TSTP Solution File: GRP263-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP263-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 0.41s 0.59s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP263-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 : Tue Jun 14 06:27:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.41/0.59
% 0.41/0.59 SPASS V 3.9
% 0.41/0.59 SPASS beiseite: Proof found.
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.59 SPASS derived 1899 clauses, backtracked 578 clauses, performed 11 splits and kept 1143 clauses.
% 0.41/0.59 SPASS allocated 64862 KBytes.
% 0.41/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.41/0.59 0:00:00.03 for the input.
% 0.41/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.59 0:00:00.01 for inferences.
% 0.41/0.59 0:00:00.00 for the backtracking.
% 0.41/0.59 0:00:00.16 for the reduction.
% 0.41/0.59
% 0.41/0.59
% 0.41/0.59 Here is a proof with depth 5, length 404 :
% 0.41/0.59 % SZS output start Refutation
% 0.41/0.59 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.41/0.59 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.41/0.59 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.41/0.59 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.41/0.59 7[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.41/0.59 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.41/0.59 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.41/0.59 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.59 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.41/0.59 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.41/0.59 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.41/0.59 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 27[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 28[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 30[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 31[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 33[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.59 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 35[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 41[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 43[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 45[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11).
% 0.41/0.59 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 48[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 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_c10),sk_c11)** 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)* -> .
% 0.41/0.59 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.41/0.59 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.41/0.59 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.41/0.59 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_c10),sk_c11)** -> .
% 0.41/0.59 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)** -> .
% 0.41/0.59 57[1:EqR:56.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11) -> .
% 0.41/0.59 58[2:Spt:49.1] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 60[2:SpL:58.0,56.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.41/0.59 61[3:Spt:39.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 63[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.41/0.59 65[5:Spt:29.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 69[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.41/0.59 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)** -> .
% 0.41/0.59 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)** -> .
% 0.41/0.59 76[3:SpR:61.0,53.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.41/0.59 77[4:SpR:63.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.41/0.59 90[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.41/0.59 91[3:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.41/0.59 92[4:SpR:77.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.41/0.59 94[3:Rew:52.0,91.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.41/0.59 95[4:Rew:52.0,92.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.41/0.59 96[0:Rew:52.0,90.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.41/0.59 100[5:SpR:65.0,94.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.41/0.59 111[6:SpR:69.0,95.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 113[6:Rew:111.0,72.5] || 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) -> .
% 0.41/0.59 115[6:Obv:113.5] || 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)** -> .
% 0.41/0.59 121[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.41/0.59 125[6:SpR:111.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.41/0.59 128[0:SpR:53.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.41/0.59 129[3:SpR:76.0,96.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.41/0.59 130[5:SpR:100.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.41/0.59 131[4:SpR:77.0,96.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.41/0.59 139[6:Rew:53.0,125.0] || -> equal(identity,sk_c10)**.
% 0.41/0.59 140[6:Rew:139.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.41/0.59 143[6:Rew:139.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.41/0.59 149[6:Rew:140.0,100.0] || -> equal(sk_c9,sk_c10)**.
% 0.41/0.59 158[6:Rew:149.0,58.0] || -> equal(multiply(sk_c10,sk_c10),sk_c11)**.
% 0.41/0.59 166[6:Rew:140.0,158.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 173[6:Rew:166.0,115.3] || 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)** -> .
% 0.41/0.59 174[6:Rew:166.0,139.0] || -> equal(identity,sk_c11)**.
% 0.41/0.59 175[6:Rew:166.0,140.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 179[6:Rew:166.0,143.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.41/0.59 182[6:Rew:175.0,179.0] || -> equal(sk_c11,sk_c1)**.
% 0.41/0.59 183[6:Rew:182.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.41/0.59 185[6:Rew:182.0,174.0] || -> equal(identity,sk_c1)**.
% 0.41/0.59 198[6:Rew:185.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.41/0.59 207[6:Rew:121.0,198.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.41/0.59 209[6:Obv:173.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.41/0.59 210[6:Rew:207.0,209.3,182.0,209.3,182.0,209.2,182.0,209.1,182.0,209.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.41/0.59 516[6:SpL:183.0,210.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.41/0.59 519[6:Obv:516.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.41/0.59 521[6:SpL:183.0,519.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.41/0.59 524[6:Obv:521.1] || -> .
% 0.41/0.59 525[6:Spt:524.0,9.1,69.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.41/0.59 526[6:Spt:524.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 527[5:Rew:53.0,130.0] || -> equal(identity,sk_c9)**.
