TSTP Solution File: GRP380-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP380-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:47:06 EDT 2022
% Result : Unsatisfiable 0.43s 0.60s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP380-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 17:24:09 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.43/0.60
% 0.43/0.60 SPASS V 3.9
% 0.43/0.60 SPASS beiseite: Proof found.
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.60 SPASS derived 1817 clauses, backtracked 571 clauses, performed 11 splits and kept 1163 clauses.
% 0.43/0.60 SPASS allocated 64572 KBytes.
% 0.43/0.60 SPASS spent 0:00:00.22 on the problem.
% 0.43/0.60 0:00:00.04 for the input.
% 0.43/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.43/0.60 0:00:00.01 for inferences.
% 0.43/0.60 0:00:00.00 for the backtracking.
% 0.43/0.60 0:00:00.14 for the reduction.
% 0.43/0.60
% 0.43/0.60
% 0.43/0.60 Here is a proof with depth 5, length 429 :
% 0.43/0.60 % SZS output start Refutation
% 0.43/0.60 1[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.43/0.60 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c11),sk_c10).
% 0.43/0.60 5[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.43/0.60 7[0:Inp] || -> equal(inverse(sk_c11),sk_c10) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c11),sk_c10).
% 0.43/0.60 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c11),sk_c10).
% 0.43/0.60 11[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11).
% 0.43/0.60 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 13[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c9),sk_c11).
% 0.43/0.60 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c10,sk_c9),sk_c11).
% 0.43/0.60 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 17[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c9),sk_c11).
% 0.43/0.60 18[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 20[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c10,sk_c9),sk_c11).
% 0.43/0.60 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 27[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 33[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 35[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 37[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 41[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 43[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 45[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 47[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 51[0:Inp] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),z) equal(inverse(x1),sk_c10) equal(inverse(x2),sk_c11) equal(inverse(sk_c11),sk_c10) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(y,z),sk_c10)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(x1,sk_c10),sk_c9)** equal(multiply(x2,sk_c11),sk_c10)** equal(multiply(z,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.43/0.60 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.43/0.60 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.43/0.60 55[1:Spt:51.0,51.1,51.2,51.7,51.8,51.10] || 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)** -> .
% 0.43/0.60 57[2:Spt:9.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.43/0.60 59[3:Spt:19.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 61[3:SpL:59.0,55.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.43/0.60 62[4:Spt:39.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 64[5:Spt:49.1] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 67[6:Spt:29.1] || -> equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 69[6:SpL:67.0,55.3] || equal(inverse(u),sk_c2)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c2) equal(sk_c10,u) equal(multiply(v,sk_c2),sk_c11)** equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.43/0.60 70[6:Rew:62.0,69.1] || equal(inverse(u),sk_c2)** equal(sk_c2,u) equal(inverse(v),sk_c2) equal(sk_c10,u) equal(multiply(v,sk_c2),sk_c11)** equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.43/0.60 74[2:SpR:57.0,53.0] || -> equal(multiply(sk_c10,sk_c11),identity)**.
% 0.43/0.60 75[4:SpR:62.0,53.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.43/0.60 87[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.43/0.60 88[2:SpR:74.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),multiply(identity,u))**.
% 0.43/0.60 89[4:SpR:75.0,54.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.43/0.60 91[2:Rew:52.0,88.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.43/0.60 92[4:Rew:52.0,89.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.43/0.60 93[0:Rew:52.0,87.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.43/0.60 102[6:SpR:67.0,92.0] || -> equal(multiply(sk_c2,sk_c10),sk_c2)**.
% 0.43/0.60 104[6:Rew:102.0,70.5] || equal(inverse(u),sk_c2)** equal(sk_c2,u) equal(inverse(v),sk_c2) equal(sk_c10,u) equal(multiply(v,sk_c2),sk_c11)** equal(sk_c2,sk_c11) -> .
