TSTP Solution File: GRP371-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP371-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:47:04 EDT 2022
% Result : Unsatisfiable 0.40s 0.59s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP371-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.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 10:32:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.40/0.59
% 0.40/0.59 SPASS V 3.9
% 0.40/0.59 SPASS beiseite: Proof found.
% 0.40/0.59 % SZS status Theorem
% 0.40/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.59 SPASS derived 2007 clauses, backtracked 486 clauses, performed 11 splits and kept 1024 clauses.
% 0.40/0.59 SPASS allocated 64998 KBytes.
% 0.40/0.59 SPASS spent 0:00:00.25 on the problem.
% 0.40/0.59 0:00:00.04 for the input.
% 0.40/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.59 0:00:00.01 for inferences.
% 0.40/0.59 0:00:00.00 for the backtracking.
% 0.40/0.59 0:00:00.16 for the reduction.
% 0.40/0.59
% 0.40/0.59
% 0.40/0.59 Here is a proof with depth 5, length 308 :
% 0.40/0.59 % SZS output start Refutation
% 0.40/0.59 1[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c11),sk_c10).
% 0.40/0.59 5[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.40/0.59 7[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.40/0.59 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c11),sk_c10).
% 0.40/0.59 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.40/0.59 11[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 21[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c1),sk_c2)**.
% 0.40/0.59 25[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.40/0.59 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.40/0.59 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 41[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 43[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 45[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11).
% 0.40/0.59 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 48[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 51[0:Inp] || equal(inverse(sk_c11),sk_c10) equal(multiply(u,v),sk_c11)** equal(inverse(u),v) equal(multiply(v,sk_c10),sk_c11)** 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)* -> .
% 0.40/0.59 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.40/0.59 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.40/0.59 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.40/0.59 55[0:Con:51.1] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(sk_c11),sk_c10) 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)** -> .
% 0.40/0.59 56[1:Spt:55.0,55.1,55.2,55.6,55.7,55.8] || 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)** -> .
% 0.40/0.59 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) -> .
% 0.40/0.59 58[2:Spt:9.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.40/0.59 63[3:Spt:29.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.40/0.59 65[4:Spt:39.1] || -> equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 68[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 70[5:SpL:68.0,56.3] || equal(inverse(u),sk_c2)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c2) equal(sk_c11,u) equal(multiply(v,sk_c2),sk_c11)** equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.40/0.59 71[5:Rew:65.0,70.5,63.0,70.1] || equal(inverse(u),sk_c2)** equal(sk_c2,u) equal(inverse(v),sk_c2) equal(sk_c11,u) equal(multiply(v,sk_c2),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.40/0.59 72[5:Obv:71.5] || equal(inverse(u),sk_c2)** equal(sk_c2,u) equal(inverse(v),sk_c2) equal(sk_c11,u) equal(multiply(v,sk_c2),sk_c11)** -> .
% 0.40/0.59 76[2:SpR:58.0,53.0] || -> equal(multiply(sk_c10,sk_c11),identity)**.
% 0.40/0.59 77[3:SpR:63.0,53.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.40/0.59 89[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.40/0.59 90[2:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),multiply(identity,u))**.
% 0.40/0.59 91[3:SpR:77.0,54.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.40/0.59 93[2:Rew:52.0,90.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.40/0.59 94[3:Rew:52.0,91.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.40/0.59 95[0:Rew:52.0,89.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.40/0.59 104[5:SpR:68.0,94.0] || -> equal(multiply(sk_c2,sk_c11),sk_c2)**.
% 0.40/0.59 112[0:SpR:95.0,95.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.40/0.59 115[4:SpR:65.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c10)**.
% 0.40/0.59 118[0:SpR:53.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.40/0.59 120[3:SpR:77.0,95.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.40/0.59 121[5:SpR:104.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c11)**.
% 0.40/0.59 129[5:Rew:53.0,121.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 130[5:Rew:129.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 133[5:Rew:129.0,77.0] || -> equal(multiply(sk_c2,sk_c1),sk_c11)**.
