TSTP Solution File: GRP295-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP295-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP295-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 08:04:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 713 clauses, backtracked 348 clauses, performed 11 splits and kept 639 clauses.
% 0.21/0.47 SPASS allocated 63567 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.05 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 5, length 300 :
% 0.21/0.47 % SZS output start Refutation
% 0.21/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 8[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 18[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 23[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 25[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 28[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 29[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 30[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.47 35[1:Spt:31.2,31.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c5)** -> .
% 0.21/0.47 36[2:Spt:16.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 38[2:SpL:36.0,35.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c5,sk_c5) -> .
% 0.21/0.47 39[2:Obv:38.1] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.21/0.47 40[3:Spt:19.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.47 42[4:Spt:17.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.47 44[5:Spt:20.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 46[6:Spt:18.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 49[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.21/0.47 51[3:SpR:40.0,33.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.21/0.47 52[4:SpR:42.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.21/0.47 61[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.47 62[3:SpR:51.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.47 64[3:Rew:32.0,62.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.21/0.47 65[0:Rew:32.0,61.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.47 67[4:SpR:52.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.21/0.47 69[4:Rew:32.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.47 72[5:SpR:44.0,64.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.47 78[6:SpR:46.0,69.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.47 81[0:SpR:65.0,65.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.47 83[2:SpR:36.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.47 87[0:SpR:33.0,65.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.47 88[3:SpR:51.0,65.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.21/0.47 90[5:SpR:72.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.21/0.47 92[4:SpR:52.0,65.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.21/0.47 98[5:Rew:83.0,90.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 99[5:Rew:98.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 100[5:Rew:98.0,40.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.47 101[5:Rew:98.0,39.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.21/0.47 104[5:Rew:98.0,51.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.47 111[6:Rew:98.0,78.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.47 112[5:Rew:98.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.47 114[6:Rew:99.0,111.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 121[6:Rew:114.0,112.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.47 122[6:Rew:33.0,121.0] || -> equal(identity,sk_c7)**.
% 0.21/0.47 123[6:Rew:122.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 127[6:Rew:122.0,104.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.21/0.47 134[6:Rew:123.0,127.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.47 135[6:Rew:134.0,100.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.47 137[6:MRR:135.0,101.0] || -> .
% 0.21/0.47 159[6:Spt:137.0,18.0,46.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.21/0.47 160[6:Spt:137.0,18.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 161[6:Rew:98.0,160.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.47 166[6:Rew:98.0,159.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.21/0.47 167[0:Rew:81.0,87.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.47 168[4:Rew:167.0,92.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.21/0.47 177[5:Rew:98.0,13.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.47 178[6:MRR:177.1,166.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 182[5:Rew:98.0,8.1,98.0,8.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 183[6:MRR:182.0,166.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 211[6:SpR:161.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.47 213[6:Rew:168.0,211.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.21/0.47 214[6:Rew:213.0,166.0] || equal(sk_c5,sk_c7)** -> .
% 0.21/0.47 220[6:SpR:183.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.47 222[6:Rew:99.0,220.0,178.0,220.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 223[6:MRR:222.0,214.0] || -> .
% 0.21/0.47 224[5:Spt:223.0,20.0,44.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.21/0.47 225[5:Spt:223.0,20.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 226[3:Rew:167.0,88.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.47 228[3:Rew:226.0,83.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.21/0.47 229[5:Rew:228.0,224.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.47 231[3:Rew:228.0,30.1] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.47 232[5:MRR:231.1,229.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 235[3:Rew:228.0,25.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 236[5:MRR:235.0,229.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 247[3:SpR:226.0,65.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.21/0.47 262[3:SpR:228.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.21/0.47 267[5:SpR:236.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 269[5:Rew:225.0,267.0,232.0,267.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 270[5:MRR:269.0,229.0] || -> .
% 0.21/0.47 271[4:Spt:270.0,17.0,42.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.21/0.47 272[4:Spt:270.0,17.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 273[4:MRR:27.0,271.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 274[4:MRR:12.0,271.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 275[4:MRR:22.0,271.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 276[4:MRR:7.0,271.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 286[4:SpR:275.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 288[4:Rew:272.0,286.0,273.0,286.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 289[4:Rew:288.0,40.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.47 291[4:Rew:288.0,51.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.47 292[4:Rew:288.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 296[4:Rew:288.0,247.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.21/0.47 298[4:Rew:288.0,276.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 306[4:SpR:298.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.47 308[4:Rew:274.0,306.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.47 309[4:Rew:292.0,308.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 314[4:Rew:309.0,49.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.47 315[4:Rew:309.0,262.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.47 323[4:Obv:314.1] || equal(inverse(identity),sk_c7)** -> .