% 0.43/0.60 111[0:SpR:93.0,93.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.43/0.60 113[3:SpR:59.0,93.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c9)**.
% 0.43/0.60 117[0:SpR:53.0,93.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.43/0.60 120[6:SpR:102.0,93.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c10)**.
% 0.43/0.60 121[2:SpR:91.0,93.0] || -> equal(multiply(inverse(sk_c10),u),multiply(sk_c11,u))**.
% 0.43/0.60 128[6:Rew:53.0,120.0] || -> equal(identity,sk_c10)**.
% 0.43/0.60 129[6:Rew:128.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.43/0.60 131[6:Rew:128.0,74.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.43/0.60 141[6:Rew:129.0,59.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 147[6:Rew:141.0,64.0] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 152[6:Rew:129.0,131.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 154[6:Rew:152.0,57.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 156[6:Rew:152.0,102.0] || -> equal(multiply(sk_c2,sk_c11),sk_c2)**.
% 0.43/0.60 161[6:Rew:152.0,104.3] || 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_c2,sk_c11) -> .
% 0.43/0.60 162[6:Rew:152.0,128.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 165[6:Rew:152.0,147.0] || -> equal(multiply(sk_c2,sk_c11),sk_c11)**.
% 0.43/0.60 166[6:Rew:165.0,156.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 180[6:Rew:162.0,117.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.43/0.60 189[6:Rew:111.0,180.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 191[6:Rew:166.0,161.5,189.0,161.4,166.0,161.4,166.0,161.2,166.0,161.1,166.0,161.0] || 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) -> .
% 0.43/0.60 192[6:Obv:191.5] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 548[6:SpL:154.0,192.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 552[6:Obv:548.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 554[6:SpL:154.0,552.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 558[6:Obv:554.1] || -> .
% 0.43/0.60 559[6:Spt:558.0,29.1,67.0] || equal(multiply(sk_c1,sk_c2),sk_c10)** -> .
% 0.43/0.60 560[6:Spt:558.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 561[3:Rew:121.0,113.0] || -> equal(multiply(sk_c11,sk_c11),sk_c9)**.
% 0.43/0.60 566[6:MRR:26.1,559.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 567[6:MRR:24.1,559.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 569[0:Rew:111.0,117.0] || -> equal(multiply(u,identity),u)**.
% 0.43/0.60 572[6:MRR:27.1,559.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 573[6:MRR:25.1,559.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 574[6:MRR:23.1,559.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 601[4:SpR:75.0,93.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.43/0.60 603[4:Rew:569.0,601.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.43/0.60 616[2:SpR:74.0,93.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c11)**.
% 0.43/0.60 618[2:Rew:569.0,616.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.43/0.60 622[3:Rew:618.0,61.1] || equal(inverse(u),sk_c9)** equal(sk_c11,u) equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.43/0.60 624[3:Obv:622.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.43/0.60 647[6:SpR:573.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 649[6:Rew:566.0,647.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 651[6:SpR:574.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 653[6:Rew:59.0,651.0,567.0,651.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 654[6:Rew:653.0,57.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 656[6:Rew:653.0,74.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.43/0.60 659[6:Rew:653.0,64.0] || -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.43/0.60 660[6:Rew:653.0,572.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 663[6:Rew:653.0,559.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.43/0.60 684[6:Rew:561.0,656.0] || -> equal(identity,sk_c9)**.
% 0.43/0.60 689[6:Rew:684.0,569.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.43/0.60 691[6:Rew:649.0,660.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 701[6:Rew:691.0,649.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 703[6:Rew:689.0,659.0] || -> equal(sk_c2,sk_c11)**.
% 0.43/0.60 705[6:Rew:703.0,603.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.43/0.60 709[6:Rew:654.0,705.0] || -> equal(sk_c1,sk_c11)**.
% 0.43/0.60 712[6:Rew:561.0,701.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 717[6:Rew:712.0,689.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 737[6:Rew:717.0,663.0,709.0,663.0,703.0,663.0] || equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 738[6:Obv:737.0] || -> .
