TSTP Solution File: GRP260-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP260-1 : 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 11:46:34 EDT 2022
% Result : Unsatisfiable 0.37s 0.57s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP260-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 02:52:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.57
% 0.37/0.57 SPASS V 3.9
% 0.37/0.57 SPASS beiseite: Proof found.
% 0.37/0.57 % SZS status Theorem
% 0.37/0.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.57 SPASS derived 1742 clauses, backtracked 591 clauses, performed 11 splits and kept 1140 clauses.
% 0.37/0.57 SPASS allocated 64452 KBytes.
% 0.37/0.57 SPASS spent 0:00:00.23 on the problem.
% 0.37/0.57 0:00:00.03 for the input.
% 0.37/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.57 0:00:00.01 for inferences.
% 0.37/0.57 0:00:00.00 for the backtracking.
% 0.37/0.57 0:00:00.15 for the reduction.
% 0.37/0.57
% 0.37/0.57
% 0.37/0.57 Here is a proof with depth 5, length 398 :
% 0.37/0.57 % SZS output start Refutation
% 0.37/0.57 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.37/0.57 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.37/0.57 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.37/0.57 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.37/0.57 7[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.37/0.57 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.37/0.57 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.37/0.57 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.57 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.37/0.57 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.37/0.57 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.37/0.57 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 31[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 33[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.57 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 35[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 41[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 43[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 45[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c9,sk_c11),sk_c10).
% 0.37/0.57 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 48[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 51[0:Inp] || equal(multiply(u,sk_c11),sk_c10)** equal(inverse(u),sk_c11) equal(multiply(v,sk_c10),sk_c9)** equal(inverse(v),sk_c10) equal(multiply(sk_c9,sk_c11),sk_c10)** equal(multiply(w,sk_c11),sk_c10)** equal(inverse(w),sk_c11) equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(y,z),sk_c11)** equal(inverse(y),z) equal(multiply(z,sk_c10),sk_c11)** equal(inverse(x1),x2) equal(inverse(x2),z)* equal(multiply(x1,z),x2)* -> .
% 0.37/0.57 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.37/0.57 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.37/0.57 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.37/0.57 55[0:Con:51.5] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(z,sk_c11),sk_c10)** equal(multiply(sk_c9,sk_c11),sk_c10)** -> .
% 0.37/0.57 56[1:Spt:55.0,55.1,55.2,55.5,55.6,55.7] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)* equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** -> .
% 0.37/0.57 58[2:Spt:49.1] || -> equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 60[2:SpL:58.0,56.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.37/0.57 61[3:Spt:39.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 63[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.37/0.57 65[5:Spt:29.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 69[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.37/0.57 71[6:SpL:69.0,56.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.37/0.57 72[6:Rew:63.0,71.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.37/0.57 76[3:SpR:61.0,53.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.37/0.57 77[4:SpR:63.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.37/0.57 90[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.37/0.57 91[3:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.37/0.57 92[4:SpR:77.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.37/0.57 94[3:Rew:52.0,91.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.37/0.57 95[4:Rew:52.0,92.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.37/0.57 96[0:Rew:52.0,90.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.37/0.57 100[5:SpR:65.0,94.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.37/0.57 109[6:SpR:69.0,95.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 111[6:Rew:109.0,72.5] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.37/0.57 114[6:Obv:111.5] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 121[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.37/0.57 124[6:SpR:109.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.37/0.57 128[0:SpR:53.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.37/0.57 129[3:SpR:76.0,96.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.37/0.57 130[5:SpR:100.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.37/0.57 131[4:SpR:77.0,96.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.37/0.57 139[6:Rew:53.0,124.0] || -> equal(identity,sk_c10)**.
% 0.37/0.57 140[6:Rew:139.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.37/0.57 143[6:Rew:139.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.37/0.57 149[6:Rew:140.0,100.0] || -> equal(sk_c9,sk_c10)**.
% 0.37/0.57 157[6:Rew:149.0,58.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.37/0.57 165[6:Rew:140.0,157.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 172[6:Rew:165.0,114.3] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 173[6:Rew:165.0,139.0] || -> equal(identity,sk_c11)**.
% 0.37/0.57 174[6:Rew:165.0,140.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.57 178[6:Rew:165.0,143.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.37/0.57 181[6:Rew:174.0,178.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.57 182[6:Rew:181.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.37/0.57 184[6:Rew:181.0,173.0] || -> equal(identity,sk_c1)**.
