TSTP Solution File: GRP218-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP218-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:46:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP218-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n015.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 22:03:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 935 clauses, backtracked 321 clauses, performed 11 splits and kept 681 clauses.
% 0.20/0.50 SPASS allocated 63861 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.07 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 5, length 285 :
% 0.20/0.50 % SZS output start Refutation
% 0.20/0.50 1[0:Inp] || -> equal(inverse(sk_c6),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.50 2[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 3[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 5[0:Inp] || -> equal(inverse(sk_c7),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.50 6[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 7[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c9),sk_c10).
% 0.20/0.50 11[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 12[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 15[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 16[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 17[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 20[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 21[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 22[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 25[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 26[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 27[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 28[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 29[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 30[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 31[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 32[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 33[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c4,sk_c10),sk_c5).
% 0.20/0.50 34[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 35[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 36[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 37[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 38[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 39[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.20/0.50 40[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 41[0:Inp] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,w),sk_c9)** equal(inverse(v),w) equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c10,x),sk_c9)** equal(multiply(y,sk_c10),x)* equal(inverse(y),sk_c10) equal(inverse(z),sk_c10) equal(multiply(z,sk_c9),sk_c10)** equal(multiply(sk_c10,x1),sk_c9)** equal(multiply(x2,sk_c10),x1)* equal(inverse(x2),sk_c10) -> .
% 0.20/0.50 42[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.50 43[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.50 44[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.50 45[0:Con:41.8] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,v),sk_c9)**+ equal(multiply(w,sk_c10),y)* equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.20/0.50 46[1:Spt:45.2,45.6] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.20/0.50 49[2:Spt:16.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.50 57[3:Spt:17.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 59[3:SpL:57.0,46.1] || equal(inverse(sk_c6),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.20/0.50 60[3:Obv:59.1] || equal(inverse(sk_c6),sk_c10)** -> .
% 0.20/0.50 61[3:Rew:49.0,60.0] || equal(sk_c10,sk_c10)* -> .
% 0.20/0.50 62[3:Obv:61.0] || -> .
% 0.20/0.50 63[3:Spt:62.0,17.1,57.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.20/0.50 64[3:Spt:62.0,17.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 66[3:MRR:2.1,63.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 71[3:MRR:7.0,63.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 80[3:SpL:71.0,46.1] || equal(inverse(sk_c1),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.20/0.50 81[3:Obv:80.1] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.20/0.50 82[3:Rew:66.0,81.0] || equal(sk_c10,sk_c10)* -> .
% 0.20/0.50 83[3:Obv:82.0] || -> .
% 0.20/0.50 84[2:Spt:83.0,16.0,49.0] || equal(inverse(sk_c6),sk_c10)** -> .
% 0.20/0.50 85[2:Spt:83.0,16.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 87[2:MRR:1.0,84.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 92[2:MRR:6.0,84.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 101[2:SpL:92.0,46.1] || equal(inverse(sk_c1),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.20/0.50 102[2:Obv:101.1] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.20/0.50 103[2:Rew:87.0,102.0] || equal(sk_c10,sk_c10)* -> .
% 0.20/0.50 104[2:Obv:103.0] || -> .
% 0.20/0.50 105[1:Spt:104.0,45.0,45.1,45.3,45.4,45.5,45.7] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(multiply(u,v),sk_c9)**+ equal(multiply(w,sk_c10),x)* equal(multiply(v,sk_c10),sk_c9)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.20/0.50 106[1:SpL:42.0,105.2] || equal(inverse(identity),u) equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),w)* equal(multiply(u,sk_c10),sk_c9)** equal(multiply(sk_c10,w),sk_c9)** -> .
% 0.20/0.50 107[2:Spt:36.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.50 109[3:Spt:40.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.50 111[4:Spt:37.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 113[4:SpL:111.0,105.2] || equal(inverse(sk_c6),sk_c9) equal(inverse(u),sk_c10) equal(sk_c10,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c9,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 114[4:Rew:107.0,113.0] || equal(sk_c10,sk_c9) equal(inverse(u),sk_c10) equal(sk_c10,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c9,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 115[4:Obv:114.0] || equal(inverse(u),sk_c10) equal(sk_c10,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c9,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 116[5:Spt:38.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 120[6:Spt:39.1] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.20/0.50 126[2:SpR:107.0,43.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.20/0.50 127[3:SpR:109.0,43.0] || -> equal(multiply(sk_c10,sk_c7),identity)**.
