TSTP Solution File: GRP266-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP266-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:46:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP266-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 19:51:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 1643 clauses, backtracked 496 clauses, performed 15 splits and kept 843 clauses.
% 0.19/0.55 SPASS allocated 64468 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.55 0:00:00.04 for the input.
% 0.19/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.01 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.12 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 4, length 362 :
% 0.19/0.55 % SZS output start Refutation
% 0.19/0.55 1[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.19/0.55 2[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 4[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 6[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.19/0.55 7[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 8[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.19/0.55 9[0:Inp] || -> equal(inverse(sk_c5),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.55 10[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.19/0.55 11[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.55 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.55 14[0:Inp] || -> equal(inverse(sk_c7),sk_c9)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.55 16[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 17[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 18[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 21[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 23[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 24[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.19/0.55 25[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 27[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.55 28[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 29[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c4),sk_c9).
% 0.19/0.55 30[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 31[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c4),sk_c9).
% 0.19/0.55 32[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 33[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c4),sk_c9).
% 0.19/0.55 34[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c4),sk_c9).
% 0.19/0.55 35[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 36[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 37[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 38[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 39[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 40[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 41[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 42[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 43[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.19/0.55 44[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 45[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.19/0.55 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 47[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.19/0.55 48[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.55 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 50[0:Inp] || equal(multiply(u,sk_c11),sk_c10)** equal(inverse(u),sk_c11) equal(multiply(v,sk_c9),sk_c10)** equal(inverse(v),sk_c9) equal(multiply(sk_c10,w),sk_c9)** equal(multiply(x,sk_c10),w)* equal(inverse(x),sk_c10) equal(multiply(y,sk_c11),sk_c10)** equal(inverse(y),sk_c11) equal(multiply(z,sk_c9),sk_c10)** equal(inverse(z),sk_c9) equal(multiply(sk_c9,x1),sk_c10)** equal(multiply(x2,sk_c9),x1)* equal(inverse(x2),sk_c9) -> .
% 0.19/0.55 51[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.55 52[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.55 53[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.55 54[0:Con:50.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(x),sk_c11) equal(multiply(u,sk_c9),y)*+ equal(multiply(v,sk_c10),z)* equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(sk_c9,y),sk_c10)** equal(multiply(sk_c10,z),sk_c9)** -> .
% 0.19/0.55 55[1:Spt:54.2,54.6] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.55 58[2:Spt:46.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.55 71[3:Spt:10.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.19/0.55 73[3:SpL:71.0,55.1] || equal(inverse(sk_c6),sk_c9)** equal(sk_c10,sk_c10) -> .
% 0.19/0.55 74[3:Obv:73.1] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.19/0.55 75[3:Rew:58.0,74.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.55 76[3:Obv:75.0] || -> .
% 0.19/0.55 77[3:Spt:76.0,10.1,71.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.19/0.55 78[3:Spt:76.0,10.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.55 80[3:MRR:24.1,77.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 83[3:MRR:17.0,77.0] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 91[3:SpL:83.0,55.1] || equal(inverse(sk_c2),sk_c9)** equal(sk_c10,sk_c10) -> .
% 0.19/0.55 92[3:Obv:91.1] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.19/0.55 93[3:Rew:80.0,92.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.55 94[3:Obv:93.0] || -> .
% 0.19/0.55 95[2:Spt:94.0,46.0,58.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.19/0.55 96[2:Spt:94.0,46.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 97[2:MRR:25.0,95.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 101[2:MRR:18.0,95.0] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 109[2:SpL:101.0,55.1] || equal(inverse(sk_c2),sk_c9)** equal(sk_c10,sk_c10) -> .
% 0.19/0.55 110[2:Obv:109.1] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.19/0.55 111[2:Rew:97.0,110.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.55 112[2:Obv:111.0] || -> .
