TSTP Solution File: GRP271-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP271-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:37 EDT 2022
% Result : Unsatisfiable 0.21s 0.60s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP271-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 01:07:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.60
% 0.21/0.60 SPASS V 3.9
% 0.21/0.60 SPASS beiseite: Proof found.
% 0.21/0.60 % SZS status Theorem
% 0.21/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.60 SPASS derived 1901 clauses, backtracked 563 clauses, performed 11 splits and kept 1170 clauses.
% 0.21/0.60 SPASS allocated 64815 KBytes.
% 0.21/0.60 SPASS spent 0:00:00.24 on the problem.
% 0.21/0.60 0:00:00.04 for the input.
% 0.21/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.60 0:00:00.01 for inferences.
% 0.21/0.60 0:00:00.01 for the backtracking.
% 0.21/0.60 0:00:00.16 for the reduction.
% 0.21/0.60
% 0.21/0.60
% 0.21/0.60 Here is a proof with depth 5, length 395 :
% 0.21/0.60 % SZS output start Refutation
% 0.21/0.60 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.21/0.60 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.21/0.60 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.21/0.60 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.21/0.60 7[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.21/0.60 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.21/0.60 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.21/0.60 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.21/0.60 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.21/0.60 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.21/0.60 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.21/0.60 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.21/0.60 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.21/0.60 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.21/0.60 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 28[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 33[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 41[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.21/0.60 45[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.21/0.60 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.21/0.60 51[0:Inp] || equal(multiply(u,sk_c11),sk_c10)** equal(inverse(u),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)** equal(multiply(v,sk_c10),sk_c9)** equal(inverse(v),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)* -> .
% 0.21/0.60 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.60 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.60 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.60 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_c11,sk_c9),sk_c10)** -> .
% 0.21/0.60 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)** -> .
% 0.21/0.60 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) -> .
% 0.21/0.60 58[2:Spt:29.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 60[2:SpL:58.0,56.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.21/0.60 61[3:Spt:49.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.21/0.60 63[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.21/0.60 65[5:Spt:39.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 69[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.21/0.60 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)** -> .
% 0.21/0.60 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)** -> .
% 0.21/0.60 76[3:SpR:61.0,53.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.21/0.60 77[4:SpR:63.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.21/0.60 88[4:SpR:77.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.21/0.60 91[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.60 92[3:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.21/0.60 94[4:Rew:52.0,88.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.21/0.60 95[3:Rew:52.0,92.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.21/0.60 96[0:Rew:52.0,91.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.60 100[6:SpR:69.0,94.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 102[6:Rew:100.0,72.5] || 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) -> .
% 0.21/0.60 104[6:Obv:102.5] || 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)** -> .
% 0.21/0.60 111[5:SpR:65.0,95.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.21/0.60 119[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.60 122[2:SpR:58.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.21/0.60 124[4:SpR:94.0,96.0] || -> equal(multiply(inverse(sk_c11),u),multiply(sk_c1,u))**.
% 0.21/0.60 125[6:SpR:100.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.21/0.60 128[0:SpR:53.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.60 129[3:SpR:76.0,96.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.21/0.60 130[5:SpR:111.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.21/0.60 137[6:Rew:53.0,125.0] || -> equal(identity,sk_c10)**.
% 0.21/0.60 138[6:Rew:137.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.21/0.60 141[6:Rew:137.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.21/0.60 148[6:Rew:138.0,111.0] || -> equal(sk_c9,sk_c10)**.
% 0.21/0.60 156[6:Rew:148.0,58.0] || -> equal(multiply(sk_c11,sk_c10),sk_c10)**.
% 0.21/0.60 165[6:Rew:100.0,156.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 172[6:Rew:165.0,104.3] || 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)** -> .
% 0.21/0.60 173[6:Rew:165.0,137.0] || -> equal(identity,sk_c11)**.
% 0.21/0.60 174[6:Rew:165.0,138.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 178[6:Rew:165.0,141.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.21/0.60 181[6:Rew:174.0,178.0] || -> equal(sk_c11,sk_c1)**.
% 0.21/0.60 182[6:Rew:181.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.60 184[6:Rew:181.0,173.0] || -> equal(identity,sk_c1)**.
% 0.21/0.60 197[6:Rew:184.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.21/0.60 206[6:Rew:119.0,197.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.60 208[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)** -> .
% 0.21/0.60 209[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) -> .
% 0.21/0.60 515[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) -> .
