TSTP Solution File: GRP226-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:46:25 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 10:49:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 498 clauses, backtracked 156 clauses, performed 9 splits and kept 362 clauses.
% 0.18/0.44 SPASS allocated 63501 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.44 0:00:00.03 for the input.
% 0.18/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.04 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 5, length 186 :
% 0.18/0.44 % SZS output start Refutation
% 0.18/0.44 1[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.18/0.44 2[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.44 3[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.44 4[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.18/0.44 5[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.44 6[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c6),sk_c7).
% 0.18/0.44 8[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.44 9[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.44 10[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.44 11[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.44 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.44 13[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.44 14[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.44 15[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.44 16[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.44 17[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.44 18[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.44 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.44 20[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.44 21[0:Inp] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,v),sk_c6)** equal(multiply(w,sk_c7),v)* equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(x,sk_c6),sk_c7)** equal(multiply(y,sk_c6),sk_c7)** equal(inverse(y),sk_c6) -> .
% 0.18/0.44 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.44 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.44 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.44 25[0:Con:21.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),x)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** -> .
% 0.18/0.44 26[1:Spt:25.2,25.5] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.18/0.44 29[2:Spt:17.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 38[3:Spt:18.1] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.44 40[3:SpL:38.0,26.1] || equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.44 41[3:Obv:40.1] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.18/0.44 42[3:Rew:29.0,41.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.44 43[3:Obv:42.0] || -> .
% 0.18/0.44 44[3:Spt:43.0,18.1,38.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.18/0.44 45[3:Spt:43.0,18.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.44 46[3:MRR:2.1,44.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.44 49[3:MRR:6.0,44.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.44 55[3:SpL:49.0,26.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.44 56[3:Obv:55.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.44 57[3:Rew:46.0,56.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.44 58[3:Obv:57.0] || -> .
% 0.18/0.44 59[2:Spt:58.0,17.0,29.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.18/0.44 60[2:Spt:58.0,17.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.44 61[2:MRR:1.0,59.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.44 64[2:MRR:5.0,59.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.44 70[2:SpL:64.0,26.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.44 71[2:Obv:70.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.44 72[2:Rew:61.0,71.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.44 73[2:Obv:72.0] || -> .
% 0.18/0.44 74[1:Spt:73.0,25.0,25.1,25.3,25.4,25.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),w)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.18/0.44 75[1:EqR:74.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.18/0.44 77[2:Spt:1.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 79[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.44 81[4:Spt:2.1] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.18/0.44 84[2:SpR:77.0,23.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.18/0.44 85[3:SpR:79.0,23.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.18/0.44 87[5:Spt:3.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.44 94[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.44 97[2:SpR:84.0,24.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.44 98[3:SpR:85.0,24.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.18/0.44 100[2:Rew:22.0,97.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.18/0.44 101[3:Rew:22.0,98.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.18/0.44 102[0:Rew:22.0,94.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.44 106[4:SpR:81.0,100.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.44 113[5:SpR:87.0,101.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.18/0.44 119[0:SpR:102.0,102.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.44 122[0:SpR:23.0,102.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.44 126[2:SpR:100.0,102.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c4,u))**.
% 0.18/0.44 129[3:SpR:101.0,102.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c5,u))**.
% 0.18/0.44 130[5:SpR:113.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.18/0.44 136[5:Rew:23.0,130.0] || -> equal(sk_c7,identity)**.
% 0.18/0.44 138[5:Rew:136.0,77.0] || -> equal(inverse(sk_c4),identity)**.
% 0.18/0.44 141[5:Rew:136.0,84.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.18/0.44 143[5:Rew:136.0,106.0] || -> equal(multiply(identity,identity),sk_c6)**.
% 0.18/0.44 145[5:Rew:136.0,75.1] || equal(inverse(u),sk_c6) equal(inverse(v),identity) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.18/0.44 157[5:Rew:22.0,141.0] || -> equal(identity,sk_c4)**.