% 0.37/0.57 197[6:Rew:184.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.37/0.57 206[6:Rew:121.0,197.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.37/0.57 208[6:Obv:172.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 209[6:Rew:206.0,208.3,181.0,208.3,181.0,208.2,181.0,208.1,181.0,208.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.37/0.57 515[6:SpL:182.0,209.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.37/0.57 518[6:Obv:515.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.37/0.57 520[6:SpL:182.0,518.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.37/0.57 523[6:Obv:520.1] || -> .
% 0.37/0.57 524[6:Spt:523.0,9.1,69.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.37/0.57 525[6:Spt:523.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 526[5:Rew:53.0,130.0] || -> equal(identity,sk_c9)**.
% 0.37/0.57 527[5:Rew:526.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c9)**.
% 0.37/0.57 529[5:Rew:526.0,52.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.37/0.57 532[5:Rew:526.0,129.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c2)**.
% 0.37/0.57 533[5:Rew:529.0,58.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 536[5:Rew:533.0,65.0] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.37/0.57 539[5:Rew:526.0,131.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.37/0.57 540[6:Rew:533.0,524.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.37/0.57 541[5:Rew:539.0,532.0,533.0,532.0] || -> equal(sk_c2,sk_c1)**.
% 0.37/0.57 543[5:Rew:541.0,536.0] || -> equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.37/0.57 545[6:Rew:543.0,540.0] || equal(sk_c9,sk_c11)** -> .
% 0.37/0.57 547[5:Rew:526.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.37/0.57 553[5:Rew:543.0,6.1,533.0,6.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c11).
% 0.37/0.57 554[6:MRR:553.1,545.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 562[5:Rew:121.0,547.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.37/0.57 566[5:Rew:543.0,7.1,533.0,7.1,533.0,7.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)** equal(sk_c9,sk_c11).
% 0.37/0.57 567[6:MRR:566.1,545.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.37/0.57 568[5:Rew:543.0,5.1,533.0,5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c9,sk_c11).
% 0.37/0.57 569[6:MRR:568.1,545.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 613[5:SpR:527.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.37/0.57 615[5:Rew:562.0,613.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.37/0.57 632[6:SpR:567.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c11)**.
% 0.37/0.57 635[6:SpR:569.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 637[6:Rew:567.0,635.0,554.0,635.0] || -> equal(sk_c8,sk_c11)**.
% 0.37/0.57 647[6:Rew:637.0,632.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.37/0.57 650[6:Rew:543.0,647.0,615.0,647.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.57 651[6:MRR:650.0,545.0] || -> .
% 0.37/0.57 654[5:Spt:651.0,29.1,65.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.37/0.57 655[5:Spt:651.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 656[0:Rew:121.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.37/0.57 657[4:Rew:656.0,131.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.37/0.57 658[3:Rew:656.0,129.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.37/0.57 662[5:MRR:26.1,654.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 664[5:MRR:22.1,654.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.57 668[5:MRR:25.1,654.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 670[5:MRR:21.1,654.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 680[4:SpR:657.0,96.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),u)**.
% 0.37/0.57 713[5:SpR:668.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 715[5:Rew:662.0,713.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.57 721[5:SpR:670.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.57 723[5:Rew:664.0,721.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 731[5:SpR:715.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.57 733[5:Rew:53.0,731.0] || -> equal(identity,sk_c11)**.
% 0.37/0.57 735[5:Rew:733.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.37/0.57 736[5:Rew:733.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.57 740[5:Rew:733.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 745[5:Rew:736.0,723.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 746[5:Rew:736.0,735.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.57 748[5:Rew:736.0,680.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.37/0.57 754[5:Rew:745.0,658.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.37/0.57 756[5:Rew:745.0,58.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.37/0.57 761[5:Rew:745.0,654.0] || equal(multiply(sk_c2,sk_c11),sk_c9)** -> .
% 0.37/0.57 776[5:Rew:746.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.37/0.57 785[5:Rew:746.0,754.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.37/0.57 787[5:Rew:785.0,776.0] || -> equal(sk_c2,sk_c1)**.
% 0.37/0.57 790[5:Rew:746.0,740.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.37/0.57 791[5:Rew:790.0,756.0,746.0,756.0] || -> equal(sk_c9,sk_c1)**.