% 0.21/0.47 324[4:Rew:296.0,315.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 326[4:Rew:324.0,291.0] || -> equal(identity,sk_c4)**.
% 0.21/0.47 334[4:Rew:326.0,323.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.21/0.47 337[4:Rew:289.0,334.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.47 338[4:Obv:337.0] || -> .
% 0.21/0.47 340[3:Spt:338.0,19.0,40.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.47 341[3:Spt:338.0,19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 342[3:MRR:29.0,340.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 344[3:MRR:24.0,340.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 348[3:SpR:341.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 358[3:SpR:344.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 360[3:Rew:341.0,358.0,342.0,358.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 363[3:Rew:360.0,39.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.21/0.47 365[3:Rew:360.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.47 369[3:Rew:360.0,348.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.47 371[3:Rew:33.0,369.0] || -> equal(identity,sk_c5)**.
% 0.21/0.47 372[3:Rew:371.0,167.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.47 378[3:Rew:372.0,365.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.47 379[3:MRR:378.0,363.0] || -> .
% 0.21/0.47 384[2:Spt:379.0,16.0,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.47 385[2:Spt:379.0,16.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 386[2:MRR:26.1,384.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 388[2:MRR:21.0,384.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 390[2:MRR:1.0,384.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 399[2:SpR:388.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 401[2:Rew:385.0,399.0,386.0,399.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 403[2:Rew:401.0,384.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.21/0.47 405[2:Rew:401.0,390.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 408[2:Rew:405.0,403.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.47 409[2:Obv:408.0] || -> .
% 0.21/0.47 420[1:Spt:409.0,31.0,31.1,31.3,31.4,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 422[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 423[2:Rew:422.0,420.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 425[2:Obv:423.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 428[2:SpR:422.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.47 430[3:Spt:17.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.47 433[4:Spt:19.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.47 436[5:Spt:18.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 438[5:SpR:436.0,65.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.21/0.47 440[5:Rew:430.0,438.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.47 444[6:Spt:20.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 446[6:SpR:444.0,65.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.21/0.47 448[6:Rew:433.0,446.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.47 450[5:SpR:440.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.47 453[6:SpR:448.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.21/0.47 455[6:Rew:428.0,453.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 456[6:Rew:455.0,422.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 457[6:Rew:455.0,433.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.47 459[6:Rew:455.0,444.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.21/0.47 460[6:Rew:455.0,440.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.47 463[6:Rew:455.0,425.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 464[6:Rew:455.0,428.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.47 471[6:Rew:456.0,460.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 473[6:Rew:471.0,459.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.47 475[6:Rew:33.0,464.0,471.0,464.0] || -> equal(identity,sk_c7)**.
% 0.21/0.47 476[6:Rew:475.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 477[6:Rew:475.0,167.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.47 481[6:Rew:477.0,473.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.47 483[6:Rew:481.0,457.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.47 493[6:Rew:455.0,463.7,476.0,463.7,471.0,463.7,471.0,463.6,476.0,463.6,477.0,463.5,455.0,463.5,477.0,463.4,455.0,463.4,477.0,463.3,471.0,463.3,455.0,463.3,455.0,463.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(sk_c7,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.21/0.47 494[6:Obv:493.7] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.21/0.47 495[6:Con:494.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.47 556[6:SpL:483.0,495.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.47 558[6:Obv:556.1] || -> .
% 0.21/0.47 559[6:Spt:558.0,20.0,444.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.21/0.47 560[6:Spt:558.0,20.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 561[6:MRR:30.1,559.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 563[6:MRR:25.0,559.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 571[6:SpR:560.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 573[6:Rew:450.0,571.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 577[6:Rew:573.0,559.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 579[6:Rew:573.0,563.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.21/0.47 608[6:SpR:579.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.21/0.47 610[6:Rew:440.0,608.0,561.0,608.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 611[6:Rew:610.0,433.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.47 616[6:Rew:610.0,450.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.47 623[6:Rew:610.0,577.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.21/0.47 627[6:Rew:33.0,616.0] || -> equal(identity,sk_c7)**.
% 0.21/0.47 628[6:Rew:627.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 629[6:Rew:627.0,167.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.47 630[6:Rew:627.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.47 645[6:Rew:629.0,623.0] || equal(sk_c4,sk_c7)** -> .
% 0.21/0.47 675[6:SpR:611.0,630.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.21/0.47 676[6:Rew:628.0,675.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.47 677[6:MRR:676.0,645.0] || -> .