% 0.43/0.60 774[5:Spt:738.0,49.1,64.0] || equal(multiply(sk_c2,sk_c9),sk_c10)** -> .
% 0.43/0.60 775[5:Spt:738.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 777[5:MRR:46.1,774.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 778[5:MRR:44.1,774.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 781[5:MRR:47.1,774.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 782[5:MRR:45.1,774.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 783[5:MRR:43.1,774.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 830[5:SpR:782.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 832[5:Rew:777.0,830.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 834[5:SpR:783.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 836[5:Rew:59.0,834.0,778.0,834.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 837[5:Rew:836.0,618.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 841[5:Rew:836.0,74.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.43/0.60 842[5:Rew:836.0,781.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 850[5:Rew:836.0,624.4] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.43/0.60 863[5:Rew:561.0,841.0] || -> equal(identity,sk_c9)**.
% 0.43/0.60 865[5:Rew:863.0,569.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.43/0.60 869[5:Rew:832.0,842.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 879[5:Rew:869.0,832.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 881[5:Rew:561.0,879.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 886[5:Rew:881.0,865.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 921[5:Rew:881.0,850.4,886.0,850.4,886.0,850.3,881.0,850.3,881.0,850.1,881.0,850.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.43/0.60 922[5:Obv:921.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1322[5:SpL:837.0,922.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 1326[5:Obv:1322.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 1396[5:SpL:837.0,1326.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 1400[5:Obv:1396.1] || -> .
% 0.43/0.60 1401[4:Spt:1400.0,39.1,62.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.43/0.60 1402[4:Spt:1400.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 1404[4:MRR:36.1,1401.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 1405[4:MRR:34.1,1401.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 1409[4:MRR:37.0,1401.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 1410[4:MRR:35.0,1401.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 1411[4:MRR:33.0,1401.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 1456[4:SpR:1410.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 1458[4:Rew:1404.0,1456.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 1460[4:SpR:1411.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 1462[4:Rew:59.0,1460.0,1405.0,1460.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1463[4:Rew:1462.0,57.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 1466[4:Rew:1462.0,74.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.43/0.60 1468[4:Rew:1462.0,1409.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 1475[4:Rew:1462.0,624.4] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c11,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c11),sk_c11)** -> .
% 0.43/0.60 1486[4:Rew:561.0,1466.0] || -> equal(identity,sk_c9)**.
% 0.43/0.60 1488[4:Rew:1486.0,569.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.43/0.60 1491[4:Rew:1458.0,1468.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 1501[4:Rew:1491.0,1458.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 1503[4:Rew:561.0,1501.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 1508[4:Rew:1503.0,1488.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1541[4:Rew:1503.0,1475.4,1508.0,1475.4,1508.0,1475.3,1503.0,1475.3,1503.0,1475.1,1503.0,1475.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.43/0.60 1542[4:Obv:1541.4] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.43/0.60 1784[4:SpL:1463.0,1542.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 1787[4:Obv:1784.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 1789[4:SpL:1463.0,1787.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 1792[4:Obv:1789.1] || -> .
% 0.43/0.60 1793[3:Spt:1792.0,19.1,59.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 1794[3:Spt:1792.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 1795[3:MRR:18.1,1793.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.43/0.60 1796[3:MRR:16.1,1793.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 1797[3:MRR:14.1,1793.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 1798[3:MRR:12.1,1793.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 1799[3:MRR:20.1,1793.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.43/0.60 1800[3:MRR:17.1,1793.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 1801[3:MRR:15.1,1793.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 1802[3:MRR:13.1,1793.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 1803[3:MRR:11.1,1793.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.43/0.60 1812[3:SpR:1796.0,93.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.43/0.60 1816[3:SpR:1798.0,93.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.43/0.60 1824[3:SpR:1799.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.43/0.60 1826[3:Rew:1795.0,1824.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.43/0.60 1827[3:SpR:1800.0,54.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),multiply(sk_c11,u))**.
