TSTP Solution File: GRP348-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP348-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:46:58 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP348-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 01:37:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 302 clauses, backtracked 148 clauses, performed 9 splits and kept 262 clauses.
% 0.21/0.43 SPASS allocated 63338 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.43 0:00:00.03 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.02 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 5, length 170 :
% 0.21/0.43 % SZS output start Refutation
% 0.21/0.43 1[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.43 2[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4).
% 0.21/0.43 3[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.43 4[0:Inp] || -> equal(multiply(sk_c3,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4).
% 0.21/0.43 5[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.43 6[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.43 7[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.43 8[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.21/0.43 9[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 10[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 11[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 12[0:Inp] || -> equal(multiply(sk_c3,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 13[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c2),sk_c5)**.
% 0.21/0.43 14[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.43 17[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c2,sk_c4),sk_c5)**.
% 0.21/0.43 18[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c4),sk_c5)**.
% 0.21/0.43 21[0:Inp] || equal(multiply(sk_c5,sk_c6),sk_c4) equal(inverse(u),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(inverse(v),sk_c5) equal(multiply(v,sk_c4),sk_c5)** equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)** equal(inverse(w),sk_c6) equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.21/0.43 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.43 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.43 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.43 25[0:Con:21.7] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(sk_c4),sk_c5) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) -> .
% 0.21/0.43 26[1:Spt:25.1,25.4] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c5),sk_c6)** -> .
% 0.21/0.43 34[2:Spt:3.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.43 36[3:Spt:4.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.21/0.43 38[3:SpL:36.0,26.1] || equal(inverse(sk_c3),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.21/0.43 39[3:Obv:38.1] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.21/0.43 40[3:Rew:34.0,39.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.43 41[3:Obv:40.0] || -> .
% 0.21/0.43 42[3:Spt:41.0,4.0,36.0] || equal(multiply(sk_c3,sk_c5),sk_c6)** -> .
% 0.21/0.43 43[3:Spt:41.0,4.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.43 45[3:MRR:8.1,42.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.43 47[3:MRR:12.0,42.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 53[3:SpL:47.0,26.1] || equal(inverse(sk_c1),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.21/0.43 54[3:Obv:53.1] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.21/0.43 55[3:Rew:45.0,54.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.43 56[3:Obv:55.0] || -> .
% 0.21/0.43 57[2:Spt:56.0,3.0,34.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.21/0.43 58[2:Spt:56.0,3.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.43 60[2:MRR:7.0,57.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.43 62[2:MRR:11.0,57.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.43 68[2:SpL:62.0,26.1] || equal(inverse(sk_c1),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.21/0.43 69[2:Obv:68.1] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.21/0.43 70[2:Rew:60.0,69.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.43 71[2:Obv:70.0] || -> .
% 0.21/0.43 72[1:Spt:71.0,25.0,25.2,25.3,25.5,25.6] || equal(inverse(u),sk_c5) equal(inverse(sk_c4),sk_c5) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) -> .
% 0.21/0.43 73[2:Spt:1.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.21/0.43 74[2:Rew:73.0,72.1] || equal(inverse(u),sk_c5) equal(sk_c5,sk_c5) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) -> .
% 0.21/0.43 75[2:Obv:74.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) -> .
% 0.21/0.43 77[3:Spt:2.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.43 78[3:Rew:77.0,75.2] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c4),sk_c5)** equal(sk_c6,sk_c6) equal(multiply(sk_c5,sk_c6),sk_c4)** -> .
% 0.21/0.43 79[3:Obv:78.2] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** -> .
% 0.21/0.43 81[4:Spt:3.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.43 84[5:Spt:4.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.21/0.43 87[2:SpR:73.0,23.0] || -> equal(multiply(sk_c5,sk_c4),identity)**.
% 0.21/0.43 88[4:SpR:81.0,23.0] || -> equal(multiply(sk_c6,sk_c3),identity)**.
% 0.21/0.43 96[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.43 97[2:SpR:87.0,24.0] || -> equal(multiply(sk_c5,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.43 98[4:SpR:88.0,24.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.21/0.43 99[2:Rew:22.0,97.0] || -> equal(multiply(sk_c5,multiply(sk_c4,u)),u)**.
% 0.21/0.43 100[4:Rew:22.0,98.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.21/0.43 101[0:Rew:22.0,96.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.43 105[3:SpR:77.0,99.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.21/0.43 106[3:Rew:105.0,79.2] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c4),sk_c5)** equal(sk_c4,sk_c5) -> .
% 0.21/0.43 112[5:SpR:84.0,100.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.43 117[0:SpR:101.0,101.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.43 122[0:SpR:23.0,101.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.43 123[2:SpR:87.0,101.0] || -> equal(multiply(inverse(sk_c5),identity),sk_c4)**.