% 0.41/0.59 528[5:Rew:527.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c9)**.
% 0.41/0.59 530[5:Rew:527.0,52.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.41/0.59 533[5:Rew:527.0,129.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c2)**.
% 0.41/0.59 534[5:Rew:530.0,58.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 537[5:Rew:534.0,65.0] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.41/0.59 540[5:Rew:527.0,131.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.41/0.59 541[6:Rew:534.0,525.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.41/0.59 542[5:Rew:540.0,533.0,534.0,533.0] || -> equal(sk_c2,sk_c1)**.
% 0.41/0.59 544[5:Rew:542.0,537.0] || -> equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.41/0.59 546[6:Rew:544.0,541.0] || equal(sk_c9,sk_c11)** -> .
% 0.41/0.59 548[5:Rew:527.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.41/0.59 554[5:Rew:544.0,6.1,534.0,6.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c11).
% 0.41/0.59 555[6:MRR:554.1,546.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.59 563[5:Rew:121.0,548.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.41/0.59 567[5:Rew:544.0,7.1,534.0,7.1,534.0,7.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)** equal(sk_c9,sk_c11).
% 0.41/0.59 568[6:MRR:567.1,546.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.41/0.59 569[5:Rew:544.0,5.1,534.0,5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c9,sk_c11).
% 0.41/0.59 570[6:MRR:569.1,546.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 613[5:SpR:528.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.41/0.59 615[5:Rew:563.0,613.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.41/0.59 632[6:SpR:568.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c11)**.
% 0.41/0.59 635[6:SpR:570.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.59 637[6:Rew:568.0,635.0,555.0,635.0] || -> equal(sk_c8,sk_c11)**.
% 0.41/0.59 647[6:Rew:637.0,632.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.41/0.59 650[6:Rew:544.0,647.0,615.0,647.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.59 651[6:MRR:650.0,546.0] || -> .
% 0.41/0.59 654[5:Spt:651.0,29.1,65.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.41/0.59 655[5:Spt:651.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 656[0:Rew:121.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.41/0.59 657[4:Rew:656.0,131.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.41/0.59 658[3:Rew:656.0,129.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.41/0.59 662[5:MRR:26.1,654.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.59 664[5:MRR:22.1,654.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.59 668[5:MRR:25.1,654.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 670[5:MRR:21.1,654.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 680[4:SpR:657.0,96.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),u)**.
% 0.41/0.59 713[5:SpR:668.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.59 715[5:Rew:662.0,713.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.59 721[5:SpR:670.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.59 723[5:Rew:664.0,721.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 729[5:SpR:715.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.59 731[5:Rew:53.0,729.0] || -> equal(identity,sk_c11)**.
% 0.41/0.59 733[5:Rew:731.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.41/0.59 734[5:Rew:731.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 738[5:Rew:731.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.59 743[5:Rew:734.0,723.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 744[5:Rew:734.0,733.0] || -> equal(sk_c11,sk_c1)**.
% 0.41/0.59 746[5:Rew:734.0,680.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.41/0.59 752[5:Rew:743.0,658.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.41/0.59 754[5:Rew:743.0,58.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.41/0.59 759[5:Rew:743.0,654.0] || equal(multiply(sk_c2,sk_c11),sk_c9)** -> .
% 0.41/0.59 774[5:Rew:744.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.41/0.59 783[5:Rew:744.0,752.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.41/0.59 785[5:Rew:783.0,774.0] || -> equal(sk_c2,sk_c1)**.
% 0.41/0.59 788[5:Rew:744.0,738.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.41/0.59 789[5:Rew:788.0,754.0,744.0,754.0] || -> equal(sk_c9,sk_c1)**.
% 0.41/0.59 818[5:Rew:746.0,759.0,785.0,759.0,744.0,759.0,789.0,759.0] || equal(sk_c1,sk_c1)* -> .
% 0.41/0.59 819[5:Obv:818.0] || -> .
% 0.41/0.59 849[4:Spt:819.0,19.1,63.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.41/0.59 850[4:Spt:819.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 852[4:MRR:16.1,849.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.59 854[4:MRR:12.1,849.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.59 857[4:MRR:15.0,849.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 859[4:MRR:11.0,849.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 890[4:SpR:857.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.59 892[4:Rew:852.0,890.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.59 898[4:SpR:859.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.59 900[4:Rew:854.0,898.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 906[4:SpR:892.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.59 908[4:Rew:53.0,906.0] || -> equal(identity,sk_c11)**.