% 0.43/0.60 1828[3:SpR:1800.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c10)**.
% 0.43/0.60 1831[3:SpR:1801.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 1833[3:Rew:1796.0,1831.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 1835[3:SpR:1802.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 1837[3:Rew:1797.0,1835.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.43/0.60 1838[3:Rew:1837.0,1793.0] || equal(sk_c10,sk_c11)** -> .
% 0.43/0.60 1849[3:SpR:1826.0,93.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.43/0.60 1851[3:Rew:1794.0,1849.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.43/0.60 1853[3:SpR:1833.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.43/0.60 1855[3:Rew:53.0,1853.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 1857[3:Rew:1855.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 1858[3:Rew:1855.0,569.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1866[3:Rew:1857.0,1816.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.43/0.60 1869[3:Rew:1857.0,1827.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),u)**.
% 0.43/0.60 1873[3:Rew:1858.0,1803.0] || -> equal(sk_c3,sk_c10)**.
% 0.43/0.60 1874[3:Rew:1858.0,1828.0] || -> equal(inverse(sk_c8),sk_c10)**.
% 0.43/0.60 1878[3:Rew:1873.0,1866.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.43/0.60 1884[3:Rew:1878.0,1869.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.43/0.60 1886[3:Rew:1884.0,1851.0] || -> equal(sk_c6,sk_c8)**.
% 0.43/0.60 1887[3:Rew:1884.0,1812.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.43/0.60 1892[3:Rew:1886.0,1794.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.43/0.60 1897[3:Rew:1874.0,1892.0] || -> equal(sk_c8,sk_c10)**.
% 0.43/0.60 1899[3:Rew:1897.0,1801.0] || -> equal(multiply(sk_c5,sk_c10),sk_c11)**.
% 0.43/0.60 1909[3:Rew:1887.0,1899.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1910[3:MRR:1909.0,1838.0] || -> .
% 0.43/0.60 1922[2:Spt:1910.0,9.1,57.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.43/0.60 1923[2:Spt:1910.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 1925[2:MRR:6.1,1922.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 1927[2:MRR:2.1,1922.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 1929[2:MRR:7.0,1922.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 1930[2:MRR:5.0,1922.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 1932[2:MRR:1.0,1922.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.43/0.60 1951[2:SpR:1930.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 1953[2:Rew:1925.0,1951.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 1959[2:SpR:1932.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.43/0.60 1961[2:Rew:1927.0,1959.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.43/0.60 1967[2:SpR:1953.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.43/0.60 1969[2:Rew:53.0,1967.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 1970[2:Rew:1969.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 1971[2:Rew:1969.0,569.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 1976[2:Rew:1970.0,1961.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 1982[2:Rew:1976.0,1922.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.43/0.60 1983[2:Rew:1976.0,1929.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 1994[2:Rew:1971.0,1983.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 1996[2:Rew:1994.0,1925.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.43/0.60 1998[2:Rew:1994.0,1930.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.43/0.60 2018[2:Rew:1971.0,1998.0] || -> equal(sk_c5,sk_c11)**.
% 0.43/0.60 2019[2:Rew:2018.0,1996.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2020[2:MRR:2019.0,1982.0] || -> .
% 0.43/0.60 2041[1:Spt:2020.0,51.3,51.4,51.5,51.6,51.9,51.11,51.12,51.13,51.14] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(inverse(sk_c11),sk_c10) equal(multiply(u,v),sk_c10)**+ equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 2045[2:Spt:8.1] || -> equal(inverse(sk_c11),sk_c10)**.
% 0.43/0.60 2046[2:Rew:2045.0,2041.3] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(sk_c10,sk_c10) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 2049[2:Obv:2046.3] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 2052[2:SpR:2045.0,93.0] || -> equal(multiply(sk_c10,multiply(sk_c11,u)),u)**.