% 0.21/0.60 518[6:Obv:515.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.60 520[6:SpL:182.0,518.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.60 523[6:Obv:520.1] || -> .
% 0.21/0.60 524[6:Spt:523.0,9.1,69.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.21/0.60 525[6:Spt:523.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 526[5:Rew:53.0,130.0] || -> equal(identity,sk_c9)**.
% 0.21/0.60 527[5:Rew:526.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c9)**.
% 0.21/0.60 534[5:Rew:526.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.21/0.60 536[4:Rew:124.0,122.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.21/0.60 539[6:MRR:6.1,524.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 548[5:Rew:119.0,534.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.60 549[5:Rew:548.0,58.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 552[6:Rew:549.0,524.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.21/0.60 553[5:Rew:549.0,536.0] || -> equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.21/0.60 557[6:Rew:553.0,552.0] || equal(sk_c9,sk_c11)** -> .
% 0.21/0.60 565[5:Rew:553.0,7.1,549.0,7.1,549.0,7.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)** equal(sk_c9,sk_c11).
% 0.21/0.60 566[6:MRR:565.1,557.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.21/0.60 567[5:Rew:553.0,5.1,549.0,5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c9,sk_c11).
% 0.21/0.60 568[6:MRR:567.1,557.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 615[5:SpR:527.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.21/0.60 617[5:Rew:548.0,615.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.21/0.60 644[6:SpR:566.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c11)**.
% 0.21/0.60 647[6:SpR:568.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 649[6:Rew:566.0,647.0,539.0,647.0] || -> equal(sk_c8,sk_c11)**.
% 0.21/0.60 659[6:Rew:649.0,644.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.21/0.60 662[6:Rew:553.0,659.0,617.0,659.0] || -> equal(sk_c9,sk_c11)**.
% 0.21/0.60 663[6:MRR:662.0,557.0] || -> .
% 0.21/0.60 666[5:Spt:663.0,39.1,65.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.21/0.60 667[5:Spt:663.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 668[0:Rew:119.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.60 670[3:Rew:668.0,129.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.21/0.60 674[5:MRR:36.1,666.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 676[5:MRR:32.1,666.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.21/0.60 680[5:MRR:35.1,666.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 682[5:MRR:31.1,666.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 731[5:SpR:680.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 733[5:Rew:674.0,731.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.21/0.60 739[5:SpR:682.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.21/0.60 741[5:Rew:676.0,739.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 750[5:SpR:733.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.21/0.60 752[5:Rew:53.0,750.0] || -> equal(identity,sk_c11)**.
% 0.21/0.60 754[5:Rew:752.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.21/0.60 755[5:Rew:752.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 759[5:Rew:752.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.21/0.60 763[5:Rew:755.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.21/0.60 765[5:Rew:755.0,741.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 770[5:Rew:755.0,754.0] || -> equal(sk_c11,sk_c1)**.
% 0.21/0.60 775[5:Rew:763.0,666.0] || equal(multiply(sk_c2,sk_c10),sk_c10)** -> .
% 0.21/0.60 781[5:Rew:765.0,670.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.21/0.60 797[5:Rew:770.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.60 804[5:Rew:770.0,765.0] || -> equal(sk_c10,sk_c1)**.
% 0.21/0.60 807[5:Rew:770.0,781.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.21/0.60 809[5:Rew:807.0,797.0] || -> equal(sk_c2,sk_c1)**.
% 0.21/0.60 812[5:Rew:770.0,759.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.60 840[5:Rew:812.0,775.0,809.0,775.0,804.0,775.0] || equal(sk_c1,sk_c1)* -> .
% 0.21/0.60 841[5:Obv:840.0] || -> .
% 0.21/0.60 871[4:Spt:841.0,19.1,63.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.21/0.60 872[4:Spt:841.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 874[4:MRR:16.1,871.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 875[4:MRR:14.1,871.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.21/0.60 876[4:MRR:12.1,871.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.21/0.60 879[4:MRR:15.0,871.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 880[4:MRR:13.0,871.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.21/0.60 881[4:MRR:11.0,871.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 912[4:SpR:879.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 914[4:Rew:874.0,912.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.21/0.60 920[4:SpR:881.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.21/0.60 922[4:Rew:876.0,920.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 928[4:SpR:914.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.21/0.60 930[4:Rew:53.0,928.0] || -> equal(identity,sk_c11)**.