% 0.40/0.59 140[5:Rew:129.0,120.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c1)**.
% 0.40/0.59 141[5:Rew:130.0,93.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 151[5:Rew:115.0,140.0] || -> equal(sk_c1,sk_c10)**.
% 0.40/0.59 153[5:Rew:151.0,68.0] || -> equal(multiply(sk_c10,sk_c2),sk_c11)**.
% 0.40/0.59 156[5:Rew:151.0,133.0] || -> equal(multiply(sk_c2,sk_c10),sk_c11)**.
% 0.40/0.59 158[5:Rew:141.0,153.0] || -> equal(sk_c2,sk_c11)**.
% 0.40/0.59 162[5:Rew:158.0,72.0] || equal(inverse(u),sk_c11)** equal(sk_c2,u) equal(inverse(v),sk_c2) equal(sk_c11,u) equal(multiply(v,sk_c2),sk_c11)** -> .
% 0.40/0.59 164[5:Rew:130.0,156.0,158.0,156.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 166[5:Rew:164.0,58.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 177[5:Rew:129.0,118.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.40/0.59 186[5:Rew:112.0,177.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 189[5:Rew:186.0,162.4,158.0,162.4,158.0,162.2,158.0,162.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.40/0.59 190[5:Obv:189.1] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.40/0.59 502[5:SpL:166.0,190.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.40/0.59 505[5:Obv:502.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.40/0.59 507[5:SpL:166.0,505.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.40/0.59 510[5:Obv:507.1] || -> .
% 0.40/0.59 511[5:Spt:510.0,19.1,68.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.40/0.59 512[5:Spt:510.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 517[5:MRR:16.1,511.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 519[5:MRR:12.1,511.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 520[0:Rew:112.0,118.0] || -> equal(multiply(u,identity),u)**.
% 0.40/0.59 524[5:MRR:15.1,511.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 526[5:MRR:11.1,511.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 551[3:SpR:77.0,95.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.40/0.59 553[3:Rew:520.0,551.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.40/0.59 566[2:SpR:76.0,95.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c11)**.
% 0.40/0.59 568[2:Rew:520.0,566.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.40/0.59 590[5:SpR:524.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 592[5:Rew:517.0,590.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 598[5:SpR:526.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 600[5:Rew:519.0,598.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 611[5:SpR:592.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 613[5:Rew:53.0,611.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 616[5:Rew:613.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 620[5:Rew:613.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 627[5:Rew:616.0,600.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 635[5:Rew:627.0,58.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 638[5:Rew:627.0,65.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.40/0.59 659[5:Rew:620.0,638.0] || -> equal(sk_c2,sk_c11)**.
% 0.40/0.59 661[5:Rew:659.0,553.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.40/0.59 662[5:Rew:659.0,511.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.40/0.59 666[5:Rew:635.0,661.0] || -> equal(sk_c1,sk_c11)**.
% 0.40/0.59 699[5:Rew:620.0,662.0,666.0,662.0] || equal(sk_c11,sk_c11)* -> .
% 0.40/0.59 700[5:Obv:699.0] || -> .
% 0.40/0.59 733[4:Spt:700.0,39.1,65.0] || equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.40/0.59 734[4:Spt:700.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 736[4:MRR:36.1,733.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 738[4:MRR:32.1,733.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 741[4:MRR:35.1,733.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 743[4:MRR:31.1,733.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 783[4:SpR:741.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 785[4:Rew:736.0,783.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 791[4:SpR:743.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 793[4:Rew:738.0,791.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 804[4:SpR:785.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 806[4:Rew:53.0,804.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 809[4:Rew:806.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 810[4:Rew:806.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 813[4:Rew:806.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 820[4:Rew:809.0,793.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 826[4:Rew:820.0,568.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 839[4:Rew:820.0,57.4] || 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) -> .
% 0.40/0.59 896[4:Rew:810.0,839.4] || 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) -> .
% 0.40/0.59 931[4:SpR:813.0,95.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.40/0.59 941[4:Rew:810.0,931.0] || -> equal(inverse(inverse(u)),u)**.