% 0.43/0.60 2054[3:Spt:18.1] || -> equal(multiply(sk_c10,sk_c9),sk_c11)**.
% 0.43/0.60 2057[3:Rew:2054.0,2049.7] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(sk_c11,sk_c11) -> .
% 0.43/0.60 2058[3:Obv:2057.7] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.43/0.60 2061[3:SpR:2054.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2062[3:SpR:2054.0,93.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c9)**.
% 0.43/0.60 2064[4:Spt:39.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.43/0.60 2065[4:SpR:2064.0,93.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.43/0.60 2067[5:Spt:29.1] || -> equal(multiply(sk_c1,sk_c2),sk_c10)**.
% 0.43/0.60 2069[5:SpR:2067.0,93.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c2)**.
% 0.43/0.60 2071[5:Rew:2064.0,2069.0] || -> equal(multiply(sk_c2,sk_c10),sk_c2)**.
% 0.43/0.60 2072[6:Spt:49.1] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.43/0.60 2073[6:SpR:2072.0,54.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.43/0.60 2080[5:SpR:2071.0,93.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c10)**.
% 0.43/0.60 2082[5:Rew:53.0,2080.0] || -> equal(identity,sk_c10)**.
% 0.43/0.60 2083[5:Rew:2082.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.43/0.60 2084[5:Rew:2082.0,569.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.43/0.60 2087[5:Rew:2083.0,2054.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 2089[5:Rew:2083.0,2052.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2091[6:Rew:2083.0,2073.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.43/0.60 2092[6:Rew:2087.0,2072.0] || -> equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 2094[5:Rew:2087.0,2058.4] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.43/0.60 2100[6:Rew:2089.0,2091.0,2087.0,2091.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.43/0.60 2102[6:Rew:2100.0,2092.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2104[6:Rew:2102.0,2045.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2108[6:Rew:2102.0,2084.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2117[6:Rew:2108.0,2094.6,2087.0,2094.6,2102.0,2094.6,2108.0,2094.5,2102.0,2094.5,2108.0,2094.4,2102.0,2094.4,2102.0,2094.3,2102.0,2094.1] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(inverse(x),sk_c11)** equal(multiply(u,v),sk_c11)** equal(w,sk_c11) equal(x,sk_c11) equal(v,sk_c11) -> .
% 0.43/0.60 2118[6:Con:2117.2] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(multiply(u,v),sk_c11)**+ equal(w,sk_c11) equal(v,sk_c11) -> .
% 0.43/0.60 2151[6:SpL:2089.0,2118.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2153[6:Obv:2151.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2154[6:Rew:2104.0,2153.0] || equal(sk_c11,u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11)* -> .
% 0.43/0.60 2155[6:Obv:2154.0] || equal(inverse(u),sk_c11)** equal(u,sk_c11) equal(v,sk_c11)* -> .
% 0.43/0.60 2156[6:Con:2155.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 2165[6:SpL:2104.0,2156.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2166[6:Obv:2165.1] || -> .
% 0.43/0.60 2167[6:Spt:2166.0,49.1,2072.0] || equal(multiply(sk_c2,sk_c9),sk_c10)** -> .
% 0.43/0.60 2168[6:Spt:2166.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 2170[6:Rew:2087.0,2167.0] || equal(multiply(sk_c2,sk_c11),sk_c10)** -> .
% 0.43/0.60 2177[5:Rew:2087.0,42.1] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 2178[6:MRR:2177.1,2170.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 2195[5:Rew:2087.0,41.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c10)**.
