TSTP Solution File: GRP276-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP276-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:38 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP276-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 : Mon Jun 13 14:44:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 402 clauses, backtracked 193 clauses, performed 13 splits and kept 340 clauses.
% 0.20/0.44 SPASS allocated 63392 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.03 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 5, length 169 :
% 0.20/0.44 % SZS output start Refutation
% 0.20/0.44 2[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.20/0.44 3[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.44 4[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.44 7[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.44 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.44 9[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.20/0.44 10[0:Inp] || -> equal(inverse(sk_c7),sk_c5)** equal(inverse(sk_c1),sk_c7).
% 0.20/0.44 13[0:Inp] || -> equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.44 16[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.44 17[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.44 18[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.44 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.44 22[0:Inp] || -> equal(inverse(sk_c7),sk_c5)** equal(inverse(sk_c2),sk_c7).
% 0.20/0.44 25[0:Inp] || -> equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.44 28[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.44 31[0:Inp] || equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)** equal(inverse(v),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(w,sk_c7),sk_c6)** equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(x,sk_c5),sk_c6)** equal(inverse(x),sk_c5) -> .
% 0.20/0.44 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.44 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.44 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.44 35[0:Con:31.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.44 36[1:Spt:35.1,35.4] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.44 41[2:Spt:10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.44 47[3:Spt:4.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.44 49[3:SpL:47.0,36.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.44 50[3:Obv:49.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.44 51[3:Rew:41.0,50.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.44 52[3:Obv:51.0] || -> .
% 0.20/0.44 53[3:Spt:52.0,4.1,47.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.20/0.44 54[3:Spt:52.0,4.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.44 56[3:MRR:3.1,53.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.44 58[3:MRR:2.1,53.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.44 65[3:SpL:58.0,36.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.44 66[3:Obv:65.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.44 67[3:Rew:56.0,66.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.44 68[3:Obv:67.0] || -> .
% 0.20/0.44 69[2:Spt:68.0,10.1,41.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.44 70[2:Spt:68.0,10.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.44 72[2:MRR:9.1,69.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.44 74[2:MRR:8.0,69.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.44 81[2:SpL:74.0,36.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.44 82[2:Obv:81.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.44 83[2:Rew:72.0,82.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.44 84[2:Obv:83.0] || -> .
% 0.20/0.44 85[1:Spt:84.0,35.0,35.2,35.3,35.5,35.6] || equal(inverse(u),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.44 87[2:Spt:16.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.20/0.44 88[2:Rew:87.0,85.4] || equal(inverse(u),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.44 91[2:Obv:88.4] || equal(inverse(u),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.44 93[3:Spt:10.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.44 94[3:Rew:93.0,91.1] || equal(inverse(u),sk_c7) equal(sk_c5,sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.44 97[3:Obv:94.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.44 99[4:Spt:7.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.44 100[4:Rew:99.0,97.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.44 103[4:Obv:100.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.44 108[3:SpR:93.0,33.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.20/0.44 110[5:Spt:9.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.44 111[5:SpR:110.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.44 115[6:Spt:8.1] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.44 123[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.44 128[3:SpR:108.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.20/0.44 131[3:Rew:32.0,128.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.20/0.44 134[0:Rew:32.0,123.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.44 138[3:SpR:87.0,131.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.44 139[5:SpR:111.0,131.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.20/0.44 144[5:SpR:139.0,34.0] || -> equal(multiply(sk_c5,multiply(identity,u)),multiply(sk_c3,u))**.
% 0.20/0.44 145[5:Rew:32.0,144.0] || -> equal(multiply(sk_c3,u),multiply(sk_c5,u))**.
% 0.20/0.44 146[6:Rew:145.0,115.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.44 149[6:Rew:108.0,146.0] || -> equal(identity,sk_c6)**.
% 0.20/0.44 150[6:Rew:149.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.44 151[6:Rew:149.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.44 157[6:Rew:150.0,99.0] || -> equal(sk_c7,sk_c5)**.
% 0.20/0.44 163[6:Rew:157.0,93.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.44 166[6:Rew:157.0,103.0] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.44 178[6:Rew:157.0,166.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.44 217[0:SpR:134.0,134.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.44 219[3:SpR:138.0,134.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c6)**.
% 0.20/0.44 224[6:SpR:151.0,134.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.44 228[6:Rew:217.0,224.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.44 229[6:Rew:228.0,178.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.20/0.44 245[6:SpL:163.0,229.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.20/0.44 247[6:Obv:245.1] || -> .
% 0.20/0.44 249[6:Spt:247.0,8.1,115.0] || equal(multiply(sk_c3,sk_c7),sk_c6)** -> .
% 0.20/0.44 250[6:Spt:247.0,8.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.44 251[3:Rew:33.0,219.0] || -> equal(identity,sk_c6)**.
% 0.20/0.44 252[5:Rew:251.0,139.0] || -> equal(multiply(sk_c5,sk_c6),sk_c3)**.
% 0.20/0.44 256[3:Rew:251.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.44 257[3:Rew:251.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.44 258[5:Rew:138.0,252.0] || -> equal(sk_c3,sk_c5)**.
% 0.20/0.44 261[4:Rew:256.0,99.0] || -> equal(sk_c7,sk_c5)**.
% 0.20/0.44 262[4:Rew:261.0,93.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.44 264[4:Rew:261.0,87.0] || -> equal(multiply(sk_c5,sk_c5),sk_c6)**.
% 0.20/0.44 267[6:Rew:264.0,249.0,258.0,249.0,261.0,249.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.44 268[6:Obv:267.0] || -> .