% 0.40/0.59 953[4:SpR:941.0,813.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.40/0.59 1403[4:SpL:813.0,896.0] || 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) -> .
% 0.40/0.59 1415[4:Rew:813.0,1403.1,941.0,1403.1,826.0,1403.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.40/0.59 1416[4:Obv:1415.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.40/0.59 1578[4:SpL:953.0,1416.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.40/0.59 1608[4:Obv:1578.1] || equal(inverse(u),sk_c11)** -> .
% 0.40/0.59 1609[4:UnC:1608.0,826.0] || -> .
% 0.40/0.59 1617[3:Spt:1609.0,29.1,63.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.40/0.59 1618[3:Spt:1609.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 1620[3:MRR:26.1,1617.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 1622[3:MRR:22.1,1617.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 1626[3:MRR:25.0,1617.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 1628[3:MRR:21.0,1617.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 1667[3:SpR:1626.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 1669[3:Rew:1620.0,1667.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 1675[3:SpR:1628.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 1677[3:Rew:1622.0,1675.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 1688[3:SpR:1669.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 1690[3:Rew:53.0,1688.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 1692[3:Rew:1690.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 1693[3:Rew:1690.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 1694[3:Rew:1690.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 1702[3:Rew:1692.0,1677.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 1708[3:Rew:1702.0,58.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 1720[3:Rew:1702.0,57.4] || 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) -> .
% 0.40/0.59 1774[3:Rew:1693.0,1720.4] || 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) -> .
% 0.40/0.59 1812[3:SpR:1694.0,95.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.40/0.59 1816[3:Rew:1693.0,1812.0] || -> equal(inverse(inverse(u)),u)**.
% 0.40/0.59 1823[3:SpR:1816.0,1694.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.40/0.59 2220[3:SpL:1694.0,1774.0] || 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) -> .
% 0.40/0.59 2230[3:Rew:1694.0,2220.1,1816.0,2220.1,1708.0,2220.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.40/0.59 2231[3:Obv:2230.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.40/0.59 2469[3:SpL:1823.0,2231.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.40/0.59 2491[3:Obv:2469.1] || equal(inverse(u),sk_c11)** -> .
% 0.40/0.59 2492[3:UnC:2491.0,1708.0] || -> .
% 0.40/0.59 2498[2:Spt:2492.0,9.1,58.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.40/0.59 2499[2:Spt:2492.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 2501[2:MRR:6.1,2498.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2503[2:MRR:2.1,2498.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 2505[2:MRR:7.0,2498.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.40/0.59 2506[2:MRR:5.0,2498.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2508[2:MRR:1.0,2498.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2527[2:SpR:2506.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2529[2:Rew:2501.0,2527.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2535[2:SpR:2508.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2537[2:Rew:2503.0,2535.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2546[2:SpR:2529.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2548[2:Rew:53.0,2546.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2549[2:Rew:2548.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2550[2:Rew:2548.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2555[2:Rew:2549.0,2537.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 2561[2:Rew:2555.0,2498.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.40/0.59 2562[2:Rew:2555.0,2505.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.40/0.59 2573[2:Rew:2550.0,2562.0] || -> equal(sk_c8,sk_c11)**.
% 0.40/0.59 2575[2:Rew:2573.0,2501.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.40/0.59 2577[2:Rew:2573.0,2506.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.40/0.59 2597[2:Rew:2550.0,2577.0] || -> equal(sk_c5,sk_c11)**.
% 0.40/0.59 2598[2:Rew:2597.0,2575.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 2599[2:MRR:2598.0,2561.0] || -> .
% 0.40/0.59 2620[1:Spt:2599.0,55.3,55.4,55.5,55.9,55.10,55.11] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(sk_c11),sk_c10) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.40/0.59 2622[2:Spt:8.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.40/0.59 2623[2:Rew:2622.0,2620.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c10,sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.40/0.59 2625[2:Obv:2623.2] || 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)** -> .