% 0.19/0.55 113[1:Spt:112.0,54.0,54.1,54.3,54.4,54.5,54.7,54.8,54.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c9),x)*+ equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c9,x),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.19/0.55 115[2:Spt:44.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.19/0.55 117[3:Spt:25.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.55 119[4:Spt:28.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.55 121[5:Spt:45.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.19/0.55 123[5:SpL:121.0,113.3] || equal(inverse(sk_c6),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 124[5:Rew:117.0,123.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 125[5:Obv:124.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 126[6:Spt:47.1] || -> equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.19/0.55 130[7:Spt:43.1] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.19/0.55 132[8:Spt:27.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.55 134[8:SpL:132.0,113.3] || equal(inverse(sk_c7),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c8,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 135[8:Rew:119.0,134.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c8,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 136[8:Obv:135.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c8,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.55 138[2:SpR:115.0,52.0] || -> equal(multiply(sk_c11,sk_c5),identity)**.
% 0.19/0.55 139[3:SpR:117.0,52.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.19/0.55 140[4:SpR:119.0,52.0] || -> equal(multiply(sk_c9,sk_c7),identity)**.
% 0.19/0.55 144[5:SpR:121.0,53.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.19/0.55 149[0:SpR:52.0,53.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.55 151[0:Rew:51.0,149.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.55 167[0:SpR:151.0,151.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.55 170[8:SpR:132.0,151.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.19/0.55 172[6:SpR:126.0,151.0] || -> equal(multiply(inverse(sk_c9),sk_c10),sk_c8)**.
% 0.19/0.55 173[3:SpR:139.0,151.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c6)**.
% 0.19/0.55 174[4:SpR:140.0,151.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c7)**.
% 0.19/0.55 176[0:SpR:52.0,151.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.55 184[8:Rew:126.0,170.0,119.0,170.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 186[8:Rew:184.0,117.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.19/0.55 188[8:Rew:184.0,121.0] || -> equal(multiply(sk_c6,sk_c10),sk_c10)**.
% 0.19/0.55 190[8:Rew:184.0,132.0] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.55 192[8:Rew:184.0,140.0] || -> equal(multiply(sk_c10,sk_c7),identity)**.
% 0.19/0.55 195[8:Rew:184.0,136.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c8,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(multiply(sk_c10,x),sk_c10)** -> .
% 0.19/0.55 206[8:Rew:184.0,172.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c8)**.
% 0.19/0.55 207[8:Rew:52.0,206.0] || -> equal(identity,sk_c8)**.
% 0.19/0.55 208[8:Rew:207.0,51.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.55 212[8:Rew:207.0,192.0] || -> equal(multiply(sk_c10,sk_c7),sk_c8)**.
% 0.19/0.55 213[8:Rew:184.0,173.0,207.0,173.0] || -> equal(multiply(inverse(sk_c10),sk_c8),sk_c6)**.
% 0.19/0.55 214[8:Rew:213.0,174.0,184.0,174.0,207.0,174.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.55 216[8:Rew:214.0,190.0] || -> equal(multiply(sk_c6,sk_c10),sk_c8)**.
% 0.19/0.55 217[8:Rew:214.0,212.0] || -> equal(multiply(sk_c10,sk_c6),sk_c8)**.
% 0.19/0.55 218[8:Rew:188.0,216.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.55 220[8:Rew:218.0,207.0] || -> equal(identity,sk_c10)**.
% 0.19/0.55 221[8:Rew:218.0,208.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.55 225[8:Rew:218.0,217.0] || -> equal(multiply(sk_c10,sk_c6),sk_c10)**.
% 0.19/0.55 226[8:Rew:221.0,225.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.55 228[8:Rew:226.0,186.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.55 236[8:Rew:220.0,176.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.19/0.55 242[8:Rew:167.0,236.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.55 247[8:Rew:221.0,195.6,221.0,195.5,184.0,195.5,242.0,195.3,218.0,195.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(sk_c10,w)* equal(u,x)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10)* equal(x,sk_c10)* -> .
% 0.19/0.55 248[8:Obv:247.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)** equal(x,sk_c10)* equal(w,sk_c10)* -> .
% 0.19/0.55 249[8:Con:248.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c10)* -> .