% 0.21/0.60 932[4:Rew:930.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 933[4:Rew:930.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.21/0.60 934[4:Rew:930.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.21/0.60 939[4:Rew:932.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.21/0.60 940[4:Rew:932.0,922.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 946[4:Rew:939.0,880.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.21/0.60 951[4:Rew:940.0,670.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.21/0.60 953[4:Rew:940.0,875.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.21/0.60 960[4:Rew:940.0,57.4] || 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) -> .
% 0.21/0.60 967[4:Rew:933.0,946.0,940.0,946.0] || -> equal(sk_c4,sk_c11)**.
% 0.21/0.60 968[4:Rew:967.0,953.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.21/0.60 969[4:Rew:951.0,968.0] || -> equal(sk_c2,sk_c11)**.
% 0.21/0.60 970[4:Rew:969.0,951.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.21/0.60 1018[4:Rew:933.0,960.4] || 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) -> .
% 0.21/0.60 1041[4:SpR:934.0,96.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.21/0.60 1048[4:Rew:933.0,1041.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.60 1063[4:SpR:1048.0,934.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.21/0.60 1389[4:SpL:934.0,1018.0] || 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) -> .
% 0.21/0.60 1398[4:Rew:934.0,1389.1,1048.0,1389.1,970.0,1389.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.21/0.60 1399[4:Obv:1398.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.21/0.60 1706[4:SpL:1063.0,1399.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.21/0.60 1728[4:Obv:1706.1] || equal(inverse(u),sk_c11)** -> .
% 0.21/0.60 1729[4:UnC:1728.0,1048.0] || -> .
% 0.21/0.60 1735[3:Spt:1729.0,49.1,61.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.21/0.60 1736[3:Spt:1729.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 1738[3:MRR:46.1,1735.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 1740[3:MRR:42.1,1735.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.21/0.60 1743[3:MRR:45.0,1735.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 1745[3:MRR:41.0,1735.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 1767[3:SpR:1743.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 1769[3:Rew:1738.0,1767.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.21/0.60 1775[3:SpR:1745.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.21/0.60 1777[3:Rew:1740.0,1775.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 1783[3:SpR:1769.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.21/0.60 1785[3:Rew:53.0,1783.0] || -> equal(identity,sk_c11)**.
% 0.21/0.60 1786[3:Rew:1785.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.21/0.60 1787[3:Rew:1785.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 1792[3:Rew:1786.0,1745.0] || -> equal(sk_c3,sk_c10)**.
% 0.21/0.60 1794[3:Rew:1792.0,1740.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.21/0.60 1797[3:Rew:1787.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.21/0.60 1798[3:Rew:1787.0,1777.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 1805[3:Rew:1797.0,60.0] || equal(inverse(u),sk_c10)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.21/0.60 1817[3:Rew:1798.0,1794.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.21/0.60 1818[3:Rew:1798.0,1797.0] || -> equal(sk_c9,sk_c11)**.
% 0.21/0.60 1861[3:Rew:1818.0,1805.5,1786.0,1805.5,1798.0,1805.5,1786.0,1805.4,1818.0,1805.4,1798.0,1805.3,1818.0,1805.2,1817.0,1805.1,1798.0,1805.0] || 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) -> .
% 0.21/0.60 1862[3:Obv:1861.5] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.21/0.60 2042[3:SpL:1817.0,1862.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.21/0.60 2044[3:Obv:2042.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.21/0.60 2046[3:SpL:1817.0,2044.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.21/0.60 2048[3:Obv:2046.1] || -> .
% 0.21/0.60 2049[2:Spt:2048.0,29.1,58.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.21/0.60 2050[2:Spt:2048.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 2052[2:MRR:26.1,2049.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 2053[2:MRR:24.1,2049.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.21/0.60 2054[2:MRR:22.1,2049.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.21/0.60 2057[2:MRR:25.1,2049.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 2058[2:MRR:23.1,2049.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.21/0.60 2059[2:MRR:21.1,2049.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 2078[2:SpR:2057.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 2080[2:Rew:2052.0,2078.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.21/0.60 2082[2:SpR:2058.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.21/0.60 2084[2:Rew:2053.0,2082.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.21/0.60 2086[2:SpR:2059.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.21/0.60 2088[2:Rew:2054.0,2086.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 2094[2:SpR:2080.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.21/0.60 2096[2:Rew:53.0,2094.0] || -> equal(identity,sk_c11)**.
