------------------------------