% 0.19/0.55 494[8:SpL:130.0,249.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c5),sk_c11)** equal(u,v)* equal(sk_c10,sk_c10) equal(v,sk_c10)* -> .
% 0.19/0.55 502[8:Obv:494.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c5),sk_c11)** equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 503[8:Rew:115.0,502.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 504[8:Obv:503.1] || equal(inverse(u),sk_c10)**+ equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 614[8:SpL:228.0,504.0] || equal(sk_c10,sk_c10)* equal(sk_c10,u)* equal(u,sk_c10)* -> .
% 0.19/0.55 619[8:Obv:614.1] || equal(u,sk_c10)* -> .
% 0.19/0.55 620[8:AED:619.0] || -> .
% 0.19/0.55 621[8:Spt:620.0,27.1,132.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.55 622[8:Spt:620.0,27.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 623[4:Rew:173.0,174.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.55 626[8:Rew:121.0,621.0,623.0,621.0] || equal(sk_c8,sk_c10)** -> .
% 0.19/0.55 631[5:Rew:121.0,13.1,623.0,13.1] || -> equal(inverse(sk_c1),sk_c11)** equal(sk_c8,sk_c10).
% 0.19/0.55 633[5:Rew:121.0,48.1,623.0,48.1] || -> equal(inverse(sk_c3),sk_c10)** equal(sk_c8,sk_c10).
% 0.19/0.55 634[8:MRR:633.1,626.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 635[0:Rew:167.0,176.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.55 636[3:Rew:635.0,173.0] || -> equal(inverse(sk_c9),sk_c6)**.
% 0.19/0.55 637[6:Rew:636.0,172.0] || -> equal(multiply(sk_c6,sk_c10),sk_c8)**.
% 0.19/0.55 639[5:Rew:121.0,41.0,623.0,41.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 640[8:MRR:639.0,626.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 641[5:Rew:121.0,34.0,623.0,34.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 642[8:MRR:641.0,626.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 645[5:Rew:121.0,6.0,623.0,6.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 658[8:SpR:634.0,151.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.19/0.55 660[3:SpR:636.0,151.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.19/0.55 662[5:Rew:144.0,660.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.55 666[5:Rew:662.0,125.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,w),sk_c10)** equal(x,sk_c9) -> .
% 0.19/0.55 667[8:Rew:662.0,658.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.55 670[8:Rew:662.0,642.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.55 674[8:Rew:670.0,640.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.55 675[8:Rew:667.0,674.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 679[8:Rew:675.0,139.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.19/0.55 687[8:Rew:662.0,679.0] || -> equal(identity,sk_c6)**.
% 0.19/0.55 689[8:Rew:687.0,51.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.55 697[8:Rew:689.0,637.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.55 698[8:MRR:697.0,626.0] || -> .
% 0.19/0.55 715[7:Spt:698.0,43.1,130.0] || equal(multiply(sk_c5,sk_c11),sk_c10)** -> .
% 0.19/0.55 716[7:Spt:698.0,43.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 723[7:MRR:8.1,715.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.55 734[7:MRR:36.0,715.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 735[5:Rew:662.0,29.1] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(sk_c4,sk_c9).
% 0.19/0.55 736[7:MRR:735.0,715.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.55 737[7:Rew:736.0,734.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.55 739[7:MRR:1.0,715.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 740[7:SpR:716.0,151.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.19/0.55 742[7:Rew:662.0,740.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.55 743[7:Rew:742.0,737.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 749[7:Rew:743.0,139.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.19/0.55 765[7:Rew:662.0,749.0] || -> equal(identity,sk_c6)**.
% 0.19/0.55 766[7:Rew:765.0,635.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.55 768[7:Rew:765.0,138.0] || -> equal(multiply(sk_c11,sk_c5),sk_c6)**.
% 0.19/0.55 801[7:SpR:739.0,151.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.19/0.55 803[7:Rew:723.0,801.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.55 806[7:SpR:768.0,151.0] || -> equal(multiply(inverse(sk_c11),sk_c6),sk_c5)**.