% 0.21/0.60 2097[2:Rew:2096.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 2098[2:Rew:2096.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.21/0.60 2103[2:Rew:2097.0,2088.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 2105[2:Rew:2097.0,2049.0] || equal(sk_c9,sk_c10)** -> .
% 0.21/0.60 2111[2:Rew:2103.0,2058.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.21/0.60 2120[2:Rew:2103.0,2084.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.21/0.60 2121[2:Rew:2103.0,2105.0] || equal(sk_c9,sk_c11)** -> .
% 0.21/0.60 2133[2:Rew:2098.0,2111.0] || -> equal(sk_c9,sk_c4)**.
% 0.21/0.60 2134[2:Rew:2133.0,2121.0] || equal(sk_c4,sk_c11)** -> .
% 0.21/0.60 2135[2:Rew:2097.0,2120.0,2133.0,2120.0] || -> equal(sk_c4,sk_c11)**.
% 0.21/0.60 2136[2:MRR:2135.0,2134.0] || -> .
% 0.21/0.60 2167[1:Spt:2136.0,55.3,55.4,55.8,55.9,55.10] || 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_c11,sk_c9),sk_c10)** -> .
% 0.21/0.60 2169[2:Spt:28.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.21/0.60 2170[2:Rew:2169.0,2167.4] || 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) -> .
% 0.21/0.60 2172[2:Obv:2170.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.21/0.60 2174[2:SpR:2169.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.21/0.60 2175[2:SpR:2169.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.21/0.60 2177[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.21/0.60 2178[3:SpR:2177.0,96.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.21/0.60 2180[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.21/0.60 2181[4:SpR:2180.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.21/0.60 2183[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.21/0.60 2184[5:SpR:2183.0,54.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),multiply(sk_c10,u))**.
% 0.21/0.60 2185[5:SpR:2183.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.21/0.60 2187[5:Rew:2177.0,2185.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 2188[6:Spt:39.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.21/0.60 2190[6:SpR:2188.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c10)**.
% 0.21/0.60 2192[6:Rew:2180.0,2190.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.21/0.60 2194[5:SpR:2187.0,96.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.21/0.60 2196[5:Rew:53.0,2194.0] || -> equal(identity,sk_c10)**.
% 0.21/0.60 2197[5:Rew:2196.0,668.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.21/0.60 2198[5:Rew:2196.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.21/0.60 2202[5:Rew:2197.0,2175.0] || -> equal(inverse(sk_c11),sk_c9)**.
% 0.21/0.60 2204[5:Rew:2197.0,2172.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.21/0.60 2208[6:Rew:2198.0,2192.0] || -> equal(sk_c9,sk_c10)**.
% 0.21/0.60 2209[5:Rew:2198.0,2174.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),u)**.
% 0.21/0.60 2210[5:Rew:2198.0,2184.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),u)**.
% 0.21/0.60 2211[6:Rew:2208.0,2169.0] || -> equal(multiply(sk_c11,sk_c10),sk_c10)**.
% 0.21/0.60 2215[6:Rew:2197.0,2211.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 2216[6:Rew:2215.0,2183.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.21/0.60 2218[6:Rew:2215.0,2197.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.21/0.60 2220[6:Rew:2215.0,2208.0] || -> equal(sk_c9,sk_c11)**.
% 0.21/0.60 2224[6:Rew:2218.0,2216.0] || -> equal(sk_c11,sk_c1)**.
% 0.21/0.60 2225[6:Rew:2224.0,2177.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.60 2227[6:Rew:2224.0,2215.0] || -> equal(sk_c10,sk_c1)**.
% 0.21/0.60 2229[6:Rew:2224.0,2220.0] || -> equal(sk_c9,sk_c1)**.
% 0.21/0.60 2232[6:Rew:2224.0,2218.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.60 2242[6:Rew:2232.0,2204.3,2224.0,2204.3,2227.0,2204.3,2229.0,2204.2,2224.0,2204.1,2227.0,2204.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.21/0.60 2243[6:Con:2242.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.60 2272[6:SpL:2225.0,2243.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.60 2273[6:Obv:2272.1] || -> .
% 0.21/0.60 2274[6:Spt:2273.0,39.1,2188.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.21/0.60 2275[6:Spt:2273.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 2276[6:Rew:2197.0,2274.0] || equal(sk_c2,sk_c9)** -> .
% 0.21/0.60 2277[5:Rew:2198.0,2181.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.21/0.60 2280[5:Rew:2277.0,34.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c9,sk_c10).