% 0.40/0.59 2627[2:SpR:2622.0,95.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.40/0.59 2629[3:Spt:48.1] || -> equal(multiply(sk_c9,sk_c10),sk_c11)**.
% 0.40/0.59 2631[3:Rew:2629.0,2625.4] || 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) -> .
% 0.40/0.59 2632[3:Obv:2631.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.40/0.59 2634[3:SpR:2629.0,54.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(sk_c11,u))**.
% 0.40/0.59 2635[3:SpR:2629.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c10)**.
% 0.40/0.59 2637[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.40/0.59 2640[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 2642[5:SpR:2640.0,95.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c2)**.
% 0.40/0.59 2644[5:Rew:2637.0,2642.0] || -> equal(multiply(sk_c2,sk_c11),sk_c2)**.
% 0.40/0.59 2650[5:SpR:2644.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c11)**.
% 0.40/0.59 2652[5:Rew:53.0,2650.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2653[5:Rew:2652.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2654[5:Rew:2652.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2655[5:Rew:2652.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 2657[5:Rew:2653.0,2627.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 2658[5:Rew:2653.0,2634.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.40/0.59 2662[5:Rew:2654.0,2635.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.40/0.59 2664[5:Rew:2654.0,2632.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11)** equal(multiply(u,sk_c10),sk_c9)** equal(v,sk_c10) -> .
% 0.40/0.59 2666[5:Rew:2657.0,2658.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.40/0.59 2667[5:Rew:2666.0,2629.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 2668[5:Rew:2667.0,2622.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 2671[5:Rew:2667.0,2662.0] || -> equal(inverse(sk_c9),sk_c11)**.
% 0.40/0.59 2684[5:Rew:2667.0,2664.3,2654.0,2664.2,2667.0,2664.2,2667.0,2664.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c9) equal(v,sk_c11) -> .
% 0.40/0.59 2704[5:SpR:2671.0,2655.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.40/0.59 2706[5:Rew:2653.0,2704.0] || -> equal(sk_c9,sk_c11)**.
% 0.40/0.59 2709[5:Rew:2706.0,2684.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.40/0.59 2712[5:Con:2709.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.40/0.59 2722[5:SpL:2668.0,2712.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.40/0.59 2723[5:Obv:2722.1] || -> .
% 0.40/0.59 2724[5:Spt:2723.0,19.1,2640.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.40/0.59 2725[5:Spt:2723.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 2727[5:MRR:16.1,2724.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2732[5:MRR:15.1,2724.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2760[5:SpR:2732.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2762[5:Rew:2727.0,2760.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2776[5:SpR:2762.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2778[5:Rew:53.0,2776.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2779[5:Rew:2778.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2782[5:Rew:2778.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 2882[5:SpR:2637.0,2782.0] || -> equal(multiply(sk_c2,sk_c1),sk_c11)**.
% 0.40/0.59 2888[5:SpR:2882.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c1)**.
% 0.40/0.59 2890[5:Rew:2779.0,2888.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.40/0.59 2893[5:SpR:2890.0,2782.0] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.40/0.59 2895[5:MRR:2893.0,2724.0] || -> .
% 0.40/0.59 2896[4:Spt:2895.0,29.1,2637.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.40/0.59 2897[4:Spt:2895.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 2899[4:MRR:26.1,2896.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2901[4:MRR:22.1,2896.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 2904[4:MRR:25.0,2896.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2906[4:MRR:21.0,2896.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2930[4:SpR:2904.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2932[4:Rew:2899.0,2930.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2938[4:SpR:2906.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2940[4:Rew:2901.0,2938.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2946[4:SpR:2932.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2948[4:Rew:53.0,2946.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2949[4:Rew:2948.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2950[4:Rew:2948.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2954[4:Rew:2949.0,2940.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 2960[4:Rew:2954.0,2622.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 2962[4:Rew:2954.0,2629.0] || -> equal(multiply(sk_c9,sk_c11),sk_c11)**.
