TSTP Solution File: GRP285-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP285-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:41 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP285-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:15:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 441 clauses, backtracked 166 clauses, performed 8 splits and kept 326 clauses.
% 0.18/0.43 SPASS allocated 63399 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 161 :
% 0.18/0.43 % SZS output start Refutation
% 0.18/0.43 1[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.18/0.43 2[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.18/0.43 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.18/0.43 5[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.18/0.43 6[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.18/0.43 7[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.18/0.44 8[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 9[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 11[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 12[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 13[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 14[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 15[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.44 16[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.18/0.44 18[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.18/0.44 19[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.44 20[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.44 21[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.18/0.44 23[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 25[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 26[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 27[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 28[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 29[0:Inp] || equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(v,sk_c9),sk_c7)** equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(x,sk_c7),sk_c8)** equal(inverse(x),sk_c7) equal(multiply(sk_c9,y),sk_c7)** equal(multiply(z,sk_c9),y)* equal(inverse(z),sk_c9) -> .
% 0.18/0.44 30[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.44 31[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.44 32[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.44 33[0:Con:29.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(w,sk_c9),sk_c7)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.18/0.44 34[1:Spt:33.1,33.4] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.18/0.44 37[2:Spt:18.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.18/0.44 39[3:Spt:11.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 41[3:SpL:39.0,34.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.18/0.44 42[3:Obv:41.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.18/0.44 43[3:Rew:37.0,42.0] || equal(sk_c9,sk_c9)* -> .
% 0.18/0.44 44[3:Obv:43.0] || -> .
% 0.18/0.44 45[3:Spt:44.0,11.1,39.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.18/0.44 46[3:Spt:44.0,11.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 48[3:MRR:9.1,45.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.44 52[3:MRR:8.1,45.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.44 63[3:SpL:52.0,34.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.18/0.44 64[3:Obv:63.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.18/0.44 65[3:Rew:48.0,64.0] || equal(sk_c9,sk_c9)* -> .
% 0.18/0.44 66[3:Obv:65.0] || -> .
% 0.18/0.44 67[2:Spt:66.0,18.1,37.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.18/0.44 68[2:Spt:66.0,18.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 70[2:MRR:16.1,67.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.44 74[2:MRR:15.0,67.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.44 85[2:SpL:74.0,34.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.18/0.44 86[2:Obv:85.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.18/0.44 87[2:Rew:70.0,86.0] || equal(sk_c9,sk_c9)* -> .
% 0.18/0.44 88[2:Obv:87.0] || -> .
% 0.18/0.44 89[1:Spt:88.0,33.0,33.2,33.3,33.5] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(v,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.18/0.44 90[2:Spt:4.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.18/0.44 91[2:Rew:90.0,89.3] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.44 92[2:Obv:91.3] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c7)** -> .
% 0.18/0.44 94[3:Spt:21.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.18/0.44 96[4:Spt:25.1] || -> equal(multiply(sk_c2,sk_c9),sk_c7)**.
% 0.18/0.44 98[5:Spt:14.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 102[3:SpR:94.0,31.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.18/0.44 111[0:SpR:31.0,32.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.44 113[0:Rew:30.0,111.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.44 116[0:SpR:113.0,113.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.44 118[2:SpR:90.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.18/0.44 119[3:SpR:102.0,113.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.18/0.44 120[4:SpR:96.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c9)**.
% 0.18/0.44 121[5:SpR:98.0,113.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.18/0.44 123[0:SpR:31.0,113.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.44 126[5:Rew:90.0,121.0,94.0,121.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.44 129[5:Rew:126.0,92.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c7)** -> .
% 0.18/0.44 132[5:Rew:126.0,118.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.18/0.44 133[5:Rew:126.0,120.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c9)**.
% 0.18/0.44 134[5:Rew:31.0,132.0] || -> equal(identity,sk_c8)**.
% 0.18/0.44 136[5:Rew:134.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.44 138[5:Rew:134.0,119.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c1)**.
% 0.18/0.44 141[5:Rew:134.0,123.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.44 142[5:Rew:116.0,141.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.44 143[5:Rew:142.0,138.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.18/0.44 146[5:Rew:126.0,129.2,126.0,129.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c9),sk_c9)** -> .
% 0.18/0.44 188[5:SpL:136.0,146.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 195[5:Obv:188.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 196[5:Rew:94.0,195.0,143.0,195.0] || equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 197[5:Obv:196.0] || equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 198[5:UnC:197.0,133.0] || -> .
