TSTP Solution File: GRP219-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP219-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:46:23 EDT 2022
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP219-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n009.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 14 10:19:23 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.46
% 0.14/0.46 SPASS V 3.9
% 0.14/0.46 SPASS beiseite: Proof found.
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 SPASS derived 1066 clauses, backtracked 245 clauses, performed 9 splits and kept 550 clauses.
% 0.14/0.46 SPASS allocated 64097 KBytes.
% 0.14/0.46 SPASS spent 0:00:00.17 on the problem.
% 0.14/0.46 0:00:00.03 for the input.
% 0.14/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.46 0:00:00.01 for inferences.
% 0.14/0.46 0:00:00.00 for the backtracking.
% 0.14/0.46 0:00:00.10 for the reduction.
% 0.14/0.46
% 0.14/0.46
% 0.14/0.46 Here is a proof with depth 5, length 253 :
% 0.14/0.46 % SZS output start Refutation
% 0.14/0.46 1[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.14/0.46 2[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.14/0.46 4[0:Inp] || -> equal(inverse(sk_c7),sk_c8)** equal(inverse(sk_c1),sk_c9).
% 0.14/0.46 5[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.46 6[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.14/0.46 8[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.46 9[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.46 10[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.46 12[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.46 13[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 14[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.14/0.46 16[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 17[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.46 18[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.46 20[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.46 21[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 22[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 23[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9) equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 24[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 25[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 26[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 27[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 28[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 29[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.46 30[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.14/0.46 31[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.14/0.46 32[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.46 33[0:Inp] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,w),sk_c8)** equal(inverse(v),w) equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c8)** equal(multiply(y,sk_c9),x)* equal(inverse(y),sk_c9) equal(inverse(z),sk_c9) equal(multiply(z,sk_c8),sk_c9)** equal(multiply(x1,sk_c8),sk_c9)** equal(inverse(x1),sk_c8) -> .
% 0.14/0.46 34[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.14/0.46 35[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.14/0.46 36[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.14/0.46 37[0:Con:33.8] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c9) equal(multiply(u,v),sk_c8)**+ equal(multiply(x,sk_c9),z)* equal(multiply(w,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(y,sk_c8),sk_c9)** equal(multiply(sk_c9,z),sk_c8)** -> .
% 0.14/0.46 38[1:Spt:37.3,37.8] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.14/0.46 41[2:Spt:13.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.14/0.46 48[3:Spt:14.1] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.14/0.46 50[3:SpL:48.0,38.1] || equal(inverse(sk_c6),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.14/0.46 51[3:Obv:50.1] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.14/0.46 52[3:Rew:41.0,51.0] || equal(sk_c9,sk_c9)* -> .
% 0.14/0.46 53[3:Obv:52.0] || -> .
% 0.14/0.46 54[3:Spt:53.0,14.1,48.0] || equal(multiply(sk_c6,sk_c8),sk_c9)** -> .
% 0.14/0.46 55[3:Spt:53.0,14.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 57[3:MRR:2.1,54.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.14/0.46 62[3:MRR:6.0,54.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.46 71[3:SpL:62.0,38.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.14/0.46 72[3:Obv:71.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.14/0.46 73[3:Rew:57.0,72.0] || equal(sk_c9,sk_c9)* -> .
% 0.14/0.46 74[3:Obv:73.0] || -> .
% 0.14/0.46 75[2:Spt:74.0,13.0,41.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.14/0.46 76[2:Spt:74.0,13.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 78[2:MRR:1.0,75.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.14/0.46 83[2:MRR:5.0,75.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.46 92[2:SpL:83.0,38.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.14/0.46 93[2:Obv:92.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.14/0.46 94[2:Rew:78.0,93.0] || equal(sk_c9,sk_c9)* -> .
% 0.14/0.46 95[2:Obv:94.0] || -> .
% 0.14/0.46 96[1:Spt:95.0,37.0,37.1,37.2,37.4,37.5,37.6,37.7,37.9] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,v),sk_c8)**+ equal(multiply(x,sk_c9),y)* equal(multiply(w,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,y),sk_c8)** -> .