% 0.20/0.50 130[2:SpL:126.0,105.2] || equal(inverse(sk_c10),sk_c6) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 137[0:SpR:43.0,44.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.50 140[2:SpR:126.0,44.0] || -> equal(multiply(sk_c10,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.20/0.50 141[3:SpR:127.0,44.0] || -> equal(multiply(sk_c10,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.20/0.50 142[4:SpR:111.0,44.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.20/0.50 144[2:Rew:42.0,140.0] || -> equal(multiply(sk_c10,multiply(sk_c6,u)),u)**.
% 0.20/0.50 145[3:Rew:42.0,141.0] || -> equal(multiply(sk_c10,multiply(sk_c7,u)),u)**.
% 0.20/0.50 146[0:Rew:42.0,137.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.50 150[4:SpR:111.0,144.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.50 164[6:SpR:120.0,145.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.20/0.50 166[6:Rew:116.0,164.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.50 168[6:Rew:166.0,107.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.50 171[6:Rew:166.0,116.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.50 173[6:Rew:166.0,126.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.50 176[6:Rew:166.0,150.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.50 185[6:Rew:166.0,115.2] || equal(inverse(u),sk_c10) equal(sk_c10,sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c9,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 195[6:Rew:166.0,185.4,176.0,185.3,166.0,185.3,166.0,185.1,166.0,185.0] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),v)* equal(sk_c9,sk_c9) equal(multiply(sk_c9,v),sk_c9)** -> .
% 0.20/0.50 196[6:Obv:195.3] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c9,v),sk_c9)** -> .
% 0.20/0.50 219[0:SpR:146.0,146.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.50 222[0:SpR:43.0,146.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.50 226[6:SpR:171.0,146.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.20/0.50 231[6:Rew:43.0,226.0] || -> equal(identity,sk_c8)**.
% 0.20/0.50 232[6:Rew:231.0,42.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 233[6:Rew:231.0,43.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.50 234[6:Rew:231.0,173.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.20/0.50 239[6:Rew:231.0,222.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.20/0.50 240[6:Rew:219.0,239.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 244[6:SpR:176.0,146.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c9)**.
% 0.20/0.50 246[6:Rew:233.0,244.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.50 249[6:Rew:246.0,232.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.50 250[6:Rew:246.0,234.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.20/0.50 254[6:Rew:246.0,240.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.50 257[6:Rew:249.0,196.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)* equal(v,sk_c9) -> .
% 0.20/0.50 260[6:Rew:249.0,250.0] || -> equal(sk_c9,sk_c6)**.
% 0.20/0.50 262[6:Rew:260.0,168.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.50 270[6:Rew:260.0,254.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 279[6:Rew:260.0,257.2,270.0,257.1,260.0,257.1,260.0,257.0] || equal(inverse(u),sk_c6)**+ equal(u,v)* equal(v,sk_c6)* -> .
% 0.20/0.50 309[0:SpR:219.0,146.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.50 484[6:SpL:262.0,279.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.50 487[6:Obv:484.1] || equal(u,sk_c6)* -> .
% 0.20/0.50 488[6:AED:487.0] || -> .
% 0.20/0.50 489[6:Spt:488.0,39.1,120.0] || equal(multiply(sk_c7,sk_c10),sk_c8)** -> .
% 0.20/0.50 490[6:Spt:488.0,39.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 493[0:Rew:219.0,222.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.50 495[6:MRR:34.0,489.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 496[6:MRR:29.0,489.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 509[3:SpR:109.0,309.0] || -> equal(multiply(sk_c7,multiply(sk_c10,u)),u)**.
% 0.20/0.50 512[2:SpR:107.0,309.0] || -> equal(multiply(sk_c6,multiply(sk_c10,u)),u)**.
% 0.20/0.50 521[6:SpR:495.0,146.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 523[6:Rew:490.0,521.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 524[6:Rew:496.0,523.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.50 531[6:Rew:524.0,127.0] || -> equal(multiply(sk_c9,sk_c7),identity)**.
% 0.20/0.50 532[6:Rew:524.0,126.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.50 533[6:Rew:524.0,116.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.50 535[6:Rew:524.0,489.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.20/0.50 539[6:Rew:524.0,142.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.20/0.50 541[6:Rew:524.0,509.0] || -> equal(multiply(sk_c7,multiply(sk_c9,u)),u)**.