% 0.37/0.57 820[5:Rew:748.0,761.0,787.0,761.0,746.0,761.0,791.0,761.0] || equal(sk_c1,sk_c1)* -> .
% 0.37/0.57 821[5:Obv:820.0] || -> .
% 0.37/0.57 851[4:Spt:821.0,19.1,63.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.37/0.57 852[4:Spt:821.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 854[4:MRR:16.1,851.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 856[4:MRR:12.1,851.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.57 859[4:MRR:15.0,851.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 861[4:MRR:11.0,851.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 892[4:SpR:859.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 894[4:Rew:854.0,892.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.57 900[4:SpR:861.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.57 902[4:Rew:856.0,900.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 903[4:Rew:902.0,60.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.37/0.57 904[4:Obv:903.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 910[4:SpR:894.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.57 912[4:Rew:53.0,910.0] || -> equal(identity,sk_c11)**.
% 0.37/0.57 914[4:Rew:912.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 915[4:Rew:912.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.57 921[4:Rew:914.0,861.0] || -> equal(sk_c3,sk_c10)**.
% 0.37/0.57 922[4:Rew:914.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.37/0.57 923[4:Rew:914.0,904.4] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11)** equal(sk_c10,u) equal(v,sk_c11) -> .
% 0.37/0.57 925[4:Rew:921.0,856.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.37/0.57 933[4:Rew:658.0,925.0] || -> equal(sk_c2,sk_c11)**.
% 0.37/0.57 934[4:Rew:933.0,658.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.37/0.57 940[4:Rew:915.0,902.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 951[4:Rew:940.0,922.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.57 953[4:Rew:940.0,934.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.37/0.57 998[4:Rew:940.0,923.3,953.0,923.1,951.0,923.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.37/0.57 999[4:Obv:998.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.37/0.57 1356[4:SpL:953.0,999.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.37/0.57 1360[4:Obv:1356.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.37/0.57 1362[4:SpL:953.0,1360.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.37/0.57 1366[4:Obv:1362.1] || -> .
% 0.37/0.57 1367[3:Spt:1366.0,39.1,61.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.37/0.57 1368[3:Spt:1366.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 1370[3:MRR:36.1,1367.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 1371[3:MRR:34.1,1367.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.57 1372[3:MRR:32.1,1367.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.57 1376[3:MRR:35.0,1367.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 1377[3:MRR:33.0,1367.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.57 1378[3:MRR:31.0,1367.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 1408[3:SpR:1376.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 1410[3:Rew:1370.0,1408.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.57 1416[3:SpR:1378.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.57 1418[3:Rew:1372.0,1416.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 1419[3:Rew:1418.0,60.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.37/0.57 1420[3:Obv:1419.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 1426[3:SpR:1410.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.57 1428[3:Rew:53.0,1426.0] || -> equal(identity,sk_c11)**.
% 0.37/0.57 1429[3:Rew:1428.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.57 1430[3:Rew:1428.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 1436[3:Rew:1429.0,1418.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 1441[3:Rew:1436.0,1371.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.37/0.57 1442[3:Rew:1436.0,58.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.37/0.57 1445[3:Rew:1436.0,1377.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.37/0.57 1456[3:Rew:1436.0,1420.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.37/0.57 1457[3:Rew:1430.0,1442.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.57 1469[3:Rew:1430.0,1445.0,1457.0,1445.0] || -> equal(sk_c4,sk_c11)**.
% 0.37/0.57 1470[3:Rew:1469.0,1441.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.37/0.57 1498[3:Rew:1430.0,1456.4,1470.0,1456.1,1457.0,1456.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.37/0.57 1499[3:Obv:1498.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.37/0.57 1807[3:SpL:1470.0,1499.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.37/0.57 1810[3:Obv:1807.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.37/0.57 1812[3:SpL:1470.0,1810.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.37/0.57 1815[3:Obv:1812.1] || -> .
% 0.37/0.57 1816[2:Spt:1815.0,49.1,58.0] || equal(multiply(sk_c9,sk_c11),sk_c10)** -> .
% 0.37/0.57 1817[2:Spt:1815.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 1820[2:MRR:46.1,1816.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 1821[2:MRR:44.1,1816.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.57 1822[2:MRR:42.1,1816.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.57 1825[2:MRR:45.1,1816.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 1826[2:MRR:43.1,1816.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.57 1827[2:MRR:41.1,1816.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 1854[2:SpR:1825.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 1856[2:Rew:1820.0,1854.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.57 1858[2:SpR:1826.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.37/0.57 1860[2:Rew:1821.0,1858.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.37/0.57 1862[2:SpR:1827.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.57 1864[2:Rew:1822.0,1862.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 1870[2:SpR:1856.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.57 1872[2:Rew:53.0,1870.0] || -> equal(identity,sk_c11)**.