% 0.14/0.46 97[2:Spt:29.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.14/0.46 99[3:Spt:16.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.14/0.46 101[4:Spt:30.1] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.14/0.46 103[4:SpL:101.0,96.3] || equal(inverse(sk_c6),sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 104[4:Rew:97.0,103.0] || equal(sk_c9,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 105[4:Obv:104.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 106[5:Spt:31.1] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.14/0.46 110[1:SpL:34.0,96.3] || equal(inverse(identity),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(u,sk_c8) equal(multiply(w,sk_c9),x)* equal(multiply(v,sk_c8),sk_c9)** equal(multiply(u,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.14/0.46 112[2:SpR:97.0,35.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.14/0.46 113[3:SpR:99.0,35.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.14/0.46 116[2:SpL:112.0,96.3] || equal(inverse(sk_c9),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 121[2:SpR:112.0,36.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.14/0.46 123[0:SpR:35.0,36.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.14/0.46 125[2:Rew:34.0,121.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.14/0.46 126[0:Rew:34.0,123.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.14/0.46 128[3:SpR:113.0,36.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.14/0.46 131[3:Rew:34.0,128.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.14/0.46 134[4:SpR:101.0,125.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.14/0.46 146[5:SpR:106.0,131.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.14/0.46 148[5:Rew:146.0,105.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(sk_c8,sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 150[5:Obv:148.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 153[0:SpR:126.0,126.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.14/0.46 161[0:SpR:35.0,126.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.14/0.46 164[3:SpR:131.0,126.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c7,u))**.
% 0.14/0.46 173[0:Rew:153.0,161.0] || -> equal(multiply(u,identity),u)**.
% 0.14/0.46 177[5:SpR:146.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.14/0.46 180[5:Rew:35.0,177.0] || -> equal(sk_c9,identity)**.
% 0.14/0.46 182[5:Rew:180.0,97.0] || -> equal(inverse(sk_c6),identity)**.
% 0.14/0.46 185[5:Rew:180.0,112.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.14/0.46 187[5:Rew:180.0,134.0] || -> equal(multiply(identity,identity),sk_c8)**.
% 0.14/0.46 189[5:Rew:180.0,150.1] || equal(inverse(u),sk_c8) equal(inverse(v),identity) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 203[5:Rew:34.0,185.0] || -> equal(identity,sk_c6)**.
% 0.14/0.46 204[5:Rew:203.0,34.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.14/0.46 208[5:Rew:203.0,173.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.14/0.46 209[5:Rew:203.0,180.0] || -> equal(sk_c9,sk_c6)**.
% 0.14/0.46 210[5:Rew:203.0,182.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.14/0.46 213[5:Rew:203.0,187.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.14/0.46 215[5:Rew:204.0,213.0] || -> equal(sk_c8,sk_c6)**.
% 0.14/0.46 233[5:Rew:204.0,189.5,209.0,189.5,215.0,189.5,208.0,189.4,215.0,189.4,209.0,189.4,208.0,189.3,209.0,189.3,209.0,189.2,215.0,189.2,203.0,189.1,215.0,189.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(sk_c6,sk_c6) equal(v,w)* equal(u,sk_c6) equal(w,sk_c6)* -> .
% 0.14/0.46 234[5:Obv:233.2] || equal(inverse(u),sk_c6)**+ equal(inverse(v),sk_c6)** equal(v,w)* equal(u,sk_c6) equal(w,sk_c6)* -> .
% 0.14/0.46 569[5:SpL:210.0,234.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c6)** equal(u,v)* equal(sk_c6,sk_c6) equal(v,sk_c6)* -> .
% 0.14/0.46 573[5:Obv:569.3] || equal(inverse(u),sk_c6)**+ equal(u,v)* equal(v,sk_c6)* -> .
% 0.14/0.46 574[5:SpL:210.0,573.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.14/0.46 578[5:Obv:574.1] || equal(u,sk_c6)* -> .
% 0.14/0.46 579[5:AED:578.0] || -> .
% 0.14/0.46 580[5:Spt:579.0,31.1,106.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.14/0.46 581[5:Spt:579.0,31.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.46 585[5:MRR:27.0,580.0] || -> equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 586[5:MRR:23.0,580.0] || -> equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 613[2:SpR:112.0,126.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c6)**.
% 0.14/0.46 615[2:Rew:173.0,613.0] || -> equal(inverse(sk_c9),sk_c6)**.