% 0.41/0.59 910[4:Rew:908.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.59 911[4:Rew:908.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 912[4:Rew:908.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.41/0.59 917[4:Rew:910.0,859.0] || -> equal(sk_c3,sk_c10)**.
% 0.41/0.59 920[4:Rew:917.0,854.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.41/0.59 924[4:Rew:658.0,920.0] || -> equal(sk_c2,sk_c11)**.
% 0.41/0.59 925[4:Rew:924.0,658.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.41/0.59 931[4:Rew:911.0,900.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 942[4:Rew:931.0,57.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(multiply(v,sk_c11),sk_c11) -> .
% 0.41/0.59 949[4:Rew:931.0,925.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.41/0.59 1001[4:Rew:910.0,942.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(v,sk_c11) -> .
% 0.41/0.59 1032[4:SpR:912.0,96.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.41/0.59 1036[4:Rew:910.0,1032.0] || -> equal(inverse(inverse(u)),u)**.
% 0.41/0.59 1042[4:SpR:1036.0,912.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.41/0.59 1666[4:SpL:912.0,1001.0] || equal(inverse(sk_c11),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.41/0.59 1676[4:Rew:912.0,1666.1,1036.0,1666.1,949.0,1666.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.41/0.59 1677[4:Obv:1676.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.41/0.59 1762[4:SpL:1042.0,1677.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.41/0.59 1784[4:Obv:1762.1] || equal(inverse(u),sk_c11)** -> .
% 0.41/0.59 1785[4:UnC:1784.0,1036.0] || -> .
% 0.41/0.59 1791[3:Spt:1785.0,39.1,61.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.41/0.59 1792[3:Spt:1785.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 1794[3:MRR:36.1,1791.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.59 1795[3:MRR:34.1,1791.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.41/0.59 1796[3:MRR:32.1,1791.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.59 1800[3:MRR:35.0,1791.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 1801[3:MRR:33.0,1791.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.59 1802[3:MRR:31.0,1791.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 1832[3:SpR:1800.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.59 1834[3:Rew:1794.0,1832.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.59 1840[3:SpR:1802.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.59 1842[3:Rew:1796.0,1840.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 1851[3:SpR:1834.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.59 1853[3:Rew:53.0,1851.0] || -> equal(identity,sk_c11)**.
% 0.41/0.59 1854[3:Rew:1853.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 1855[3:Rew:1853.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.59 1860[3:Rew:1854.0,1842.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 1866[3:Rew:1860.0,1795.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.41/0.59 1867[3:Rew:1860.0,58.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.41/0.59 1870[3:Rew:1860.0,1801.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.41/0.59 1876[3:Rew:1860.0,60.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c9),u)* equal(inverse(v),sk_c10) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.41/0.59 1882[3:Rew:1855.0,1867.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.59 1894[3:Rew:1855.0,1870.0,1882.0,1870.0] || -> equal(sk_c4,sk_c11)**.
% 0.41/0.59 1895[3:Rew:1894.0,1866.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.41/0.59 1924[3:Rew:1855.0,1876.5,1860.0,1876.5,1855.0,1876.4,1860.0,1876.2,1895.0,1876.1,1882.0,1876.1,1860.0,1876.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.41/0.59 1925[3:Obv:1924.5] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.41/0.59 2139[3:SpL:1895.0,1925.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.41/0.59 2141[3:Obv:2139.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.41/0.59 2143[3:SpL:1895.0,2141.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.41/0.59 2145[3:Obv:2143.1] || -> .
% 0.41/0.59 2146[2:Spt:2145.0,49.1,58.0] || equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.41/0.59 2147[2:Spt:2145.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 2149[2:MRR:46.1,2146.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.59 2150[2:MRR:44.1,2146.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.41/0.59 2151[2:MRR:42.1,2146.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.59 2154[2:MRR:45.1,2146.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.59 2155[2:MRR:43.1,2146.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.59 2156[2:MRR:41.1,2146.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.59 2175[2:SpR:2154.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.59 2177[2:Rew:2149.0,2175.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.59 2179[2:SpR:2155.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.41/0.59 2181[2:Rew:2150.0,2179.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.41/0.59 2183[2:SpR:2156.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.59 2185[2:Rew:2151.0,2183.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 2191[2:SpR:2177.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.59 2193[2:Rew:53.0,2191.0] || -> equal(identity,sk_c11)**.