% 0.19/0.55 808[7:Rew:766.0,806.0] || -> equal(inverse(sk_c11),sk_c5)**.
% 0.19/0.55 814[7:SpR:803.0,151.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.19/0.55 816[7:Rew:808.0,814.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.19/0.55 817[7:MRR:816.0,715.0] || -> .
% 0.19/0.55 819[6:Spt:817.0,47.1,126.0] || equal(multiply(sk_c9,sk_c8),sk_c10)** -> .
% 0.19/0.55 820[6:Spt:817.0,47.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 826[6:MRR:40.0,819.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 829[5:Rew:662.0,33.1] || -> equal(multiply(sk_c9,sk_c8),sk_c10)** equal(sk_c4,sk_c9).
% 0.19/0.55 830[6:MRR:829.0,819.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.55 831[6:Rew:830.0,826.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.55 834[6:SpR:820.0,151.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.19/0.55 836[6:Rew:662.0,834.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.55 837[6:Rew:836.0,831.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 838[6:Rew:837.0,117.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.19/0.55 839[6:Rew:837.0,636.0] || -> equal(inverse(sk_c10),sk_c6)**.
% 0.19/0.55 840[6:Rew:837.0,139.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.19/0.55 843[6:Rew:837.0,819.0] || equal(multiply(sk_c10,sk_c8),sk_c10)** -> .
% 0.19/0.55 852[6:Rew:837.0,666.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c10,w),sk_c10)** equal(x,sk_c9) -> .
% 0.19/0.55 857[6:Rew:662.0,840.0] || -> equal(identity,sk_c6)**.
% 0.19/0.55 859[6:Rew:857.0,51.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.55 860[6:Rew:857.0,635.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.55 861[6:Rew:857.0,52.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.55 863[6:Rew:662.0,843.0] || equal(sk_c8,sk_c10)** -> .
% 0.19/0.55 864[6:MRR:631.1,863.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.55 865[6:MRR:645.0,863.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 871[6:Rew:837.0,852.6,662.0,852.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,w)* equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10)* equal(x,sk_c10) -> .
% 0.19/0.55 872[6:Obv:871.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(x,sk_c10)* equal(w,sk_c10) -> .
% 0.19/0.55 873[6:Con:872.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10) -> .
% 0.19/0.55 937[6:SpR:839.0,861.0] || -> equal(multiply(sk_c6,sk_c10),sk_c6)**.
% 0.19/0.55 944[6:Rew:859.0,937.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.55 947[6:Rew:944.0,838.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.55 952[6:Rew:944.0,860.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.55 961[6:Rew:952.0,873.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c10)* -> .
% 0.19/0.55 1364[6:SpL:865.0,961.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(sk_c10,sk_c10) equal(v,sk_c10)* -> .
% 0.19/0.55 1365[6:Obv:1364.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1366[6:Rew:864.0,1365.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1367[6:Obv:1366.1] || equal(inverse(u),sk_c10)**+ equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1496[6:SpL:947.0,1367.0] || equal(sk_c10,sk_c10)* equal(sk_c10,u)* equal(u,sk_c10)* -> .
% 0.19/0.55 1501[6:Obv:1496.1] || equal(u,sk_c10)* -> .
% 0.19/0.55 1502[6:AED:1501.0] || -> .
% 0.19/0.55 1503[5:Spt:1502.0,45.1,121.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.19/0.55 1504[5:Spt:1502.0,45.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 1506[5:MRR:24.1,1503.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 1508[5:MRR:38.0,1503.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 1509[5:MRR:31.0,1503.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 1510[5:MRR:17.0,1503.0] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 1544[5:SpR:1508.0,151.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.55 1546[5:Rew:1504.0,1544.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.55 1547[5:Rew:1509.0,1546.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 1548[5:Rew:1547.0,636.0] || -> equal(inverse(sk_c10),sk_c6)**.
% 0.19/0.55 1550[5:Rew:1547.0,1506.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.55 1552[5:Rew:1547.0,1503.0] || equal(multiply(sk_c6,sk_c10),sk_c10)** -> .