% 0.20/0.50 542[6:Rew:524.0,512.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.20/0.50 562[6:Rew:542.0,539.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.50 564[6:Rew:562.0,541.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 572[6:Rew:562.0,533.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.50 573[6:Rew:562.0,532.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 574[6:Rew:562.0,531.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 577[6:Rew:572.0,535.0] || equal(multiply(sk_c7,sk_c9),sk_c9)** -> .
% 0.20/0.50 582[6:Rew:573.0,574.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.50 584[6:Rew:582.0,564.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 586[6:Rew:584.0,577.0,582.0,577.0] || equal(sk_c9,sk_c9)* -> .
% 0.20/0.50 587[6:Obv:586.0] || -> .
% 0.20/0.50 606[5:Spt:587.0,38.1,116.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.20/0.50 607[5:Spt:587.0,38.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 608[5:MRR:3.1,606.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 610[5:MRR:33.0,606.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 611[5:MRR:28.0,606.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 631[5:SpR:610.0,146.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 633[5:Rew:607.0,631.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 634[5:Rew:611.0,633.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.50 638[5:Rew:634.0,608.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.50 641[5:Rew:634.0,126.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.50 642[5:Rew:634.0,127.0] || -> equal(multiply(sk_c9,sk_c7),identity)**.
% 0.20/0.50 645[5:Rew:634.0,512.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.20/0.50 647[5:Rew:634.0,142.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.20/0.50 661[5:Rew:634.0,115.0] || equal(inverse(u),sk_c9) equal(sk_c10,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c9,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.50 669[5:Rew:645.0,647.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.50 680[5:Rew:669.0,642.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 681[5:Rew:669.0,641.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 684[5:Rew:680.0,493.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 687[5:Rew:680.0,43.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.50 688[5:Rew:680.0,681.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.50 693[5:Rew:688.0,684.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 696[5:Rew:688.0,687.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.50 698[5:Rew:669.0,661.4,634.0,661.4,634.0,661.3,669.0,661.3,634.0,661.2,634.0,661.1] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),v)* equal(sk_c9,sk_c9) equal(v,sk_c9) -> .
% 0.20/0.50 699[5:Obv:698.3] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)* equal(v,sk_c9) -> .
% 0.20/0.50 769[5:SpR:638.0,696.0] || -> equal(multiply(sk_c9,sk_c1),sk_c6)**.
% 0.20/0.50 773[5:Rew:669.0,769.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.50 777[5:Rew:773.0,696.0] || -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.20/0.50 779[5:Rew:773.0,693.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 808[5:SpR:779.0,669.0] || -> equal(sk_c9,sk_c1)**.
% 0.20/0.50 810[5:SpR:779.0,777.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 817[5:Rew:808.0,699.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c9),v)* equal(v,sk_c9) -> .
% 0.20/0.50 824[5:Rew:808.0,817.2,808.0,817.1] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c1),v)* equal(v,sk_c1) -> .
% 0.20/0.50 825[5:Rew:779.0,824.1] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.20/0.50 846[5:SpL:810.0,825.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.20/0.50 847[5:Obv:846.1] || equal(u,sk_c1)* -> .
% 0.20/0.50 848[5:AED:847.0] || -> .
% 0.20/0.50 849[4:Spt:848.0,37.1,111.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.20/0.50 850[4:Spt:848.0,37.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 852[4:MRR:17.1,849.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 853[4:MRR:32.0,849.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 854[4:MRR:27.0,849.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 855[4:MRR:22.0,849.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 856[4:MRR:12.0,849.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 871[4:SpR:852.0,309.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.50 874[4:SpR:853.0,146.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 876[4:Rew:850.0,874.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 877[4:Rew:854.0,876.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.50 884[4:Rew:877.0,126.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.50 885[4:Rew:877.0,849.0] || equal(multiply(sk_c6,sk_c9),sk_c9)** -> .
% 0.20/0.50 893[4:Rew:877.0,855.0] || -> equal(multiply(sk_c3,sk_c9),sk_c9)**.
% 0.20/0.50 927[4:SpR:856.0,44.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c9,u))**.
% 0.20/0.50 928[4:SpR:856.0,146.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c3)**.
% 0.20/0.50 930[4:Rew:852.0,928.0] || -> equal(multiply(sk_c3,sk_c9),sk_c3)**.
% 0.20/0.50 931[4:Rew:893.0,930.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.50 935[4:Rew:931.0,871.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.20/0.50 937[4:Rew:935.0,927.0,931.0,927.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.50 956[4:Rew:937.0,884.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 960[4:Rew:956.0,42.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 972[4:UnC:960.0,885.0] || -> .