% 0.20/0.44 280[4:Rew:261.0,103.1,261.0,103.0] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.44 281[5:Spt:268.0,9.0,110.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.44 282[5:Spt:268.0,9.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.44 284[5:Rew:261.0,281.0] || equal(inverse(sk_c3),sk_c5)** -> .
% 0.20/0.44 290[4:Rew:261.0,3.1,261.0,3.0] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.20/0.44 291[5:MRR:290.0,284.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.20/0.44 327[5:SpR:291.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.44 331[5:Rew:256.0,327.0] || -> equal(multiply(sk_c1,multiply(sk_c5,u)),u)**.
% 0.20/0.45 343[3:SpR:257.0,134.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.45 348[3:Rew:217.0,343.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.45 349[4:Rew:348.0,280.1] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.20/0.45 364[5:SpR:264.0,331.0] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 365[5:Rew:348.0,364.0] || -> equal(sk_c5,sk_c1)**.
% 0.20/0.45 367[5:Rew:365.0,262.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.45 377[5:Rew:365.0,349.0] || equal(inverse(u),sk_c1)** equal(u,sk_c5) -> .
% 0.20/0.45 380[5:Rew:365.0,377.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.45 416[5:SpL:367.0,380.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.45 418[5:Obv:416.1] || -> .
% 0.20/0.45 420[4:Spt:418.0,7.1,99.0] || equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.45 421[4:Spt:418.0,7.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.45 422[4:Rew:256.0,420.0] || equal(sk_c7,sk_c5)** -> .
% 0.20/0.45 429[3:Rew:256.0,19.1] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c7,sk_c5).
% 0.20/0.45 430[4:MRR:429.1,422.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.45 440[3:Rew:348.0,25.1,256.0,25.0] || -> equal(sk_c7,sk_c5) equal(sk_c7,sk_c2)**.
% 0.20/0.45 441[4:MRR:440.0,422.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.45 442[4:Rew:441.0,93.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.45 446[4:Rew:441.0,422.0] || equal(sk_c2,sk_c5)** -> .
% 0.20/0.45 449[4:Rew:441.0,430.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.20/0.45 452[4:Rew:442.0,449.0] || -> equal(sk_c2,sk_c5)**.
% 0.20/0.45 453[4:MRR:452.0,446.0] || -> .
% 0.20/0.45 459[3:Spt:453.0,10.0,93.0] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.20/0.45 460[3:Spt:453.0,10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.45 461[3:MRR:22.0,459.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.45 462[3:MRR:4.0,459.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.45 463[3:MRR:28.0,459.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.45 469[2:SpR:87.0,134.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.20/0.45 472[3:SpR:462.0,134.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.45 474[3:Rew:460.0,472.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.45 475[3:SpR:463.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.45 480[3:SpR:474.0,134.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.45 482[3:Rew:33.0,480.0] || -> equal(identity,sk_c6)**.
% 0.20/0.45 483[3:Rew:482.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.45 484[3:Rew:482.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.45 487[3:Rew:483.0,475.0] || -> equal(multiply(sk_c7,u),multiply(sk_c2,u))**.
% 0.20/0.45 489[3:Rew:487.0,87.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.45 498[3:SpR:489.0,134.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.45 500[3:Rew:461.0,498.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.45 501[3:Rew:487.0,500.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.45 502[3:Rew:463.0,501.0] || -> equal(sk_c7,sk_c5)**.
% 0.20/0.45 504[3:Rew:502.0,461.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.45 505[3:Rew:502.0,459.0] || equal(inverse(sk_c5),sk_c5)** -> .
% 0.20/0.45 508[3:Rew:502.0,469.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c5)**.
% 0.20/0.45 541[3:SpR:508.0,34.0] || -> equal(multiply(inverse(sk_c5),multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.45 545[3:Rew:483.0,541.0] || -> equal(multiply(inverse(sk_c5),u),multiply(sk_c5,u))**.
% 0.20/0.45 548[3:SpR:484.0,134.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.45 550[3:SpR:504.0,484.0] || -> equal(multiply(sk_c5,sk_c2),sk_c6)**.
% 0.20/0.45 552[3:Rew:217.0,548.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.45 555[3:SpR:550.0,134.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c2)**.
% 0.20/0.45 557[3:Rew:552.0,555.0,545.0,555.0] || -> equal(sk_c2,sk_c5)**.
% 0.20/0.45 558[3:Rew:557.0,504.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.45 561[3:MRR:558.0,505.0] || -> .
% 0.20/0.45 564[2:Spt:561.0,16.1,87.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.20/0.45 565[2:Spt:561.0,16.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.45 566[2:MRR:18.1,564.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.45 568[2:MRR:17.1,564.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.45 570[2:MRR:13.1,564.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.45 578[2:SpR:568.0,134.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.45 580[2:Rew:566.0,578.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.45 589[2:SpR:580.0,134.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c6)**.
% 0.20/0.45 591[2:Rew:33.0,589.0] || -> equal(identity,sk_c6)**.
% 0.20/0.45 592[2:Rew:591.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.45 593[2:Rew:591.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.45 594[2:Rew:592.0,570.0] || -> equal(sk_c7,sk_c5)**.
% 0.20/0.45 598[2:Rew:594.0,565.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.45 601[2:Rew:594.0,564.0] || equal(multiply(sk_c5,sk_c5),sk_c6)** -> .
% 0.20/0.45 627[2:SpR:598.0,593.0] || -> equal(multiply(sk_c5,sk_c5),sk_c6)**.
% 0.20/0.45 629[2:MRR:627.0,601.0] || -> .
% 0.20/0.45 % SZS output end Refutation
% 0.20/0.45 Formulae used in the proof : prove_this_2 prove_this_3 prove_this_4 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_13 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_22 prove_this_25 prove_this_28 prove_this_31 left_identity left_inverse associativity
% 0.20/0.45
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