% 0.41/0.59 2194[2:Rew:2193.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 2195[2:Rew:2193.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.59 2201[2:Rew:2194.0,2185.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 2207[2:Rew:2201.0,2155.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.41/0.59 2209[2:Rew:2201.0,2146.0] || equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.41/0.59 2217[2:Rew:2201.0,2181.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.41/0.59 2229[2:Rew:2195.0,2207.0] || -> equal(sk_c9,sk_c4)**.
% 0.41/0.59 2230[2:Rew:2194.0,2217.0,2229.0,2217.0] || -> equal(sk_c4,sk_c11)**.
% 0.41/0.59 2232[2:Rew:2230.0,2229.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.59 2245[2:Rew:2195.0,2209.0,2232.0,2209.0] || equal(sk_c11,sk_c11)* -> .
% 0.41/0.59 2246[2:Obv:2245.0] || -> .
% 0.41/0.59 2265[1:Spt:2246.0,55.3,55.4,55.8,55.9,55.10] || 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_c10),sk_c11)** -> .
% 0.41/0.59 2267[2:Spt:48.1] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.41/0.59 2268[2:Rew:2267.0,2265.4] || 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_c11,sk_c11) -> .
% 0.41/0.59 2270[2:Obv:2268.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.41/0.59 2275[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.41/0.59 2276[3:SpR:2275.0,96.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.41/0.59 2278[4:Spt:39.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.41/0.59 2279[4:SpR:2278.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.41/0.59 2281[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.41/0.59 2283[5:SpR:2281.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.41/0.59 2285[5:Rew:2275.0,2283.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.59 2286[6:Spt:29.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.41/0.59 2288[6:SpR:2286.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c10)**.
% 0.41/0.59 2290[6:Rew:2278.0,2288.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.41/0.59 2292[5:SpR:2285.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.41/0.59 2294[5:Rew:53.0,2292.0] || -> equal(identity,sk_c10)**.
% 0.41/0.59 2295[5:Rew:2294.0,656.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.41/0.59 2296[5:Rew:2294.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.41/0.59 2300[5:Rew:2295.0,2267.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.59 2302[5:Rew:2295.0,2270.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.41/0.59 2308[6:Rew:2300.0,2290.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.41/0.59 2312[6:Rew:2296.0,2308.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.59 2313[6:Rew:2312.0,2281.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.41/0.59 2315[6:Rew:2312.0,2295.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.59 2318[6:Rew:2315.0,2313.0] || -> equal(sk_c11,sk_c1)**.
% 0.41/0.59 2319[6:Rew:2318.0,2275.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.41/0.59 2321[6:Rew:2318.0,2300.0] || -> equal(sk_c9,sk_c1)**.
% 0.41/0.59 2323[6:Rew:2318.0,2312.0] || -> equal(sk_c10,sk_c1)**.
% 0.41/0.59 2326[6:Rew:2318.0,2315.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.41/0.59 2337[6:Rew:2326.0,2302.3,2318.0,2302.3,2323.0,2302.3,2321.0,2302.2,2318.0,2302.1,2323.0,2302.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.41/0.59 2338[6:Con:2337.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.41/0.59 2367[6:SpL:2319.0,2338.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.41/0.59 2368[6:Obv:2367.1] || -> .
% 0.41/0.59 2369[6:Spt:2368.0,29.1,2286.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.41/0.59 2370[6:Spt:2368.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.59 2371[6:Rew:2295.0,2369.0,2300.0,2369.0] || equal(sk_c2,sk_c11)** -> .
% 0.41/0.59 2372[5:Rew:2296.0,2279.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.41/0.59 2373[5:Rew:2372.0,28.1,2300.0,28.1] || -> equal(inverse(sk_c7),sk_c6)** equal(sk_c10,sk_c11).
% 0.41/0.59 2375[5:Rew:2372.0,24.1,2300.0,24.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c10,sk_c11).
% 0.41/0.59 2379[5:Rew:2372.0,30.1,2300.0,30.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c10,sk_c11).
% 0.41/0.59 2380[5:Rew:2372.0,27.1,2300.0,27.1,2295.0,27.0] || -> equal(sk_c8,sk_c11)** equal(sk_c10,sk_c11).
% 0.41/0.59 2382[5:Rew:2380.0,2379.0] || -> equal(multiply(sk_c7,sk_c11),sk_c6)** equal(sk_c10,sk_c11).