% 0.19/0.55 1555[5:Rew:1547.0,1509.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.55 1556[5:Rew:1547.0,1510.0] || -> equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.19/0.55 1581[5:SpR:1555.0,151.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c4)**.
% 0.19/0.55 1583[5:Rew:1548.0,1581.0] || -> equal(multiply(sk_c6,sk_c10),sk_c4)**.
% 0.19/0.55 1584[5:Rew:1583.0,1552.0] || equal(sk_c4,sk_c10)** -> .
% 0.19/0.55 1591[5:SpR:1556.0,151.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c10)**.
% 0.19/0.55 1593[5:Rew:1550.0,1591.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.19/0.55 1609[5:SpR:1593.0,151.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.19/0.55 1611[5:Rew:1583.0,1609.0,1548.0,1609.0] || -> equal(sk_c4,sk_c10)**.
% 0.19/0.55 1612[5:MRR:1611.0,1584.0] || -> .
% 0.19/0.55 1613[4:Spt:1612.0,28.0,119.0] || equal(inverse(sk_c7),sk_c9)** -> .
% 0.19/0.55 1614[4:Spt:1612.0,28.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 1615[4:MRR:14.0,1613.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.55 1616[4:MRR:49.0,1613.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.55 1617[4:MRR:42.0,1613.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.55 1618[4:MRR:35.0,1613.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.55 1619[4:MRR:21.0,1613.0] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.55 1620[4:MRR:7.0,1613.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.55 1638[4:SpR:1617.0,151.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.55 1640[4:Rew:1616.0,1638.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.55 1641[4:Rew:1618.0,1640.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.55 1642[4:Rew:1641.0,1614.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.55 1643[4:Rew:1641.0,117.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.19/0.55 1644[4:Rew:1641.0,636.0] || -> equal(inverse(sk_c10),sk_c6)**.
% 0.19/0.55 1645[4:Rew:1641.0,139.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.19/0.55 1649[4:Rew:1641.0,1618.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.55 1650[4:Rew:1641.0,1619.0] || -> equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.19/0.55 1654[4:Rew:1641.0,113.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c9,x),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.19/0.55 1660[4:Rew:1641.0,1654.7,1641.0,1654.6,1641.0,1654.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c10,x),sk_c10)** equal(multiply(sk_c10,y),sk_c10)** -> .
% 0.19/0.55 1661[4:Con:1660.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c10,w),sk_c10)** -> .
% 0.19/0.55 1680[4:SpR:1649.0,151.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c4)**.
% 0.19/0.55 1682[4:Rew:1644.0,1680.0] || -> equal(multiply(sk_c6,sk_c10),sk_c4)**.
% 0.19/0.55 1684[4:SpR:1650.0,151.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c10)**.
% 0.19/0.55 1686[4:Rew:1642.0,1684.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.19/0.55 1692[0:SpR:52.0,151.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.55 1699[4:SpR:1644.0,52.0] || -> equal(multiply(sk_c6,sk_c10),identity)**.
% 0.19/0.55 1700[4:Rew:1682.0,1699.0] || -> equal(identity,sk_c4)**.
% 0.19/0.55 1702[4:Rew:1700.0,51.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.55 1703[4:Rew:1700.0,1645.0] || -> equal(multiply(sk_c10,sk_c6),sk_c4)**.
% 0.19/0.55 1705[4:Rew:1700.0,635.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.55 1722[4:SpR:1686.0,151.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.19/0.55 1724[4:Rew:1682.0,1722.0,1644.0,1722.0] || -> equal(sk_c4,sk_c10)**.
% 0.19/0.55 1729[4:Rew:1724.0,1702.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.55 1730[4:Rew:1724.0,1703.0] || -> equal(multiply(sk_c10,sk_c6),sk_c10)**.
% 0.19/0.55 1731[4:Rew:1724.0,1705.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.55 1737[4:Rew:1729.0,1661.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10) -> .