% 0.37/0.57 1873[2:Rew:1872.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 1874[2:Rew:1872.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.57 1881[2:Rew:1873.0,1816.0] || equal(sk_c9,sk_c10)** -> .
% 0.37/0.57 1885[2:Rew:1874.0,1864.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 1890[2:Rew:1885.0,1826.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.37/0.57 1897[2:Rew:1885.0,1860.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.37/0.57 1900[2:Rew:1885.0,1881.0] || equal(sk_c9,sk_c11)** -> .
% 0.37/0.57 1914[2:Rew:1873.0,1890.0] || -> equal(sk_c9,sk_c4)**.
% 0.37/0.57 1915[2:Rew:1914.0,1900.0] || equal(sk_c4,sk_c11)** -> .
% 0.37/0.57 1916[2:Rew:1874.0,1897.0,1914.0,1897.0] || -> equal(sk_c4,sk_c11)**.
% 0.37/0.57 1917[2:MRR:1916.0,1915.0] || -> .
% 0.37/0.57 1948[1:Spt:1917.0,55.3,55.4,55.8,55.9,55.10] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,sk_c11),sk_c10)** -> .
% 0.37/0.57 1950[2:Spt:48.1] || -> equal(multiply(sk_c9,sk_c11),sk_c10)**.
% 0.37/0.57 1951[2:Rew:1950.0,1948.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.37/0.57 1953[2:Obv:1951.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.37/0.57 1956[2:SpR:1950.0,96.0] || -> equal(multiply(inverse(sk_c9),sk_c10),sk_c11)**.
% 0.37/0.57 1958[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.37/0.57 1959[3:SpR:1958.0,96.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.37/0.57 1961[4:Spt:39.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.57 1962[4:SpR:1961.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.37/0.57 1964[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.37/0.57 1966[5:SpR:1964.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.37/0.57 1968[5:Rew:1958.0,1966.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 1969[6:Spt:29.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.37/0.57 1971[6:SpR:1969.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c10)**.
% 0.37/0.57 1973[6:Rew:1961.0,1971.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.37/0.57 1975[5:SpR:1968.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.37/0.57 1977[5:Rew:53.0,1975.0] || -> equal(identity,sk_c10)**.
% 0.37/0.57 1978[5:Rew:1977.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.37/0.57 1979[5:Rew:1977.0,656.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.37/0.57 1982[6:Rew:1978.0,1973.0] || -> equal(sk_c9,sk_c10)**.
% 0.37/0.57 1983[5:Rew:1978.0,1962.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.37/0.57 1987[6:Rew:1982.0,1950.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.37/0.57 1989[6:Rew:1982.0,1953.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.37/0.57 1992[6:Rew:1978.0,1987.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 1994[6:Rew:1992.0,1964.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.37/0.57 1998[6:Rew:1992.0,1979.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 2000[6:Rew:1998.0,1994.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.57 2001[6:Rew:2000.0,1958.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.37/0.57 2002[6:Rew:2000.0,1992.0] || -> equal(sk_c10,sk_c1)**.
% 0.37/0.57 2007[6:Rew:2000.0,1998.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.37/0.57 2015[6:Rew:2007.0,1989.3,2000.0,1989.3,2002.0,1989.3,2007.0,1989.2,2002.0,1989.2,2000.0,1989.1,2002.0,1989.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.37/0.57 2016[6:Con:2015.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.37/0.57 2052[6:SpL:2001.0,2016.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.37/0.57 2053[6:Obv:2052.1] || -> .
% 0.37/0.57 2054[6:Spt:2053.0,29.1,1969.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.37/0.57 2055[6:Spt:2053.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 2056[5:Rew:1979.0,1956.0] || -> equal(inverse(sk_c9),sk_c11)**.
% 0.37/0.57 2057[6:Rew:1983.0,2054.0] || equal(sk_c9,sk_c10)** -> .
% 0.37/0.57 2062[5:Rew:1983.0,24.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c9,sk_c10).
% 0.37/0.57 2063[6:MRR:2062.1,2057.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.57 2076[5:Rew:1983.0,23.1,1979.0,23.0] || -> equal(sk_c9,sk_c4)** equal(sk_c9,sk_c10).