% 0.43/0.60 2196[6:MRR:2195.1,2170.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.43/0.60 2197[5:Rew:2087.0,2094.6] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.43/0.60 2198[5:Rew:2084.0,2197.4] || equal(inverse(u),v) equal(inverse(w),sk_c10)** equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(w,sk_c11) equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.43/0.60 2213[6:SpR:2178.0,93.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.43/0.60 2215[6:Rew:2089.0,2213.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.43/0.60 2216[6:Rew:2215.0,2196.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2218[6:Rew:2216.0,2045.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2220[6:Rew:2216.0,2084.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2226[6:Rew:2216.0,2198.1] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(w,sk_c11) equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.43/0.60 2241[6:Rew:2220.0,2226.6,2216.0,2226.6,2220.0,2226.5,2216.0,2226.5,2216.0,2226.3] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(inverse(x),sk_c11)** equal(multiply(u,v),sk_c11)** equal(w,sk_c11) equal(x,sk_c11) equal(v,sk_c11) -> .
% 0.43/0.60 2242[6:Con:2241.2] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(multiply(u,v),sk_c11)**+ equal(w,sk_c11) equal(v,sk_c11) -> .
% 0.43/0.60 2295[6:SpL:2089.0,2242.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2303[6:Obv:2295.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2304[6:Rew:2218.0,2303.0] || equal(sk_c11,u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11)* -> .
% 0.43/0.60 2305[6:Obv:2304.0] || equal(inverse(u),sk_c11)** equal(u,sk_c11) equal(v,sk_c11)* -> .
% 0.43/0.60 2306[6:Con:2305.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 2327[6:SpL:2218.0,2306.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2329[6:Obv:2327.1] || -> .
% 0.43/0.60 2330[5:Spt:2329.0,29.1,2067.0] || equal(multiply(sk_c1,sk_c2),sk_c10)** -> .
% 0.43/0.60 2331[5:Spt:2329.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 2333[5:MRR:26.1,2330.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 2334[5:MRR:24.1,2330.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 2337[5:MRR:27.1,2330.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 2338[5:MRR:25.1,2330.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 2339[5:MRR:23.1,2330.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 2364[5:SpR:2338.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 2366[5:Rew:2333.0,2364.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 2368[5:SpR:2339.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 2370[5:Rew:2054.0,2368.0,2334.0,2368.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2371[5:Rew:2370.0,2045.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2374[5:Rew:2370.0,2337.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 2376[5:Rew:2370.0,2062.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c9)**.
% 0.43/0.60 2377[5:Rew:2370.0,2330.0] || equal(multiply(sk_c1,sk_c2),sk_c11)** -> .
% 0.43/0.60 2378[5:Rew:2370.0,2052.0] || -> equal(multiply(sk_c11,multiply(sk_c11,u)),u)**.
% 0.43/0.60 2379[5:Rew:2370.0,2061.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2387[5:Rew:2366.0,2374.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 2397[5:Rew:2387.0,2366.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 2398[5:Rew:2397.0,2376.0,2371.0,2376.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 2403[5:Rew:2378.0,2379.0,2398.0,2379.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2447[4:SpR:569.0,2065.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.43/0.60 2452[4:SpR:2447.0,93.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.43/0.60 2454[4:Rew:569.0,2452.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.43/0.60 2461[5:SpR:2403.0,569.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 2466[5:Rew:2461.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.43/0.60 2491[5:SpR:2454.0,2466.0] || -> equal(multiply(sk_c1,sk_c2),sk_c11)**.
% 0.43/0.60 2504[5:MRR:2491.0,2377.0] || -> .
% 0.43/0.60 2507[4:Spt:2504.0,39.1,2064.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.43/0.60 2508[4:Spt:2504.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 2510[4:MRR:36.1,2507.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 2511[4:MRR:34.1,2507.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 2514[4:MRR:37.0,2507.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 2515[4:MRR:35.0,2507.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 2516[4:MRR:33.0,2507.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 2541[4:SpR:2515.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 2543[4:Rew:2510.0,2541.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.43/0.60 2545[4:SpR:2516.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.43/0.60 2547[4:Rew:2054.0,2545.0,2511.0,2545.0] || -> equal(sk_c10,sk_c11)**.