% 0.41/0.59 2384[5:Rew:2372.0,23.1,2300.0,23.1,2295.0,23.0,2300.0,23.0] || -> equal(sk_c4,sk_c11)** equal(sk_c10,sk_c11).
% 0.41/0.59 2385[5:Rew:2384.0,2375.0] || -> equal(inverse(sk_c11),sk_c10)** equal(sk_c10,sk_c11).
% 0.41/0.59 2389[6:SpR:2370.0,96.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.41/0.59 2415[5:SpR:2372.0,2295.0] || -> equal(sk_c2,sk_c10)**.
% 0.41/0.59 2417[6:Rew:2415.0,2371.0] || equal(sk_c10,sk_c11)** -> .
% 0.41/0.59 2420[6:MRR:2373.1,2417.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.41/0.59 2422[6:MRR:2380.1,2417.0] || -> equal(sk_c8,sk_c11)**.
% 0.41/0.59 2424[6:MRR:2382.1,2417.0] || -> equal(multiply(sk_c7,sk_c11),sk_c6)**.
% 0.41/0.59 2427[6:MRR:2385.1,2417.0] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.41/0.59 2429[6:Rew:2422.0,2370.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.41/0.59 2430[6:Rew:2422.0,2389.0] || -> equal(multiply(sk_c11,multiply(sk_c6,u)),u)**.
% 0.41/0.59 2441[6:SpR:2420.0,96.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.41/0.59 2447[6:SpR:2427.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.41/0.59 2449[6:Rew:2296.0,2447.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.59 2452[6:Rew:2449.0,2430.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.41/0.59 2457[6:Rew:2452.0,2441.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.41/0.59 2460[6:Rew:2457.0,2424.0] || -> equal(sk_c6,sk_c11)**.
% 0.41/0.59 2462[6:Rew:2460.0,2429.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.41/0.60 2464[6:Rew:2427.0,2462.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.60 2465[6:MRR:2464.0,2417.0] || -> .
% 0.41/0.60 2466[5:Spt:2465.0,9.1,2281.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.41/0.60 2467[5:Spt:2465.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.60 2469[5:MRR:6.1,2466.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.60 2471[5:MRR:2.1,2466.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.60 2474[5:MRR:5.1,2466.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.60 2476[5:MRR:1.1,2466.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.60 2500[5:SpR:2474.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.60 2502[5:Rew:2469.0,2500.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.60 2508[5:SpR:2476.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.60 2510[5:Rew:2471.0,2508.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.60 2516[5:SpR:2502.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.60 2518[5:Rew:53.0,2516.0] || -> equal(identity,sk_c11)**.
% 0.41/0.60 2519[5:Rew:2518.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.60 2524[5:Rew:2519.0,2276.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.41/0.60 2525[5:Rew:2519.0,2510.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.60 2537[5:Rew:2525.0,2466.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.41/0.60 2573[5:Rew:2524.0,2537.0] || equal(sk_c11,sk_c11)* -> .
% 0.41/0.60 2574[5:Obv:2573.0] || -> .
% 0.41/0.60 2593[4:Spt:2574.0,39.1,2278.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.41/0.60 2594[4:Spt:2574.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.60 2596[4:MRR:36.1,2593.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.60 2598[4:MRR:32.1,2593.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.60 2601[4:MRR:35.0,2593.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.60 2603[4:MRR:31.0,2593.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.60 2625[4:SpR:2601.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.60 2627[4:Rew:2596.0,2625.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.60 2633[4:SpR:2603.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.60 2635[4:Rew:2598.0,2633.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.60 2641[4:SpR:2627.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.60 2643[4:Rew:53.0,2641.0] || -> equal(identity,sk_c11)**.
% 0.41/0.60 2644[4:Rew:2643.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.60 2645[4:Rew:2643.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.60 2651[4:Rew:2644.0,2270.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11)** equal(multiply(u,sk_c10),sk_c9)** equal(v,sk_c10) -> .
% 0.41/0.60 2656[4:Rew:2645.0,2276.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.41/0.60 2657[4:Rew:2645.0,2635.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.60 2662[4:Rew:2657.0,2267.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.41/0.60 2673[4:Rew:2644.0,2662.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.60 2715[4:Rew:2657.0,2651.3,2644.0,2651.2,2657.0,2651.2,2673.0,2651.2,2657.0,2651.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.41/0.60 2716[4:Con:2715.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.41/0.60 2744[4:SpR:2656.0,2644.0] || -> equal(sk_c11,sk_c1)**.