% 0.37/0.57 2077[6:MRR:2076.1,2057.0] || -> equal(sk_c9,sk_c4)**.
% 0.37/0.57 2078[6:Rew:2077.0,1950.0] || -> equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.37/0.57 2079[6:Rew:2077.0,2056.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.37/0.57 2080[6:Rew:2077.0,2057.0] || equal(sk_c4,sk_c10)** -> .
% 0.37/0.57 2082[6:Rew:2063.0,2079.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.57 2085[6:Rew:2082.0,1964.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.37/0.57 2086[6:Rew:2082.0,1979.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.57 2091[6:Rew:2082.0,2080.0] || equal(sk_c4,sk_c11)** -> .
% 0.37/0.57 2092[6:Rew:2082.0,2078.0] || -> equal(multiply(sk_c4,sk_c11),sk_c11)**.
% 0.37/0.57 2093[6:Rew:2086.0,2085.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.57 2094[6:Rew:2086.0,2092.0] || -> equal(sk_c4,sk_c11)**.
% 0.37/0.57 2106[6:Rew:2093.0,2091.0] || equal(sk_c4,sk_c1)** -> .
% 0.37/0.57 2110[6:Rew:2093.0,2094.0] || -> equal(sk_c4,sk_c1)**.
% 0.37/0.57 2116[6:Rew:2110.0,2106.0] || equal(sk_c1,sk_c1)* -> .
% 0.37/0.57 2117[6:Obv:2116.0] || -> .
% 0.37/0.57 2133[5:Spt:2117.0,9.1,1964.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.37/0.57 2134[5:Spt:2117.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.57 2136[5:MRR:6.1,2133.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.57 2138[5:MRR:2.1,2133.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.57 2141[5:MRR:5.1,2133.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.57 2143[5:MRR:1.1,2133.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.57 2169[5:SpR:2141.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.57 2171[5:Rew:2136.0,2169.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.57 2177[5:SpR:2143.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.57 2179[5:Rew:2138.0,2177.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.57 2185[5:SpR:2171.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.57 2187[5:Rew:53.0,2185.0] || -> equal(identity,sk_c11)**.
% 0.37/0.58 2188[5:Rew:2187.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.58 2189[5:Rew:2187.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.58 2197[5:Rew:2188.0,2133.0] || equal(sk_c10,sk_c1)** -> .
% 0.37/0.58 2206[5:Rew:2189.0,2179.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.58 2207[5:Rew:2189.0,1959.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.37/0.58 2218[5:Rew:2206.0,2197.0] || equal(sk_c11,sk_c1)** -> .
% 0.37/0.58 2293[5:SpR:2207.0,2188.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.58 2295[5:MRR:2293.0,2218.0] || -> .
% 0.37/0.58 2297[4:Spt:2295.0,39.1,1961.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.37/0.58 2298[4:Spt:2295.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.58 2300[4:MRR:36.1,2297.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.58 2302[4:MRR:32.1,2297.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.58 2305[4:MRR:35.0,2297.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.58 2307[4:MRR:31.0,2297.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.58 2329[4:SpR:2305.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.58 2331[4:Rew:2300.0,2329.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.58 2337[4:SpR:2307.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.58 2339[4:Rew:2302.0,2337.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.58 2348[4:SpR:2331.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.58 2350[4:Rew:53.0,2348.0] || -> equal(identity,sk_c11)**.
% 0.37/0.58 2351[4:Rew:2350.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.58 2352[4:Rew:2350.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.58 2354[4:Rew:2350.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.37/0.58 2355[4:Rew:2351.0,2339.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.58 2363[4:Rew:2355.0,1950.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.37/0.58 2370[4:Rew:2355.0,1953.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.37/0.58 2375[4:Rew:2352.0,2363.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.58 2416[4:Rew:2352.0,2370.3,2355.0,2370.3,2352.0,2370.2,2355.0,2370.2,2375.0,2370.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.37/0.58 2417[4:Con:2416.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.37/0.58 2446[4:SpR:1958.0,2354.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.37/0.58 2449[4:Rew:2351.0,2446.0] || -> equal(sk_c11,sk_c1)**.
% 0.37/0.58 2450[4:Rew:2449.0,1958.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.37/0.58 2465[4:Rew:2449.0,2417.0] || equal(inverse(u),sk_c1)** equal(u,sk_c11) -> .