% 0.21/0.60 2288[5:Rew:2277.0,33.1,2197.0,33.0] || -> equal(sk_c9,sk_c4)** equal(sk_c9,sk_c10).
% 0.21/0.60 2322[5:SpR:2277.0,2197.0] || -> equal(sk_c2,sk_c10)**.
% 0.21/0.60 2324[6:Rew:2322.0,2276.0] || equal(sk_c9,sk_c10)** -> .
% 0.21/0.60 2325[5:Rew:2322.0,2180.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.21/0.60 2328[6:MRR:2280.1,2324.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.21/0.60 2334[6:MRR:2288.1,2324.0] || -> equal(sk_c9,sk_c4)**.
% 0.21/0.60 2338[6:Rew:2334.0,2202.0] || -> equal(inverse(sk_c11),sk_c4)**.
% 0.21/0.60 2340[6:Rew:2334.0,2209.0] || -> equal(multiply(sk_c11,multiply(sk_c4,u)),u)**.
% 0.21/0.60 2343[6:Rew:2334.0,2324.0] || equal(sk_c4,sk_c10)** -> .
% 0.21/0.60 2356[6:SpR:2328.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.21/0.60 2358[6:Rew:2198.0,2356.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.21/0.60 2359[6:Rew:2358.0,2340.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.21/0.60 2361[6:Rew:2359.0,2210.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.60 2366[6:Rew:2361.0,2183.0] || -> equal(sk_c10,sk_c11)**.
% 0.21/0.60 2371[6:Rew:2366.0,2325.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.21/0.60 2374[6:Rew:2366.0,2343.0] || equal(sk_c4,sk_c11)** -> .
% 0.21/0.60 2377[6:Rew:2338.0,2371.0] || -> equal(sk_c4,sk_c11)**.
% 0.21/0.60 2382[6:Rew:2377.0,2374.0] || equal(sk_c11,sk_c11)* -> .
% 0.21/0.60 2383[6:Obv:2382.0] || -> .
% 0.21/0.60 2400[5:Spt:2383.0,9.1,2183.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.21/0.60 2401[5:Spt:2383.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.60 2403[5:MRR:6.1,2400.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.60 2405[5:MRR:2.1,2400.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.21/0.60 2408[5:MRR:5.1,2400.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.21/0.60 2410[5:MRR:1.1,2400.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.21/0.60 2434[5:SpR:2408.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.21/0.60 2436[5:Rew:2403.0,2434.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.21/0.60 2442[5:SpR:2410.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.21/0.60 2444[5:Rew:2405.0,2442.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.21/0.60 2450[5:SpR:2436.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 2452[5:Rew:53.0,2450.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 2453[5:Rew:2452.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 2458[5:Rew:2453.0,2444.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 2464[5:Rew:2453.0,2178.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.45/0.61 2475[5:Rew:2458.0,2400.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.45/0.61 2507[5:Rew:2464.0,2475.0] || equal(sk_c11,sk_c11)* -> .
% 0.45/0.61 2508[5:Obv:2507.0] || -> .
% 0.45/0.61 2527[4:Spt:2508.0,49.1,2180.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.45/0.61 2528[4:Spt:2508.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.45/0.61 2530[4:MRR:46.1,2527.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.45/0.61 2532[4:MRR:42.1,2527.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.45/0.61 2535[4:MRR:45.0,2527.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.45/0.61 2537[4:MRR:41.0,2527.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.45/0.61 2559[4:SpR:2535.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.45/0.61 2561[4:Rew:2530.0,2559.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.45/0.61 2567[4:SpR:2537.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.45/0.61 2569[4:Rew:2532.0,2567.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.45/0.61 2578[4:SpR:2561.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 2580[4:Rew:53.0,2578.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 2581[4:Rew:2580.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 2582[4:Rew:2580.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.45/0.61 2584[4:Rew:2580.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.45/0.61 2585[4:Rew:2581.0,2169.0] || -> equal(sk_c9,sk_c10)**.
% 0.45/0.61 2587[4:Rew:2581.0,2569.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 2596[4:Rew:2585.0,2172.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.45/0.61 2646[4:Rew:2582.0,2596.3,2587.0,2596.3,2582.0,2596.2,2587.0,2596.2,2587.0,2596.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.45/0.61 2647[4:Con:2646.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.45/0.61 2685[4:SpR:2177.0,2584.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.45/0.61 2687[4:Rew:2581.0,2685.0] || -> equal(sk_c11,sk_c1)**.