% 0.20/0.50 980[3:Spt:972.0,40.0,109.0] || equal(inverse(sk_c7),sk_c10)** -> .
% 0.20/0.50 981[3:Spt:972.0,40.1] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 982[3:MRR:5.0,980.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 983[3:MRR:20.0,980.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 984[3:MRR:35.0,980.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 985[3:MRR:30.0,980.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 986[3:MRR:25.0,980.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.51 987[3:MRR:15.0,980.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.51 995[3:SpR:982.0,146.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.20/0.51 999[3:SpR:983.0,309.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.51 1002[2:SpR:126.0,146.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c6)**.
% 0.20/0.51 1004[2:Rew:493.0,1002.0] || -> equal(inverse(sk_c10),sk_c6)**.
% 0.20/0.51 1005[2:Rew:1004.0,130.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.51 1008[2:Obv:1005.0] || equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c10),v)* equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.51 1013[3:SpR:984.0,146.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.51 1015[3:Rew:981.0,1013.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.51 1016[3:Rew:985.0,1015.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.51 1019[3:Rew:1016.0,982.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.51 1021[3:Rew:1016.0,126.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.20/0.51 1022[3:Rew:1016.0,1004.0] || -> equal(inverse(sk_c9),sk_c6)**.
% 0.20/0.51 1027[3:Rew:1016.0,144.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.20/0.51 1029[3:Rew:1016.0,986.0] || -> equal(multiply(sk_c3,sk_c9),sk_c9)**.
% 0.20/0.51 1033[3:Rew:1016.0,1008.2] || equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.20/0.51 1038[3:Rew:1016.0,995.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.20/0.51 1040[3:Rew:1016.0,1033.4,1016.0,1033.3,1016.0,1033.0] || equal(inverse(u),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c6,sk_c9),sk_c9) equal(multiply(sk_c9,v),sk_c9)** -> .
% 0.20/0.51 1059[3:SpR:987.0,44.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c9,u))**.
% 0.20/0.51 1060[3:SpR:987.0,146.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c3)**.
% 0.20/0.51 1062[3:Rew:983.0,1060.0] || -> equal(multiply(sk_c3,sk_c9),sk_c3)**.
% 0.20/0.51 1063[3:Rew:1029.0,1062.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.51 1067[3:Rew:1063.0,999.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.20/0.51 1069[3:Rew:1067.0,1059.0,1063.0,1059.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.51 1075[3:Rew:1069.0,1040.4] || equal(inverse(u),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c6,sk_c9),sk_c9)** equal(v,sk_c9) -> .
% 0.20/0.51 1077[3:Rew:1069.0,1038.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.51 1079[3:Rew:1069.0,1027.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.51 1085[3:Rew:1069.0,1021.0] || -> equal(identity,sk_c6)**.
% 0.20/0.51 1088[3:Rew:1085.0,493.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.51 1091[3:Rew:1085.0,43.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.51 1093[3:Rew:1079.0,1075.3,1085.0,1075.1] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c6) equal(multiply(u,sk_c9),v)* equal(sk_c9,sk_c9) equal(v,sk_c9) -> .
% 0.20/0.51 1094[3:Obv:1093.3] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c6) equal(multiply(u,sk_c9),v)* equal(v,sk_c9) -> .
% 0.20/0.51 1112[3:SpR:1019.0,1091.0] || -> equal(multiply(sk_c9,sk_c1),sk_c6)**.
% 0.20/0.51 1115[3:SpR:1022.0,1091.0] || -> equal(multiply(sk_c6,sk_c9),sk_c6)**.
% 0.20/0.51 1117[3:Rew:1069.0,1112.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.51 1123[3:Rew:1117.0,1088.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.51 1124[3:Rew:1117.0,1094.1] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c1) equal(multiply(u,sk_c9),v)* equal(v,sk_c9) -> .
% 0.20/0.51 1128[3:Rew:1077.0,1115.0,1117.0,1115.0] || -> equal(sk_c9,sk_c1)**.
% 0.20/0.51 1130[3:Rew:1128.0,1019.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1146[3:Rew:1128.0,1124.3,1123.0,1124.2,1128.0,1124.2,1128.0,1124.1,1128.0,1124.0] || equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,v)* equal(v,sk_c1)* -> .
% 0.20/0.51 1147[3:Obv:1146.1] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.20/0.51 1197[3:SpL:1130.0,1147.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.20/0.51 1199[3:Obv:1197.1] || equal(u,sk_c1)* -> .