% 0.19/0.55 1746[4:Rew:1729.0,1730.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.55 1747[4:Rew:1746.0,1643.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.55 1763[4:Rew:1731.0,1737.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c10)* -> .
% 0.19/0.55 1841[4:SpL:1620.0,1763.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(sk_c10,sk_c10) equal(v,sk_c10)* -> .
% 0.19/0.55 1846[4:Obv:1841.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1847[4:Rew:1615.0,1846.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1848[4:Obv:1847.1] || equal(inverse(u),sk_c10)**+ equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.55 1856[0:SpR:167.0,151.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.55 2056[4:SpL:1747.0,1848.0] || equal(sk_c10,sk_c10)* equal(sk_c10,u)* equal(u,sk_c10)* -> .
% 0.19/0.55 2060[4:Obv:2056.1] || equal(u,sk_c10)* -> .
% 0.19/0.55 2061[4:AED:2060.0] || -> .
% 0.19/0.55 2062[3:Spt:2061.0,25.0,117.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.19/0.55 2063[3:Spt:2061.0,25.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.55 2064[0:Rew:635.0,1692.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.55 2065[3:MRR:11.0,2062.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.55 2066[3:MRR:46.0,2062.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.56 2071[3:MRR:39.0,2062.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.56 2072[3:MRR:32.0,2062.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.56 2074[3:MRR:4.0,2062.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.56 2091[3:SpR:2065.0,1856.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),u)**.
% 0.19/0.56 2102[3:SpR:2071.0,151.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.56 2104[3:Rew:2066.0,2102.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.56 2105[3:Rew:2072.0,2104.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.56 2106[3:Rew:2105.0,2063.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.56 2110[3:Rew:2105.0,113.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c9,x),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.19/0.56 2121[3:Rew:2105.0,2110.7,2105.0,2110.6,2105.0,2110.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c10,x),sk_c10)** equal(multiply(sk_c10,y),sk_c10)** -> .
% 0.19/0.56 2122[3:Con:2121.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c10,w),sk_c10)** -> .
% 0.19/0.56 2128[3:SpR:2074.0,53.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),multiply(sk_c10,u))**.
% 0.19/0.56 2132[3:Rew:2091.0,2128.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.56 2133[3:Rew:2132.0,2122.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10) -> .
% 0.19/0.56 2162[3:SpR:2066.0,52.0] || -> equal(multiply(sk_c10,sk_c3),identity)**.
% 0.19/0.56 2163[3:SpR:2106.0,52.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.19/0.56 2164[3:Rew:2132.0,2162.0] || -> equal(identity,sk_c3)**.
% 0.19/0.56 2167[3:Rew:2164.0,52.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.56 2168[3:Rew:2164.0,635.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.56 2171[3:Rew:2132.0,2163.0,2164.0,2163.0] || -> equal(sk_c3,sk_c2)**.
% 0.19/0.56 2177[3:Rew:2171.0,2168.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.56 2179[3:Rew:2171.0,2167.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.56 2217[3:SpR:2065.0,2064.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.19/0.56 2224[3:SpR:2217.0,2179.0] || -> equal(multiply(sk_c1,sk_c11),sk_c2)**.
% 0.19/0.56 2227[3:Rew:2074.0,2224.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.56 2228[3:Rew:2227.0,2106.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.56 2234[3:Rew:2227.0,2177.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.56 2237[3:Rew:2234.0,2133.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c10)* -> .
% 0.19/0.56 2315[3:SpL:2074.0,2237.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(sk_c10,sk_c10) equal(v,sk_c10)* -> .
% 0.19/0.56 2319[3:Obv:2315.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2320[3:Rew:2065.0,2319.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2321[3:Obv:2320.1] || equal(inverse(u),sk_c10)**+ equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2448[3:SpL:2228.0,2321.0] || equal(sk_c10,sk_c10)* equal(sk_c10,u)* equal(u,sk_c10)* -> .
% 0.19/0.56 2450[3:Obv:2448.1] || equal(u,sk_c10)* -> .
% 0.19/0.56 2451[3:AED:2450.0] || -> .