% 0.43/0.60 2548[4:Rew:2547.0,2045.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.43/0.60 2551[4:Rew:2547.0,2514.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.43/0.60 2553[4:Rew:2547.0,2062.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c9)**.
% 0.43/0.60 2554[4:Rew:2547.0,2052.0] || -> equal(multiply(sk_c11,multiply(sk_c11,u)),u)**.
% 0.43/0.60 2555[4:Rew:2547.0,2061.0] || -> equal(multiply(sk_c11,multiply(sk_c9,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2558[4:Rew:2547.0,2058.1] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c10)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.43/0.60 2563[4:Rew:2543.0,2551.0] || -> equal(sk_c8,sk_c11)**.
% 0.43/0.60 2573[4:Rew:2563.0,2543.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.43/0.60 2574[4:Rew:2573.0,2553.0,2548.0,2553.0] || -> equal(sk_c9,sk_c11)**.
% 0.43/0.60 2579[4:Rew:2554.0,2555.0,2574.0,2555.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.43/0.60 2594[4:Rew:2574.0,2558.6,2547.0,2558.6,2547.0,2558.5,2547.0,2558.4,2574.0,2558.4,2547.0,2558.3] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c11) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c11)** equal(multiply(x,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.43/0.60 2595[4:Con:2594.2] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.43/0.60 2628[4:SpR:2579.0,569.0] || -> equal(identity,sk_c11)**.
% 0.43/0.60 2631[4:Rew:2628.0,569.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.43/0.60 2636[4:Rew:2631.0,2595.3] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(multiply(u,v),sk_c11)** equal(w,sk_c11) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.43/0.60 2639[4:Rew:2631.0,2636.4] || equal(inverse(u),v) equal(inverse(w),sk_c11)** equal(multiply(u,v),sk_c11)**+ equal(w,sk_c11) equal(v,sk_c11) -> .
% 0.43/0.60 2675[4:SpL:2579.0,2639.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2677[4:Obv:2675.2] || equal(inverse(sk_c11),u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11) -> .
% 0.43/0.60 2678[4:Rew:2548.0,2677.0] || equal(sk_c11,u)* equal(inverse(v),sk_c11)** equal(v,sk_c11) equal(u,sk_c11)* -> .
% 0.43/0.60 2679[4:Obv:2678.0] || equal(inverse(u),sk_c11)** equal(u,sk_c11) equal(v,sk_c11)* -> .
% 0.43/0.60 2680[4:Con:2679.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.43/0.60 2690[4:SpL:2548.0,2680.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.43/0.60 2691[4:Obv:2690.1] || -> .
% 0.43/0.60 2692[3:Spt:2691.0,18.1,2054.0] || equal(multiply(sk_c10,sk_c9),sk_c11)** -> .
% 0.43/0.60 2693[3:Spt:2691.0,18.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.43/0.60 2694[3:MRR:16.1,2692.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.43/0.60 2695[3:MRR:14.1,2692.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.43/0.60 2696[3:MRR:12.1,2692.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.43/0.60 2697[3:MRR:19.1,2692.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.43/0.60 2698[3:MRR:20.1,2692.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.43/0.60 2699[3:MRR:17.1,2692.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.43/0.60 2700[3:MRR:15.1,2692.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.43/0.60 2701[3:MRR:13.1,2692.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.43/0.60 2702[3:MRR:11.1,2692.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.43/0.60 2707[3:SpR:2694.0,93.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.43/0.60 2711[3:SpR:2696.0,93.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.43/0.60 2716[3:SpR:2698.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.43/0.60 2718[3:Rew:2693.0,2716.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.43/0.60 2719[3:SpR:2699.0,54.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),multiply(sk_c11,u))**.
% 0.43/0.60 2720[3:SpR:2699.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c10)**.