% 0.18/0.44 158[5:Rew:157.0,22.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.18/0.44 163[5:Rew:157.0,136.0] || -> equal(sk_c7,sk_c4)**.
% 0.18/0.44 164[5:Rew:157.0,138.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.18/0.44 167[5:Rew:157.0,143.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.18/0.44 169[5:Rew:158.0,167.0] || -> equal(sk_c6,sk_c4)**.
% 0.18/0.44 181[5:Rew:157.0,122.0] || -> equal(multiply(inverse(inverse(u)),sk_c4),u)**.
% 0.18/0.44 188[5:Rew:119.0,181.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.18/0.44 194[5:Rew:188.0,145.3,158.0,145.3,163.0,145.3,169.0,145.3,188.0,145.2,169.0,145.2,163.0,145.2,157.0,145.1,169.0,145.0] || equal(inverse(u),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c4) equal(v,sk_c4) -> .
% 0.18/0.44 195[5:Con:194.1] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.18/0.44 241[5:SpL:164.0,195.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.18/0.44 243[5:Obv:241.1] || -> .
% 0.18/0.44 244[5:Spt:243.0,3.1,87.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.44 245[5:Spt:243.0,3.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.44 249[5:MRR:19.1,244.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.44 250[0:Rew:119.0,122.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.44 251[5:MRR:15.0,244.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.44 252[5:MRR:11.0,244.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.44 267[5:SpR:251.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.18/0.44 269[5:Rew:249.0,267.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.18/0.44 270[5:Rew:252.0,269.0] || -> equal(sk_c7,sk_c6)**.
% 0.18/0.44 277[5:Rew:270.0,81.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.18/0.44 278[5:Rew:270.0,244.0] || equal(multiply(sk_c5,sk_c6),sk_c6)** -> .
% 0.18/0.44 280[5:Rew:270.0,126.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c4,u))**.
% 0.18/0.44 293[5:Rew:129.0,280.0] || -> equal(multiply(sk_c5,u),multiply(sk_c4,u))**.
% 0.18/0.44 294[5:Rew:293.0,278.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.18/0.44 297[5:Rew:277.0,294.0] || equal(sk_c6,sk_c6)* -> .
% 0.18/0.44 298[5:Obv:297.0] || -> .
% 0.18/0.44 306[4:Spt:298.0,2.1,81.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.18/0.45 307[4:Spt:298.0,2.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 308[4:MRR:18.1,306.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.45 309[4:MRR:14.0,306.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.45 310[4:MRR:10.0,306.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.45 311[4:MRR:6.0,306.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.45 329[4:SpR:309.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.18/0.45 331[4:Rew:308.0,329.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.18/0.45 332[4:Rew:310.0,331.0] || -> equal(sk_c7,sk_c6)**.
% 0.18/0.45 333[4:Rew:332.0,307.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.18/0.45 338[4:Rew:332.0,306.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.18/0.45 340[4:Rew:332.0,126.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c4,u))**.
% 0.18/0.45 341[4:Rew:332.0,310.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.18/0.45 342[4:Rew:332.0,311.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.18/0.45 350[4:Rew:129.0,340.0] || -> equal(multiply(sk_c5,u),multiply(sk_c4,u))**.
% 0.18/0.45 352[4:Rew:350.0,129.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c4,u))**.
% 0.18/0.45 376[4:SpR:341.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c3)**.
% 0.18/0.45 378[4:Rew:352.0,376.0] || -> equal(multiply(sk_c4,sk_c6),sk_c3)**.
% 0.18/0.45 379[4:Rew:378.0,338.0] || equal(sk_c3,sk_c6)** -> .
% 0.18/0.45 381[4:SpR:342.0,102.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.18/0.45 383[4:Rew:333.0,381.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.18/0.45 392[4:SpR:383.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.18/0.45 394[4:Rew:352.0,392.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.18/0.45 395[4:Rew:378.0,394.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.45 396[4:MRR:395.0,379.0] || -> .