% 0.14/0.46 618[2:Rew:615.0,116.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 621[2:Obv:618.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 622[2:SpR:615.0,126.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.14/0.46 629[5:SpR:585.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c9)**.
% 0.14/0.46 631[5:Rew:581.0,629.0] || -> equal(multiply(sk_c9,sk_c5),sk_c9)**.
% 0.14/0.46 632[5:Rew:586.0,631.0] || -> equal(sk_c9,sk_c8)**.
% 0.14/0.46 638[5:Rew:632.0,615.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.14/0.46 639[5:Rew:632.0,101.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.14/0.46 641[5:Rew:632.0,580.0] || equal(multiply(sk_c7,sk_c8),sk_c8)** -> .
% 0.14/0.46 662[5:Rew:638.0,164.0] || -> equal(multiply(sk_c7,u),multiply(sk_c6,u))**.
% 0.14/0.46 663[5:Rew:662.0,641.0] || equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.14/0.46 665[5:Rew:639.0,663.0] || equal(sk_c8,sk_c8)* -> .
% 0.14/0.46 666[5:Obv:665.0] || -> .
% 0.14/0.46 702[4:Spt:666.0,30.1,101.0] || equal(multiply(sk_c6,sk_c8),sk_c9)** -> .
% 0.14/0.46 703[4:Spt:666.0,30.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.46 705[4:MRR:14.1,702.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 706[4:MRR:26.0,702.0] || -> equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 707[4:MRR:22.0,702.0] || -> equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 708[4:MRR:18.0,702.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.46 709[4:MRR:10.0,702.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.46 734[4:SpR:706.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c9)**.
% 0.14/0.46 736[4:Rew:703.0,734.0] || -> equal(multiply(sk_c9,sk_c5),sk_c9)**.
% 0.14/0.46 737[4:Rew:707.0,736.0] || -> equal(sk_c9,sk_c8)**.
% 0.14/0.46 739[4:Rew:737.0,615.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.14/0.46 744[4:Rew:737.0,702.0] || equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.14/0.46 747[4:Rew:737.0,707.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.46 748[4:Rew:737.0,708.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.46 783[4:SpR:709.0,126.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.14/0.46 785[4:Rew:705.0,783.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.14/0.46 786[4:Rew:748.0,785.0] || -> equal(sk_c3,sk_c8)**.
% 0.14/0.46 790[4:Rew:786.0,748.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.14/0.46 805[4:SpR:747.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.14/0.46 807[4:Rew:739.0,805.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.14/0.46 808[4:Rew:807.0,744.0] || equal(sk_c5,sk_c8)** -> .
% 0.14/0.46 818[4:SpR:790.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.14/0.46 820[4:Rew:739.0,818.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.14/0.46 821[4:Rew:807.0,820.0] || -> equal(sk_c5,sk_c8)**.
% 0.14/0.46 822[4:MRR:821.0,808.0] || -> .
% 0.14/0.46 823[3:Spt:822.0,16.0,99.0] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.14/0.46 824[3:Spt:822.0,16.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.46 825[3:MRR:4.0,823.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.14/0.46 826[3:MRR:32.0,823.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.46 827[3:MRR:28.0,823.0] || -> equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.46 828[3:MRR:24.0,823.0] || -> equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.46 829[3:MRR:20.0,823.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.46 830[3:MRR:12.0,823.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.46 831[3:MRR:8.0,823.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.46 848[3:SpR:827.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c9)**.
% 0.14/0.46 850[3:Rew:826.0,848.0] || -> equal(multiply(sk_c9,sk_c5),sk_c9)**.
% 0.14/0.46 851[3:Rew:828.0,850.0] || -> equal(sk_c9,sk_c8)**.
% 0.14/0.46 853[3:Rew:851.0,825.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.14/0.46 854[3:Rew:851.0,615.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.14/0.46 856[3:Rew:851.0,112.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.14/0.46 859[3:Rew:851.0,622.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.14/0.46 860[3:Rew:851.0,828.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.46 861[3:Rew:851.0,829.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.46 862[3:Rew:851.0,831.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.14/0.46 863[3:Rew:851.0,621.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.14/0.46 873[3:Rew:851.0,863.6,851.0,863.5,851.0,863.4,851.0,863.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c8) equal(multiply(sk_c8,w),sk_c8)** -> .