% 0.21/0.47 681[5:Spt:677.0,18.0,436.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.21/0.47 682[5:Spt:677.0,18.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 683[5:MRR:28.1,681.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 684[5:MRR:13.1,681.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 685[5:MRR:23.0,681.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 686[5:MRR:8.0,681.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 693[5:SpR:682.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 704[5:SpR:685.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 706[5:Rew:682.0,704.0,683.0,704.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 709[5:Rew:706.0,422.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 711[5:Rew:706.0,681.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.21/0.48 714[5:Rew:706.0,686.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 718[5:Rew:706.0,693.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.48 720[5:Rew:33.0,718.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 721[5:Rew:720.0,167.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 722[5:Rew:720.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.48 724[5:Rew:720.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.21/0.48 740[5:SpR:714.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 742[5:Rew:684.0,740.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.48 743[5:Rew:709.0,742.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 747[5:Rew:743.0,721.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 748[5:Rew:743.0,722.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 750[5:Rew:743.0,724.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.48 754[5:Rew:747.0,711.0] || equal(sk_c3,sk_c7)** -> .
% 0.21/0.48 798[5:SpR:430.0,750.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.48 800[5:Rew:748.0,798.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.48 801[5:MRR:800.0,754.0] || -> .
% 0.21/0.48 805[4:Spt:801.0,19.0,433.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.48 806[4:Spt:801.0,19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.48 807[4:MRR:29.0,805.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 808[4:MRR:14.0,805.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 809[4:MRR:24.0,805.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.48 810[4:MRR:9.0,805.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 811[4:MRR:4.0,805.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 812[4:Rew:811.0,425.7,806.0,425.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) equal(sk_c5,sk_c5) -> .
% 0.21/0.48 813[4:Obv:812.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 817[4:SpR:806.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.48 827[4:SpR:809.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.48 829[4:Rew:806.0,827.0,807.0,827.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 831[4:Rew:829.0,422.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 833[4:Rew:829.0,428.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.48 835[4:Rew:829.0,810.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 837[4:Rew:829.0,813.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 839[4:Rew:829.0,817.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.48 841[4:Rew:33.0,839.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 843[4:Rew:841.0,167.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 846[4:Rew:843.0,833.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 850[4:Rew:829.0,837.5,829.0,837.4,843.0,837.3,829.0,837.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 851[4:Con:850.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 864[4:SpR:835.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 866[4:Rew:831.0,864.0,808.0,864.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 871[4:Rew:866.0,843.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 881[4:Rew:871.0,851.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.48 889[4:Con:881.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 953[4:SpL:846.0,889.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 955[4:Obv:953.1] || -> .
% 0.21/0.48 956[3:Spt:955.0,17.0,430.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.21/0.48 957[3:Spt:955.0,17.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.48 958[3:MRR:27.0,956.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 959[3:MRR:12.0,956.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 960[3:MRR:22.0,956.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.48 961[3:MRR:7.0,956.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 962[3:MRR:2.0,956.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 963[3:Rew:962.0,425.7,957.0,425.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) equal(sk_c5,sk_c5) -> .
% 0.21/0.48 964[3:Obv:963.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 968[3:SpR:957.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.48 978[3:SpR:960.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.48 980[3:Rew:957.0,978.0,958.0,978.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 982[3:Rew:980.0,422.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 983[3:Rew:980.0,428.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.48 985[3:Rew:980.0,961.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 987[3:Rew:980.0,964.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 989[3:Rew:980.0,968.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.48 991[3:Rew:33.0,989.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 992[3:Rew:991.0,167.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 996[3:Rew:992.0,983.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 1000[3:Rew:980.0,987.5,980.0,987.4,992.0,987.3,980.0,987.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 1001[3:Con:1000.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 1005[3:SpR:985.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 1007[3:Rew:959.0,1005.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.48 1008[3:Rew:982.0,1007.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 1012[3:Rew:1008.0,992.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 1018[3:Rew:1012.0,1001.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.48 1030[3:Con:1018.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 1058[3:SpL:996.0,1030.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 1059[3:Obv:1058.1] || -> .
% 0.21/0.48 1060[2:Spt:1059.0,1.0,422.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.48 1061[2:Spt:1059.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 1062[2:MRR:26.1,1060.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 1064[2:MRR:21.0,1060.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.48 1066[2:MRR:16.0,1060.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.48 1075[2:SpR:1064.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.48 1077[2:Rew:1062.0,1075.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.48 1078[2:Rew:1066.0,1077.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 1079[2:Rew:1078.0,1061.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 1080[2:Rew:1078.0,1060.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.21/0.48 1085[2:Rew:1079.0,1080.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.48 1086[2:Obv:1085.0] || -> .
% 0.21/0.48 % SZS output end Refutation
% 0.21/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_7 prove_this_8 prove_this_9 prove_this_12 prove_this_13 prove_this_14 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 left_identity left_inverse associativity
% 0.21/0.48
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