% 0.37/0.58 2471[4:Rew:2449.0,2465.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.37/0.58 2536[4:SpL:2450.0,2471.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.37/0.58 2538[4:Obv:2536.1] || -> .
% 0.37/0.58 2539[3:Spt:2538.0,19.1,1958.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.37/0.58 2540[3:Spt:2538.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.37/0.58 2542[3:MRR:16.1,2539.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.58 2543[3:MRR:14.1,2539.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.58 2544[3:MRR:12.1,2539.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.58 2547[3:MRR:15.0,2539.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.58 2548[3:MRR:13.0,2539.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.58 2549[3:MRR:11.0,2539.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.58 2571[3:SpR:2547.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.58 2573[3:Rew:2542.0,2571.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.58 2579[3:SpR:2549.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.58 2581[3:Rew:2544.0,2579.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.58 2587[3:SpR:2573.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.58 2589[3:Rew:53.0,2587.0] || -> equal(identity,sk_c11)**.
% 0.37/0.58 2590[3:Rew:2589.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.58 2591[3:Rew:2589.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.58 2595[3:Rew:2590.0,2581.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.58 2600[3:Rew:2595.0,2543.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.37/0.58 2601[3:Rew:2595.0,1950.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.37/0.58 2603[3:Rew:2595.0,2548.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.37/0.58 2607[3:Rew:2595.0,1953.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.37/0.58 2612[3:Rew:2591.0,2601.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.58 2624[3:Rew:2591.0,2603.0,2612.0,2603.0] || -> equal(sk_c4,sk_c11)**.
% 0.37/0.58 2625[3:Rew:2624.0,2600.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.37/0.58 2653[3:Rew:2591.0,2607.3,2595.0,2607.3,2591.0,2607.2,2595.0,2607.2,2612.0,2607.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.37/0.58 2654[3:Con:2653.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.37/0.58 2727[3:SpL:2625.0,2654.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.37/0.58 2729[3:Obv:2727.1] || -> .
% 0.37/0.58 2730[2:Spt:2729.0,48.1,1950.0] || equal(multiply(sk_c9,sk_c11),sk_c10)** -> .
% 0.37/0.58 2731[2:Spt:2729.0,48.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.37/0.58 2732[2:MRR:46.1,2730.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.37/0.58 2733[2:MRR:44.1,2730.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.37/0.58 2734[2:MRR:42.1,2730.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.37/0.58 2738[2:MRR:45.1,2730.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.37/0.58 2739[2:MRR:43.1,2730.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.37/0.58 2740[2:MRR:41.1,2730.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.37/0.58 2759[2:SpR:2738.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.37/0.58 2761[2:Rew:2732.0,2759.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.37/0.58 2763[2:SpR:2739.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.37/0.58 2765[2:Rew:2733.0,2763.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.37/0.58 2767[2:SpR:2740.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.37/0.58 2769[2:Rew:2734.0,2767.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.37/0.58 2778[2:SpR:2761.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.37/0.58 2780[2:Rew:53.0,2778.0] || -> equal(identity,sk_c11)**.
% 0.37/0.58 2781[2:Rew:2780.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.37/0.58 2782[2:Rew:2780.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.37/0.58 2785[2:Rew:2781.0,2769.0] || -> equal(sk_c10,sk_c11)**.
% 0.37/0.58 2792[2:Rew:2785.0,2739.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.37/0.58 2794[2:Rew:2785.0,2730.0] || equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.37/0.58 2798[2:Rew:2785.0,2765.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.37/0.58 2810[2:Rew:2782.0,2792.0] || -> equal(sk_c9,sk_c4)**.
% 0.37/0.58 2811[2:Rew:2781.0,2798.0,2810.0,2798.0] || -> equal(sk_c4,sk_c11)**.
% 0.37/0.58 2813[2:Rew:2811.0,2810.0] || -> equal(sk_c9,sk_c11)**.
% 0.37/0.58 2826[2:Rew:2781.0,2794.0,2813.0,2794.0] || equal(sk_c11,sk_c11)* -> .
% 0.37/0.58 2827[2:Obv:2826.0] || -> .
% 0.37/0.58 % SZS output end Refutation
% 0.37/0.58 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_7 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_29 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_48 prove_this_49 prove_this_51 left_identity left_inverse associativity
% 0.37/0.58
%------------------------------------------------------------------------------