% 0.19/0.56 2452[2:Spt:2451.0,44.0,115.0] || equal(inverse(sk_c5),sk_c11)** -> .
% 0.19/0.56 2453[2:Spt:2451.0,44.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.56 2455[2:MRR:23.0,2452.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.56 2456[2:MRR:9.0,2452.0] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.56 2457[2:MRR:37.0,2452.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.56 2458[2:MRR:30.0,2452.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.56 2459[2:MRR:16.0,2452.0] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.19/0.56 2460[2:MRR:2.0,2452.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.56 2464[2:SpR:2453.0,2064.0] || -> equal(inverse(sk_c10),sk_c3)**.
% 0.19/0.56 2467[2:SpR:2455.0,1856.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.19/0.56 2468[2:SpR:2455.0,2064.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.19/0.56 2486[2:SpR:2457.0,53.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c4,u))**.
% 0.19/0.56 2487[2:SpR:2457.0,151.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.56 2489[2:Rew:2453.0,2487.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.56 2490[2:Rew:2458.0,2489.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.56 2491[2:Rew:2490.0,2455.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.56 2492[2:Rew:2490.0,2468.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.19/0.56 2494[2:Rew:2490.0,2459.0] || -> equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.19/0.56 2498[2:Rew:2490.0,113.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c9,x),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.19/0.56 2501[2:Rew:2490.0,2467.0] || -> equal(multiply(sk_c2,multiply(sk_c10,u)),u)**.
% 0.19/0.56 2502[2:Rew:2464.0,2492.0] || -> equal(sk_c3,sk_c2)**.
% 0.19/0.56 2505[2:Rew:2502.0,2457.0] || -> equal(multiply(sk_c2,sk_c10),sk_c4)**.
% 0.19/0.56 2508[2:Rew:2494.0,2505.0] || -> equal(sk_c4,sk_c10)**.
% 0.19/0.56 2510[2:Rew:2501.0,2486.0,2502.0,2486.0,2508.0,2486.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.56 2518[2:Rew:2510.0,2498.7,2490.0,2498.7,2510.0,2498.6,2490.0,2498.6,2490.0,2498.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),x)* equal(multiply(v,sk_c10),y)* equal(multiply(w,sk_c11),sk_c10)** equal(x,sk_c10) equal(y,sk_c10) -> .
% 0.19/0.56 2519[2:Con:2518.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),w)* equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c10) -> .
% 0.19/0.56 2562[2:SpR:2510.0,635.0] || -> equal(identity,sk_c10)**.
% 0.19/0.56 2565[2:Rew:2562.0,635.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.56 2566[2:Rew:2562.0,52.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.19/0.56 2569[2:Rew:2565.0,2519.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,w)* equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c10)* -> .
% 0.19/0.56 2587[2:SpR:2491.0,2566.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.19/0.56 2589[2:Rew:2510.0,2587.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.56 2591[2:Rew:2589.0,2491.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.56 2612[2:SpL:2460.0,2569.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(sk_c10,sk_c10) equal(v,sk_c10)* -> .
% 0.19/0.56 2617[2:Obv:2612.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c11)** equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2618[2:Rew:2456.0,2617.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2619[2:Obv:2618.1] || equal(inverse(u),sk_c10)**+ equal(u,v)* equal(v,sk_c10)* -> .
% 0.19/0.56 2669[2:SpL:2591.0,2619.0] || equal(sk_c10,sk_c10)* equal(sk_c10,u)* equal(u,sk_c10)* -> .
% 0.19/0.56 2670[2:Obv:2669.1] || equal(u,sk_c10)* -> .
% 0.19/0.56 2671[2:AED:2670.0] || -> .
% 0.19/0.56 % SZS output end Refutation
% 0.19/0.56 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_13 prove_this_14 prove_this_16 prove_this_17 prove_this_18 prove_this_21 prove_this_23 prove_this_24 prove_this_25 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 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_48 prove_this_49 prove_this_50 left_identity left_inverse associativity
% 0.19/0.56
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