% 0.20/0.51 1200[3:AED:1199.0] || -> .
% 0.20/0.51 1201[2:Spt:1200.0,36.0,107.0] || equal(inverse(sk_c6),sk_c10)** -> .
% 0.20/0.51 1202[2:Spt:1200.0,36.1] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.51 1203[2:MRR:1.0,1201.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.51 1204[2:MRR:16.0,1201.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1205[2:MRR:31.0,1201.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.51 1206[2:MRR:26.0,1201.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.51 1207[2:MRR:21.0,1201.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.51 1208[2:MRR:11.0,1201.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.51 1217[2:SpR:1204.0,309.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.51 1220[2:SpR:1205.0,146.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.51 1222[2:Rew:1202.0,1220.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.51 1223[2:Rew:1206.0,1222.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.51 1225[2:Rew:1223.0,1203.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.51 1229[2:Rew:1223.0,1207.0] || -> equal(multiply(sk_c3,sk_c9),sk_c9)**.
% 0.20/0.51 1232[2:Rew:1223.0,106.1] || equal(inverse(identity),u) equal(inverse(v),sk_c9) equal(u,sk_c9) equal(multiply(v,sk_c10),w)* equal(multiply(u,sk_c10),sk_c9)** equal(multiply(sk_c10,w),sk_c9)** -> .
% 0.20/0.51 1240[2:Rew:1223.0,1232.5,1223.0,1232.4,1223.0,1232.3] || equal(inverse(identity),u) equal(inverse(v),sk_c9) equal(u,sk_c9) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c9),sk_c9)** equal(multiply(sk_c9,w),sk_c9)** -> .
% 0.20/0.51 1251[2:SpR:1208.0,44.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c9,u))**.
% 0.20/0.51 1252[2:SpR:1208.0,146.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c3)**.
% 0.20/0.51 1254[2:Rew:1204.0,1252.0] || -> equal(multiply(sk_c3,sk_c9),sk_c3)**.
% 0.20/0.51 1255[2:Rew:1229.0,1254.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.51 1259[2:Rew:1255.0,1217.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.20/0.51 1261[2:Rew:1259.0,1251.0,1255.0,1251.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.51 1266[2:Rew:1261.0,1240.5] || equal(inverse(identity),u) equal(inverse(v),sk_c9) equal(u,sk_c9) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c9),sk_c9)** equal(w,sk_c9) -> .
% 0.20/0.51 1297[0:SpR:43.0,493.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.51 1300[2:SpR:1225.0,43.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.20/0.51 1304[2:Rew:1297.0,1266.0] || equal(identity,u) equal(inverse(v),sk_c9) equal(u,sk_c9) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c9),sk_c9)** equal(w,sk_c9) -> .
% 0.20/0.51 1305[2:Rew:1261.0,1300.0] || -> equal(identity,sk_c1)**.
% 0.20/0.51 1307[2:Rew:1305.0,493.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.51 1311[2:Rew:1305.0,1297.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1312[2:Rew:1225.0,1311.0] || -> equal(sk_c9,sk_c1)**.
% 0.20/0.51 1313[2:Rew:1312.0,1225.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1333[2:Rew:1312.0,1304.5,1307.0,1304.4,1312.0,1304.4,1307.0,1304.3,1312.0,1304.3,1312.0,1304.2,1312.0,1304.1,1305.0,1304.0] || equal(sk_c1,u)* equal(inverse(v),sk_c1)** equal(u,sk_c1)* equal(v,w)* equal(u,sk_c1)* equal(w,sk_c1)* -> .
% 0.20/0.51 1334[2:Obv:1333.2] || equal(inverse(u),sk_c1)** equal(u,v)* equal(w,sk_c1)* equal(v,sk_c1)* -> .
% 0.20/0.51 1335[2:Con:1334.2] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.20/0.51 1391[2:SpL:1313.0,1335.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.20/0.51 1393[2:Obv:1391.1] || equal(u,sk_c1)* -> .
% 0.20/0.51 1394[2:AED:1393.0] || -> .
% 0.20/0.51 % SZS output end Refutation
% 0.20/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_5 prove_this_6 prove_this_7 prove_this_11 prove_this_12 prove_this_15 prove_this_16 prove_this_17 prove_this_20 prove_this_21 prove_this_22 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 left_identity left_inverse associativity
% 0.20/0.51
%------------------------------------------------------------------------------