% 0.43/0.60 2723[3:SpR:2700.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.43/0.60 2725[3:Rew:2694.0,2723.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.45/0.61 2727[3:SpR:2701.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.45/0.61 2729[3:Rew:2695.0,2727.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.45/0.61 2730[3:Rew:2729.0,2692.0] || equal(sk_c10,sk_c11)** -> .
% 0.45/0.61 2736[3:SpR:2718.0,93.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.45/0.61 2738[3:Rew:2697.0,2736.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.45/0.61 2743[3:SpR:2725.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 2745[3:Rew:53.0,2743.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 2746[3:Rew:2745.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 2747[3:Rew:2745.0,569.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.45/0.61 2751[3:Rew:2746.0,2711.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.45/0.61 2753[3:Rew:2746.0,2719.0] || -> equal(multiply(sk_c8,multiply(sk_c10,u)),u)**.
% 0.45/0.61 2757[3:Rew:2747.0,2702.0] || -> equal(sk_c3,sk_c10)**.
% 0.45/0.61 2758[3:Rew:2747.0,2720.0] || -> equal(inverse(sk_c8),sk_c10)**.
% 0.45/0.61 2760[3:Rew:2757.0,2751.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.45/0.61 2766[3:Rew:2760.0,2753.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.45/0.61 2769[3:Rew:2766.0,2707.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.45/0.61 2770[3:Rew:2766.0,2738.0] || -> equal(sk_c6,sk_c8)**.
% 0.45/0.61 2775[3:Rew:2770.0,2697.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.45/0.61 2779[3:Rew:2758.0,2775.0] || -> equal(sk_c8,sk_c10)**.
% 0.45/0.61 2781[3:Rew:2779.0,2700.0] || -> equal(multiply(sk_c5,sk_c10),sk_c11)**.
% 0.45/0.61 2791[3:Rew:2769.0,2781.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 2792[3:MRR:2791.0,2730.0] || -> .
% 0.45/0.61 2800[2:Spt:2792.0,8.1,2045.0] || equal(inverse(sk_c11),sk_c10)** -> .
% 0.45/0.61 2801[2:Spt:2792.0,8.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.45/0.61 2802[2:MRR:6.1,2800.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.45/0.61 2804[2:MRR:2.1,2800.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.45/0.61 2807[2:MRR:7.0,2800.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.45/0.61 2808[2:MRR:5.0,2800.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.45/0.61 2810[2:MRR:1.0,2800.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.45/0.61 2829[2:SpR:2808.0,93.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.45/0.61 2831[2:Rew:2802.0,2829.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.45/0.61 2837[2:SpR:2810.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.45/0.61 2839[2:Rew:2804.0,2837.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.45/0.61 2845[2:SpR:2831.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.45/0.61 2847[2:Rew:53.0,2845.0] || -> equal(identity,sk_c11)**.
% 0.45/0.61 2848[2:Rew:2847.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.45/0.61 2849[2:Rew:2847.0,569.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.45/0.61 2852[2:Rew:2848.0,2839.0] || -> equal(sk_c10,sk_c11)**.
% 0.45/0.61 2858[2:Rew:2852.0,2800.0] || equal(inverse(sk_c11),sk_c11)** -> .
% 0.45/0.61 2859[2:Rew:2852.0,2807.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.45/0.61 2866[2:Rew:2849.0,2859.0] || -> equal(sk_c8,sk_c11)**.
% 0.45/0.61 2867[2:Rew:2866.0,2802.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.45/0.61 2870[2:Rew:2866.0,2808.0] || -> equal(multiply(sk_c5,sk_c11),sk_c11)**.
% 0.45/0.61 2890[2:Rew:2849.0,2870.0] || -> equal(sk_c5,sk_c11)**.
% 0.45/0.61 2891[2:Rew:2890.0,2867.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.45/0.61 2892[2:MRR:2891.0,2858.0] || -> .
% 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_8 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_29 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_49 prove_this_51 left_identity left_inverse associativity
% 0.45/0.61
%------------------------------------------------------------------------------