% 0.18/0.45 397[3:Spt:396.0,4.0,79.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.18/0.45 398[3:Spt:396.0,4.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 399[3:MRR:20.0,397.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.45 400[3:MRR:16.0,397.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.45 401[3:MRR:12.0,397.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.45 402[3:MRR:8.0,397.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.45 415[3:SpR:400.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.18/0.45 417[3:Rew:399.0,415.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.18/0.45 418[3:Rew:401.0,417.0] || -> equal(sk_c7,sk_c6)**.
% 0.18/0.45 419[3:Rew:418.0,398.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.18/0.45 427[3:Rew:418.0,402.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.18/0.45 429[3:Rew:418.0,75.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.18/0.45 436[3:Rew:418.0,429.3,418.0,429.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(v,sk_c6)),sk_c6)** -> .
% 0.18/0.45 461[3:SpR:427.0,24.0] || -> equal(multiply(sk_c1,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.18/0.45 488[3:SpR:419.0,23.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.18/0.45 523[3:SpR:488.0,461.0] || -> equal(multiply(sk_c1,identity),identity)**.
% 0.18/0.45 525[3:Rew:250.0,523.0] || -> equal(identity,sk_c1)**.
% 0.18/0.45 526[3:Rew:525.0,22.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.45 528[3:Rew:525.0,488.0] || -> equal(multiply(sk_c6,sk_c1),sk_c1)**.
% 0.18/0.45 531[3:Rew:525.0,250.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.45 535[3:Rew:531.0,528.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.45 538[3:Rew:535.0,419.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.45 543[3:Rew:535.0,436.0] || equal(inverse(u),sk_c1) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(v,sk_c6)),sk_c6)** -> .
% 0.18/0.45 549[3:Rew:531.0,543.3,526.0,543.3,535.0,543.3,531.0,543.2,535.0,543.2,535.0,543.1] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.18/0.45 550[3:Con:549.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.45 616[3:SpL:538.0,550.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.45 618[3:Obv:616.1] || -> .
% 0.18/0.45 619[2:Spt:618.0,1.0,77.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.18/0.45 620[2:Spt:618.0,1.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 621[2:MRR:17.0,619.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.45 622[2:MRR:13.0,619.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.18/0.45 623[2:MRR:9.0,619.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.18/0.45 624[2:MRR:5.0,619.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.45 630[2:SpR:622.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c7)**.
% 0.18/0.45 632[2:Rew:621.0,630.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.18/0.45 633[2:Rew:623.0,632.0] || -> equal(sk_c7,sk_c6)**.
% 0.18/0.45 634[2:Rew:633.0,620.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.18/0.45 638[2:Rew:633.0,623.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.18/0.45 639[2:Rew:633.0,624.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.18/0.45 641[2:Rew:633.0,75.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.18/0.45 648[2:Rew:633.0,641.3,633.0,641.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(v,sk_c6)),sk_c6)** -> .
% 0.18/0.45 663[2:SpR:638.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c3)**.
% 0.18/0.45 665[2:Rew:23.0,663.0] || -> equal(identity,sk_c3)**.
% 0.18/0.45 666[2:Rew:665.0,22.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.18/0.45 667[2:Rew:665.0,250.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.18/0.45 668[2:Rew:665.0,23.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.18/0.45 676[2:SpR:639.0,102.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.18/0.45 678[2:Rew:634.0,676.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.18/0.45 680[2:SpR:678.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.18/0.45 682[2:Rew:668.0,680.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.45 685[2:Rew:682.0,666.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.45 686[2:Rew:682.0,667.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.45 695[2:Rew:685.0,648.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.18/0.45 698[2:Rew:686.0,639.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.45 701[2:Rew:698.0,634.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.45 707[2:Rew:698.0,686.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.45 715[2:Con:695.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.18/0.45 716[2:Rew:707.0,715.1,698.0,715.1,698.0,715.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.45 751[2:SpL:701.0,716.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.45 752[2:Obv:751.1] || -> .
% 0.18/0.45 % SZS output end Refutation
% 0.18/0.45 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_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 left_identity left_inverse associativity
% 0.18/0.45
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