% 0.18/0.44 199[5:Spt:198.0,14.1,98.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.18/0.44 200[5:Spt:198.0,14.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.44 203[0:Rew:116.0,123.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.44 204[3:Rew:203.0,119.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.18/0.44 205[3:Rew:204.0,118.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.18/0.44 206[5:MRR:13.1,199.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.44 207[5:MRR:12.1,199.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.44 216[3:SpR:204.0,113.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),u)**.
% 0.18/0.44 222[5:SpR:206.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.44 224[5:Rew:200.0,222.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.44 225[5:Rew:207.0,224.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.44 232[5:Rew:225.0,205.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.18/0.44 237[5:MRR:232.0,199.0] || -> .
% 0.18/0.44 239[4:Spt:237.0,25.1,96.0] || equal(multiply(sk_c2,sk_c9),sk_c7)** -> .
% 0.18/0.44 240[4:Spt:237.0,25.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 241[4:MRR:28.1,239.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.44 242[4:MRR:23.1,239.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.44 243[4:MRR:27.1,239.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.44 244[4:MRR:26.1,239.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.44 258[3:SpR:205.0,32.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.18/0.44 263[4:SpR:243.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.44 265[4:Rew:241.0,263.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.44 266[4:Rew:244.0,265.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.44 272[4:Rew:266.0,258.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.18/0.44 275[4:Rew:266.0,92.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c7)** -> .
% 0.18/0.44 277[4:Rew:216.0,272.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.44 279[4:Rew:266.0,275.2,266.0,275.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c9),sk_c9)** -> .
% 0.18/0.44 330[4:SpR:277.0,203.0] || -> equal(identity,sk_c8)**.
% 0.18/0.44 334[4:Rew:330.0,203.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.44 335[4:Rew:330.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.44 367[4:SpR:241.0,335.0] || -> equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.18/0.44 368[4:SpR:242.0,335.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.18/0.44 375[4:SpR:367.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c5)**.
% 0.18/0.44 377[4:Rew:334.0,375.0,204.0,375.0] || -> equal(sk_c1,sk_c5)**.
% 0.18/0.44 379[4:Rew:377.0,204.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.18/0.44 390[4:SpR:368.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.18/0.44 392[4:Rew:334.0,390.0,379.0,390.0] || -> equal(sk_c5,sk_c3)**.
% 0.18/0.44 397[4:Rew:392.0,379.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.18/0.44 430[4:SpL:335.0,279.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 437[4:Obv:430.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 438[4:Rew:242.0,437.0,397.0,437.0] || equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 439[4:Obv:438.0] || equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 440[4:UnC:439.0,277.0] || -> .
% 0.18/0.44 441[3:Spt:440.0,21.1,94.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.18/0.44 442[3:Spt:440.0,21.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.44 445[3:MRR:20.0,441.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.44 446[3:MRR:19.0,441.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.44 459[3:SpR:445.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.44 461[3:Rew:442.0,459.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.44 462[3:Rew:446.0,461.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.44 465[3:Rew:462.0,118.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.18/0.44 469[3:Rew:462.0,92.0] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c7)** -> .
% 0.18/0.44 471[3:Rew:31.0,465.0] || -> equal(identity,sk_c8)**.
% 0.18/0.44 472[3:Rew:471.0,203.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.44 473[3:Rew:471.0,30.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.44 475[3:Rew:471.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.44 477[3:Rew:462.0,469.2,462.0,469.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c9),sk_c9)** -> .
% 0.18/0.44 529[3:SpR:475.0,113.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.44 536[3:Rew:472.0,529.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.44 635[3:SpL:475.0,477.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 642[3:Obv:635.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 643[3:Rew:536.0,642.0] || equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 644[3:Obv:643.0] || equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.18/0.44 645[3:UnC:644.0,473.0] || -> .
% 0.18/0.44 646[2:Spt:645.0,4.1,90.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.18/0.44 647[2:Spt:645.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.44 648[2:MRR:2.1,646.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.44 649[2:MRR:7.1,646.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.44 650[2:MRR:6.1,646.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.44 651[2:MRR:5.1,646.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.44 653[2:MRR:1.1,646.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.44 661[2:SpR:650.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.44 663[2:Rew:649.0,661.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.44 664[2:Rew:651.0,663.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.44 666[2:Rew:664.0,646.0] || equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.18/0.44 672[2:SpR:653.0,113.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c9)**.
% 0.18/0.44 674[2:Rew:648.0,672.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.18/0.44 675[2:MRR:674.0,666.0] || -> .
% 0.18/0.44 % SZS output end Refutation
% 0.18/0.44 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_11 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_23 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 left_identity left_inverse associativity
% 0.18/0.44
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