% 0.14/0.46 890[3:SpR:830.0,126.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.14/0.46 892[3:Rew:824.0,890.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.14/0.46 893[3:Rew:861.0,892.0] || -> equal(sk_c3,sk_c8)**.
% 0.14/0.46 897[3:Rew:893.0,861.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.14/0.46 912[3:SpR:860.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.14/0.46 914[3:Rew:854.0,912.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.14/0.46 915[3:Rew:914.0,873.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(sk_c5,sk_c8) equal(multiply(sk_c8,w),sk_c8)** -> .
% 0.14/0.46 916[3:SpR:862.0,36.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.14/0.46 925[3:SpR:897.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.14/0.46 927[3:Rew:854.0,925.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.14/0.46 928[3:Rew:914.0,927.0] || -> equal(sk_c5,sk_c8)**.
% 0.14/0.46 933[3:Rew:928.0,914.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.14/0.46 934[3:Rew:928.0,915.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(sk_c8,sk_c8) equal(multiply(sk_c8,w),sk_c8)** -> .
% 0.14/0.46 935[3:Obv:934.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(multiply(sk_c8,w),sk_c8)** -> .
% 0.14/0.46 941[3:SpR:933.0,36.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.14/0.46 945[3:Rew:859.0,941.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.46 946[3:Rew:945.0,856.0] || -> equal(identity,sk_c6)**.
% 0.14/0.46 947[3:Rew:945.0,935.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c8) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.14/0.47 955[3:Rew:945.0,916.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.14/0.47 961[3:Rew:946.0,173.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.14/0.47 964[3:Rew:946.0,35.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.14/0.47 966[3:Rew:946.0,947.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c8,sk_c6) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.14/0.47 980[3:SpR:853.0,964.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.14/0.47 981[3:SpR:854.0,964.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.14/0.47 984[3:Rew:945.0,980.0] || -> equal(sk_c6,sk_c1)**.
% 0.14/0.47 990[3:Rew:984.0,961.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.14/0.47 991[3:Rew:984.0,966.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c8,sk_c1) equal(multiply(v,sk_c8),w)* equal(multiply(u,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.14/0.47 992[3:Rew:955.0,981.0,984.0,981.0] || -> equal(sk_c8,sk_c1)**.
% 0.14/0.47 995[3:Rew:992.0,853.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.14/0.47 1015[3:Rew:992.0,991.5,990.0,991.4,992.0,991.4,990.0,991.3,992.0,991.3,992.0,991.2,992.0,991.1,992.0,991.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.14/0.47 1016[3:Obv:1015.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.14/0.47 1186[3:SpL:995.0,1016.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.14/0.47 1188[3:Obv:1186.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.14/0.47 1291[3:SpL:995.0,1188.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.14/0.47 1295[3:Obv:1291.1] || equal(u,sk_c1)* -> .
% 0.14/0.47 1296[3:AED:1295.0] || -> .
% 0.14/0.47 1297[2:Spt:1296.0,29.0,97.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.14/0.47 1298[2:Spt:1296.0,29.1] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.14/0.47 1300[2:MRR:13.0,1297.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.14/0.47 1302[2:MRR:25.0,1297.0] || -> equal(multiply(sk_c4,sk_c9),sk_c5)**.
% 0.14/0.47 1303[2:MRR:21.0,1297.0] || -> equal(multiply(sk_c9,sk_c5),sk_c8)**.
% 0.14/0.47 1304[2:MRR:17.0,1297.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.14/0.47 1305[2:MRR:9.0,1297.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.14/0.47 1306[2:MRR:5.0,1297.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.14/0.47 1315[2:SpR:1302.0,126.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c9)**.
% 0.14/0.47 1317[2:Rew:1298.0,1315.0] || -> equal(multiply(sk_c9,sk_c5),sk_c9)**.
% 0.14/0.47 1318[2:Rew:1303.0,1317.0] || -> equal(sk_c9,sk_c8)**.