% 0.40/0.59 2968[4:Rew:2954.0,2632.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.40/0.59 2974[4:Rew:2950.0,2962.0] || -> equal(sk_c9,sk_c11)**.
% 0.40/0.59 3015[4:Rew:2950.0,2968.3,2954.0,2968.3,2950.0,2968.2,2954.0,2968.2,2974.0,2968.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) -> .
% 0.40/0.59 3016[4:Con:3015.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.40/0.59 3084[4:SpL:2960.0,3016.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.40/0.59 3086[4:Obv:3084.1] || -> .
% 0.40/0.59 3087[3:Spt:3086.0,48.1,2629.0] || equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.40/0.59 3088[3:Spt:3086.0,48.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.40/0.59 3089[3:MRR:46.1,3087.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 3090[3:MRR:44.1,3087.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 3091[3:MRR:42.1,3087.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 3095[3:MRR:45.1,3087.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 3096[3:MRR:43.1,3087.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 3097[3:MRR:41.1,3087.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 3118[3:SpR:3095.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 3120[3:Rew:3089.0,3118.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 3122[3:SpR:3096.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.40/0.59 3124[3:Rew:3090.0,3122.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.40/0.59 3126[3:SpR:3097.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 3128[3:Rew:3091.0,3126.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 3134[3:SpR:3120.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 3136[3:Rew:53.0,3134.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 3137[3:Rew:3136.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 3138[3:Rew:3136.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 3146[3:Rew:3138.0,3128.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 3153[3:Rew:3146.0,3096.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.40/0.59 3154[3:Rew:3146.0,3087.0] || equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.40/0.59 3157[3:Rew:3146.0,3124.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.40/0.59 3174[3:Rew:3137.0,3153.0] || -> equal(sk_c9,sk_c4)**.
% 0.40/0.59 3175[3:Rew:3138.0,3157.0,3174.0,3157.0] || -> equal(sk_c4,sk_c11)**.
% 0.40/0.59 3177[3:Rew:3175.0,3174.0] || -> equal(sk_c9,sk_c11)**.
% 0.40/0.59 3190[3:Rew:3138.0,3154.0,3177.0,3154.0] || equal(sk_c11,sk_c11)* -> .
% 0.40/0.59 3191[3:Obv:3190.0] || -> .
% 0.40/0.59 3204[2:Spt:3191.0,8.1,2622.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.40/0.59 3205[2:Spt:3191.0,8.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.40/0.59 3206[2:MRR:6.1,3204.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 3208[2:MRR:2.1,3204.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 3211[2:MRR:7.0,3204.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.40/0.59 3212[2:MRR:5.0,3204.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 3214[2:MRR:1.0,3204.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 3233[2:SpR:3212.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 3235[2:Rew:3206.0,3233.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 3241[2:SpR:3214.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 3243[2:Rew:3208.0,3241.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 3249[2:SpR:3235.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 3251[2:Rew:53.0,3249.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 3252[2:Rew:3251.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 3253[2:Rew:3251.0,520.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 3256[2:Rew:3252.0,3243.0] || -> equal(sk_c10,sk_c11)**.
% 0.40/0.59 3262[2:Rew:3256.0,3204.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.40/0.61 3263[2:Rew:3256.0,3211.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.40/0.61 3270[2:Rew:3253.0,3263.0] || -> equal(sk_c8,sk_c11)**.
% 0.40/0.61 3271[2:Rew:3270.0,3206.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.40/0.61 3274[2:Rew:3270.0,3212.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.40/0.61 3294[2:Rew:3253.0,3274.0] || -> equal(sk_c5,sk_c11)**.
% 0.40/0.61 3295[2:Rew:3294.0,3271.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.61 3296[2:MRR:3295.0,3262.0] || -> .
% 0.40/0.61 % SZS output end Refutation
% 0.40/0.61 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_11 prove_this_12 prove_this_15 prove_this_16 prove_this_19 prove_this_21 prove_this_22 prove_this_25 prove_this_26 prove_this_29 prove_this_31 prove_this_32 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_51 left_identity left_inverse associativity
% 0.40/0.61
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