% 0.45/0.61 2688[4:Rew:2687.0,2177.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.45/0.61 2702[4:Rew:2687.0,2647.0] || equal(inverse(u),sk_c1)** equal(u,sk_c11) -> .
% 0.45/0.61 2706[4:Rew:2687.0,2702.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.45/0.61 2771[4:SpL:2688.0,2706.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.45/0.61 2773[4:Obv:2771.1] || -> .
% 0.45/0.61 2774[3:Spt:2773.0,19.1,2177.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.45/0.61 2775[3:Spt:2773.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.45/0.61 2777[3:MRR:16.1,2774.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.45/0.61 2778[3:MRR:14.1,2774.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.45/0.61 2779[3:MRR:12.1,2774.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.45/0.61 2782[3:MRR:15.0,2774.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.45/0.61 2783[3:MRR:13.0,2774.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.45/0.61 2784[3:MRR:11.0,2774.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.45/0.61 2806[3:SpR:2782.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.45/0.61 2808[3:Rew:2777.0,2806.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.45/0.61 2814[3:SpR:2784.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.45/0.61 2816[3:Rew:2779.0,2814.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.45/0.61 2822[3:SpR:2808.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 2824[3:Rew:53.0,2822.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 2825[3:Rew:2824.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 2826[3:Rew:2824.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.45/0.61 2829[3:Rew:2825.0,2169.0] || -> equal(sk_c9,sk_c10)**.
% 0.45/0.61 2831[3:Rew:2825.0,2816.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 2836[3:Rew:2829.0,2783.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.45/0.61 2839[3:Rew:2829.0,2172.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.45/0.61 2842[3:Rew:2831.0,2778.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.45/0.61 2848[3:Rew:2826.0,2836.0,2831.0,2836.0] || -> equal(sk_c4,sk_c11)**.
% 0.45/0.61 2849[3:Rew:2848.0,2842.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.45/0.61 2888[3:Rew:2826.0,2839.3,2831.0,2839.3,2826.0,2839.2,2831.0,2839.2,2831.0,2839.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.45/0.61 2889[3:Con:2888.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.45/0.61 2962[3:SpL:2849.0,2889.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.45/0.61 2964[3:Obv:2962.1] || -> .
% 0.45/0.61 2965[2:Spt:2964.0,28.1,2169.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.45/0.61 2966[2:Spt:2964.0,28.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.45/0.61 2967[2:MRR:26.1,2965.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.45/0.61 2968[2:MRR:24.1,2965.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.45/0.61 2969[2:MRR:22.1,2965.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.45/0.61 2973[2:MRR:25.1,2965.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.45/0.61 2974[2:MRR:23.1,2965.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.45/0.61 2975[2:MRR:21.1,2965.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.45/0.61 2994[2:SpR:2973.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.45/0.61 2996[2:Rew:2967.0,2994.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.45/0.61 2998[2:SpR:2974.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.45/0.61 3000[2:Rew:2968.0,2998.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.45/0.61 3002[2:SpR:2975.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.45/0.61 3004[2:Rew:2969.0,3002.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.45/0.61 3013[2:SpR:2996.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 3015[2:Rew:53.0,3013.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 3016[2:Rew:3015.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 3017[2:Rew:3015.0,668.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.45/0.61 3020[2:Rew:3016.0,3004.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 3022[2:Rew:3016.0,2965.0] || equal(sk_c9,sk_c10)** -> .
% 0.45/0.61 3028[2:Rew:3020.0,2974.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.45/0.61 3033[2:Rew:3020.0,3000.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.45/0.61 3034[2:Rew:3020.0,3022.0] || equal(sk_c9,sk_c11)** -> .
% 0.45/0.61 3046[2:Rew:3017.0,3028.0] || -> equal(sk_c9,sk_c4)**.
% 0.45/0.61 3047[2:Rew:3046.0,3034.0] || equal(sk_c4,sk_c11)** -> .
% 0.45/0.61 3048[2:Rew:3016.0,3033.0,3046.0,3033.0] || -> equal(sk_c4,sk_c11)**.
% 0.45/0.61 3049[2:MRR:3048.0,3047.0] || -> .
% 0.45/0.61 % SZS output end Refutation
% 0.45/0.61 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_28 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_45 prove_this_46 prove_this_49 prove_this_51 left_identity left_inverse associativity
% 0.45/0.61
%------------------------------------------------------------------------------