% 0.41/0.60 2746[4:Rew:2744.0,2275.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.41/0.60 2761[4:Rew:2744.0,2716.0] || equal(inverse(u),sk_c1)** equal(u,sk_c11) -> .
% 0.41/0.60 2763[4:Rew:2744.0,2761.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.41/0.60 2822[4:SpL:2746.0,2763.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.41/0.60 2824[4:Obv:2822.1] || -> .
% 0.41/0.60 2825[3:Spt:2824.0,19.1,2275.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.41/0.60 2826[3:Spt:2824.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.41/0.60 2828[3:MRR:16.1,2825.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.60 2829[3:MRR:14.1,2825.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.41/0.60 2830[3:MRR:12.1,2825.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.60 2833[3:MRR:15.0,2825.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.60 2834[3:MRR:13.0,2825.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.60 2835[3:MRR:11.0,2825.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.60 2857[3:SpR:2833.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.60 2859[3:Rew:2828.0,2857.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.60 2865[3:SpR:2835.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.60 2867[3:Rew:2830.0,2865.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.60 2873[3:SpR:2859.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.60 2875[3:Rew:53.0,2873.0] || -> equal(identity,sk_c11)**.
% 0.41/0.60 2876[3:Rew:2875.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.60 2877[3:Rew:2875.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.60 2881[3:Rew:2876.0,2867.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.60 2886[3:Rew:2881.0,2829.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.41/0.60 2887[3:Rew:2881.0,2267.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.41/0.60 2889[3:Rew:2881.0,2834.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.41/0.60 2893[3:Rew:2881.0,2270.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.41/0.60 2898[3:Rew:2877.0,2887.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.60 2910[3:Rew:2877.0,2889.0,2898.0,2889.0] || -> equal(sk_c4,sk_c11)**.
% 0.41/0.60 2911[3:Rew:2910.0,2886.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.41/0.60 2939[3:Rew:2877.0,2893.3,2881.0,2893.3,2877.0,2893.2,2881.0,2893.2,2898.0,2893.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.41/0.60 2940[3:Con:2939.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.41/0.60 3013[3:SpL:2911.0,2940.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.41/0.60 3015[3:Obv:3013.1] || -> .
% 0.41/0.60 3016[2:Spt:3015.0,48.1,2267.0] || equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.41/0.60 3017[2:Spt:3015.0,48.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.41/0.60 3018[2:MRR:46.1,3016.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.41/0.60 3019[2:MRR:44.1,3016.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.41/0.60 3020[2:MRR:42.1,3016.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.41/0.60 3024[2:MRR:45.1,3016.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.41/0.60 3025[2:MRR:43.1,3016.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.41/0.60 3026[2:MRR:41.1,3016.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.41/0.60 3045[2:SpR:3024.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.41/0.60 3047[2:Rew:3018.0,3045.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.41/0.60 3049[2:SpR:3025.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.41/0.60 3051[2:Rew:3019.0,3049.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.41/0.60 3053[2:SpR:3026.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.41/0.60 3055[2:Rew:3020.0,3053.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.41/0.60 3064[2:SpR:3047.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.41/0.60 3066[2:Rew:53.0,3064.0] || -> equal(identity,sk_c11)**.
% 0.41/0.60 3067[2:Rew:3066.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.41/0.60 3068[2:Rew:3066.0,656.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.41/0.60 3072[2:Rew:3067.0,3055.0] || -> equal(sk_c10,sk_c11)**.
% 0.41/0.60 3078[2:Rew:3072.0,3025.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.41/0.60 3080[2:Rew:3072.0,3016.0] || equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.41/0.60 3084[2:Rew:3072.0,3051.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.41/0.60 3096[2:Rew:3068.0,3078.0] || -> equal(sk_c9,sk_c4)**.
% 0.41/0.60 3097[2:Rew:3067.0,3084.0,3096.0,3084.0] || -> equal(sk_c4,sk_c11)**.
% 0.41/0.60 3099[2:Rew:3097.0,3096.0] || -> equal(sk_c9,sk_c11)**.
% 0.41/0.60 3112[2:Rew:3067.0,3080.0,3099.0,3080.0] || equal(sk_c11,sk_c11)* -> .
% 0.41/0.60 3113[2:Obv:3112.0] || -> .
% 0.41/0.60 % SZS output end Refutation
% 0.41/0.60 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_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_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
% 0.41/0.60
%------------------------------------------------------------------------------