% 0.21/0.43 125[3:SpR:105.0,101.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c6)**.
% 0.21/0.43 134[3:Rew:23.0,125.0] || -> equal(sk_c6,identity)**.
% 0.21/0.43 136[4:Rew:134.0,81.0] || -> equal(inverse(sk_c3),identity)**.
% 0.21/0.43 138[4:Rew:134.0,88.0] || -> equal(multiply(identity,sk_c3),identity)**.
% 0.21/0.43 139[3:Rew:134.0,105.0] || -> equal(multiply(sk_c5,identity),sk_c5)**.
% 0.21/0.43 141[5:Rew:134.0,112.0] || -> equal(multiply(identity,identity),sk_c5)**.
% 0.21/0.43 146[4:Rew:22.0,138.0] || -> equal(identity,sk_c3)**.
% 0.21/0.43 147[4:Rew:146.0,22.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.43 149[4:Rew:146.0,87.0] || -> equal(multiply(sk_c5,sk_c4),sk_c3)**.
% 0.21/0.43 152[4:Rew:146.0,134.0] || -> equal(sk_c6,sk_c3)**.
% 0.21/0.43 153[4:Rew:146.0,136.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.21/0.43 157[5:Rew:146.0,141.0] || -> equal(multiply(sk_c3,sk_c3),sk_c5)**.
% 0.21/0.43 158[5:Rew:147.0,157.0] || -> equal(sk_c3,sk_c5)**.
% 0.21/0.43 159[5:Rew:158.0,146.0] || -> equal(identity,sk_c5)**.
% 0.21/0.43 161[5:Rew:158.0,153.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.21/0.43 163[5:Rew:158.0,147.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.43 164[5:Rew:158.0,149.0] || -> equal(multiply(sk_c5,sk_c4),sk_c5)**.
% 0.21/0.43 168[5:Rew:163.0,164.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.43 170[5:Rew:168.0,106.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c5),sk_c5)** equal(sk_c4,sk_c5) -> .
% 0.21/0.43 178[5:Rew:159.0,122.0] || -> equal(multiply(inverse(inverse(u)),sk_c5),u)**.
% 0.21/0.43 184[5:Rew:117.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.43 190[5:Rew:168.0,170.2,184.0,170.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) equal(sk_c5,sk_c5) -> .
% 0.21/0.43 191[5:Obv:190.2] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.21/0.43 223[5:SpL:161.0,191.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.21/0.43 225[5:Obv:223.1] || -> .
% 0.21/0.43 226[5:Spt:225.0,4.0,84.0] || equal(multiply(sk_c3,sk_c5),sk_c6)** -> .
% 0.21/0.43 227[5:Spt:225.0,4.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.43 235[5:Rew:147.0,226.0,152.0,226.0] || equal(sk_c3,sk_c5)** -> .
% 0.21/0.43 245[4:Rew:147.0,8.1,152.0,8.1,152.0,8.0] || -> equal(inverse(sk_c1),sk_c3)** equal(sk_c3,sk_c5).
% 0.21/0.43 246[5:MRR:245.1,235.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.21/0.43 252[4:Rew:152.0,12.1,147.0,12.0,152.0,12.0] || -> equal(sk_c3,sk_c5) equal(multiply(sk_c1,sk_c5),sk_c3)**.
% 0.21/0.43 253[5:MRR:252.0,235.0] || -> equal(multiply(sk_c1,sk_c5),sk_c3)**.
% 0.21/0.43 266[5:SpR:246.0,101.0] || -> equal(multiply(sk_c3,multiply(sk_c1,u)),u)**.
% 0.21/0.44 268[5:Rew:147.0,266.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.44 269[5:Rew:268.0,253.0] || -> equal(sk_c3,sk_c5)**.
% 0.21/0.44 270[5:MRR:269.0,235.0] || -> .
% 0.21/0.44 271[4:Spt:270.0,3.0,81.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.21/0.44 272[4:Spt:270.0,3.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.44 273[4:Rew:139.0,272.0,134.0,272.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.44 274[4:Rew:273.0,73.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.21/0.44 277[4:Rew:134.0,271.0] || equal(inverse(sk_c3),identity)** -> .
% 0.21/0.44 281[0:Rew:117.0,122.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.44 285[3:Rew:134.0,7.1,134.0,7.0] || -> equal(inverse(sk_c3),identity) equal(inverse(sk_c1),identity)**.
% 0.21/0.44 286[4:MRR:285.0,277.0] || -> equal(inverse(sk_c1),identity)**.
% 0.21/0.44 291[3:Rew:134.0,11.1,134.0,11.0] || -> equal(inverse(sk_c3),identity) equal(multiply(sk_c1,sk_c5),identity)**.