% 0.14/0.47 1323[2:Rew:1318.0,1303.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.14/0.47 1324[2:Rew:1318.0,1304.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.14/0.47 1325[2:Rew:1318.0,1306.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.14/0.47 1327[2:Rew:1318.0,110.2] || equal(inverse(identity),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(u,sk_c8) equal(multiply(w,sk_c9),x)* equal(multiply(v,sk_c8),sk_c9)** equal(multiply(u,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.14/0.47 1334[2:Rew:1318.0,1327.7,1318.0,1327.6,1318.0,1327.5,1318.0,1327.4] || equal(inverse(identity),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(u,sk_c8) equal(multiply(w,sk_c8),x)* equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(sk_c8,x),sk_c8)** -> .
% 0.14/0.47 1344[2:SpR:1305.0,36.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.14/0.47 1345[2:SpR:1305.0,126.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.14/0.47 1347[2:Rew:1300.0,1345.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.14/0.47 1348[2:Rew:1324.0,1347.0] || -> equal(sk_c3,sk_c8)**.
% 0.14/0.47 1349[2:Rew:1348.0,1300.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.14/0.47 1350[2:Rew:1348.0,1305.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.14/0.47 1352[2:Rew:1348.0,1324.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.14/0.47 1353[2:Rew:1348.0,1344.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.14/0.47 1362[2:SpR:1323.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.14/0.47 1364[2:Rew:35.0,1362.0] || -> equal(identity,sk_c5)**.
% 0.14/0.47 1365[2:Rew:1364.0,34.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.14/0.47 1366[2:Rew:1364.0,173.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.14/0.47 1367[2:Rew:1364.0,35.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.14/0.47 1369[2:Rew:1364.0,1334.0] || equal(inverse(sk_c5),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(u,sk_c8) equal(multiply(w,sk_c8),x)* equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(sk_c8,x),sk_c8)** -> .
% 0.14/0.47 1383[2:SpR:1352.0,126.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.14/0.47 1385[2:Rew:1367.0,1383.0] || -> equal(sk_c5,sk_c8)**.
% 0.14/0.47 1388[2:Rew:1385.0,1365.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.14/0.47 1389[2:Rew:1385.0,1366.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.14/0.47 1392[2:Rew:1385.0,1369.0] || equal(inverse(sk_c8),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(u,sk_c8) equal(multiply(w,sk_c8),x)* equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** equal(multiply(sk_c8,x),sk_c8)** -> .
% 0.14/0.47 1397[2:Rew:1388.0,1353.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.14/0.47 1403[2:Rew:1389.0,1350.0] || -> equal(sk_c2,sk_c8)**.
% 0.14/0.47 1404[2:Rew:1389.0,1325.0] || -> equal(sk_c8,sk_c1)**.
% 0.14/0.47 1406[2:Rew:1403.0,1349.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.14/0.47 1415[2:Rew:1404.0,1389.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.14/0.47 1416[2:Rew:1404.0,1403.0] || -> equal(sk_c2,sk_c1)**.
% 0.14/0.47 1418[2:Rew:1404.0,1406.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.14/0.47 1420[2:Rew:1416.0,1397.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.14/0.47 1427[2:Rew:1420.0,1392.7,1404.0,1392.7,1415.0,1392.6,1404.0,1392.6,1415.0,1392.5,1404.0,1392.5,1415.0,1392.4,1404.0,1392.4,1404.0,1392.3,1404.0,1392.2,1404.0,1392.1,1418.0,1392.0,1404.0,1392.0] || equal(sk_c1,u)* equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1)* equal(w,x)* equal(v,sk_c1) equal(u,sk_c1)* equal(x,sk_c1)* -> .
% 0.14/0.47 1428[2:Obv:1427.3] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(x,sk_c1)* equal(w,sk_c1)* -> .
% 0.14/0.47 1429[2:Con:1428.4] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.14/0.47 1597[2:SpL:1418.0,1429.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.14/0.47 1599[2:Obv:1597.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.14/0.47 1702[2:SpL:1418.0,1599.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.14/0.47 1706[2:Obv:1702.1] || equal(u,sk_c1)* -> .
% 0.14/0.47 1707[2:AED:1706.0] || -> .
% 0.14/0.47 % SZS output end Refutation
% 0.14/0.47 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_10 prove_this_12 prove_this_13 prove_this_14 prove_this_16 prove_this_17 prove_this_18 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 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 left_identity left_inverse associativity
% 0.14/0.47
%------------------------------------------------------------------------------