% 0.21/0.44 292[4:MRR:291.0,277.0] || -> equal(multiply(sk_c1,sk_c5),identity)**.
% 0.21/0.44 297[4:Rew:273.0,106.2,273.0,106.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c5),sk_c5)** equal(sk_c5,sk_c5) -> .
% 0.21/0.44 298[4:Obv:297.2] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c5),sk_c5)** -> .
% 0.21/0.44 305[4:SpR:286.0,101.0] || -> equal(multiply(identity,multiply(sk_c1,u)),u)**.
% 0.21/0.44 307[4:Rew:22.0,305.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.44 308[4:Rew:307.0,292.0] || -> equal(identity,sk_c5)**.
% 0.21/0.44 316[4:Rew:308.0,281.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.44 319[4:Rew:316.0,298.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.21/0.44 362[4:SpL:274.0,319.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.21/0.44 364[4:Obv:362.1] || -> .
% 0.21/0.44 365[3:Spt:364.0,2.0,77.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.21/0.44 366[3:Spt:364.0,2.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.44 367[2:Rew:281.0,123.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.21/0.44 369[3:MRR:14.1,365.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.21/0.44 370[3:MRR:6.1,365.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.44 371[3:MRR:18.0,365.0] || -> equal(multiply(sk_c2,sk_c4),sk_c5)**.
% 0.21/0.44 372[3:MRR:10.0,365.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.44 374[3:SpR:366.0,101.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.44 376[3:Rew:367.0,374.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.21/0.44 386[3:SpR:371.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c4)**.
% 0.21/0.44 388[3:Rew:369.0,386.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.44 395[3:SpR:372.0,101.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c5)**.
% 0.21/0.44 397[3:Rew:370.0,395.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.44 403[3:SpR:388.0,101.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.44 405[3:Rew:376.0,403.0,367.0,403.0] || -> equal(sk_c6,sk_c5)**.
% 0.21/0.44 410[3:Rew:405.0,365.0] || equal(multiply(sk_c4,sk_c5),sk_c5)** -> .
% 0.21/0.44 415[3:Rew:405.0,397.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.21/0.44 416[3:Rew:388.0,415.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.44 420[3:Rew:416.0,87.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.21/0.44 421[3:Rew:416.0,388.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.21/0.44 426[3:Rew:420.0,421.0] || -> equal(identity,sk_c5)**.
% 0.21/0.44 428[3:Rew:426.0,22.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.44 437[3:Rew:428.0,410.0,416.0,410.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.44 438[3:Obv:437.0] || -> .
% 0.21/0.44 449[2:Spt:438.0,1.0,73.0] || equal(inverse(sk_c4),sk_c5)** -> .
% 0.21/0.44 450[2:Spt:438.0,1.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.44 451[2:MRR:13.0,449.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.21/0.44 452[2:MRR:5.0,449.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.44 453[2:MRR:17.0,449.0] || -> equal(multiply(sk_c2,sk_c4),sk_c5)**.
% 0.21/0.44 454[2:MRR:9.0,449.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.44 456[2:SpR:450.0,101.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.44 463[2:SpR:453.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c4)**.
% 0.21/0.44 465[2:Rew:451.0,463.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.44 467[2:SpR:454.0,101.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c5)**.
% 0.21/0.44 469[2:Rew:452.0,467.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.44 474[2:SpR:465.0,101.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.44 476[2:Rew:456.0,474.0] || -> equal(sk_c6,sk_c5)**.
% 0.21/0.44 478[2:Rew:476.0,452.0] || -> equal(inverse(sk_c1),sk_c5)**.
% 0.21/0.44 479[2:Rew:476.0,454.0] || -> equal(multiply(sk_c1,sk_c5),sk_c5)**.
% 0.21/0.44 480[2:Rew:476.0,456.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.44 484[2:Rew:476.0,469.0] || -> equal(multiply(sk_c5,sk_c5),sk_c5)**.
% 0.21/0.44 485[2:Rew:465.0,484.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.44 486[2:Rew:485.0,449.0] || equal(inverse(sk_c5),sk_c5)** -> .
% 0.21/0.44 490[2:Rew:23.0,480.0,485.0,480.0] || -> equal(identity,sk_c5)**.
% 0.21/0.44 492[2:Rew:490.0,281.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.44 497[2:Rew:492.0,479.0] || -> equal(sk_c1,sk_c5)**.
% 0.21/0.44 499[2:Rew:497.0,478.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.21/0.44 501[2:MRR:499.0,486.0] || -> .
% 0.21/0.44 % SZS output end Refutation
% 0.21/0.44 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_11 prove_this_12 prove_this_13 prove_this_14 prove_this_17 prove_this_18 prove_this_21 left_identity left_inverse associativity
% 0.21/0.44
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