TSTP Solution File: GRP382-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP382-1 : 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 11:47:07 EDT 2022
% Result : Unsatisfiable 0.42s 0.63s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP382-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % 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 10:41:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.42/0.63
% 0.42/0.63 SPASS V 3.9
% 0.42/0.63 SPASS beiseite: Proof found.
% 0.42/0.63 % SZS status Theorem
% 0.42/0.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.63 SPASS derived 2157 clauses, backtracked 891 clauses, performed 15 splits and kept 1474 clauses.
% 0.42/0.63 SPASS allocated 64799 KBytes.
% 0.42/0.63 SPASS spent 0:00:00.27 on the problem.
% 0.42/0.63 0:00:00.04 for the input.
% 0.42/0.63 0:00:00.00 for the FLOTTER CNF translation.
% 0.42/0.63 0:00:00.01 for inferences.
% 0.42/0.63 0:00:00.01 for the backtracking.
% 0.42/0.63 0:00:00.19 for the reduction.
% 0.42/0.63
% 0.42/0.63
% 0.42/0.63 Here is a proof with depth 5, length 444 :
% 0.42/0.63 % SZS output start Refutation
% 0.42/0.63 1[0:Inp] || -> equal(inverse(sk_c12),sk_c11) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 2[0:Inp] || -> equal(inverse(sk_c4),sk_c12)** equal(inverse(sk_c12),sk_c11).
% 0.42/0.63 5[0:Inp] || -> equal(inverse(sk_c12),sk_c11) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 6[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c12),sk_c11).
% 0.42/0.63 7[0:Inp] || -> equal(inverse(sk_c12),sk_c11) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c12),sk_c11).
% 0.42/0.63 9[0:Inp] || -> equal(inverse(sk_c7),sk_c9)** equal(inverse(sk_c12),sk_c11).
% 0.42/0.63 10[0:Inp] || -> equal(inverse(sk_c12),sk_c11) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.42/0.63 11[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c12).
% 0.42/0.63 12[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 13[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c10),sk_c12).
% 0.42/0.63 14[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 15[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12).
% 0.42/0.63 16[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 17[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12).
% 0.42/0.63 18[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 19[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 20[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(multiply(sk_c11,sk_c10),sk_c12).
% 0.42/0.63 21[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 22[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 23[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 24[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 25[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 26[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 27[0:Inp] || -> equal(inverse(sk_c1),sk_c12) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 29[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 31[0:Inp] || -> equal(multiply(sk_c4,sk_c12),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 32[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 35[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 36[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 39[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 43[0:Inp] || -> equal(multiply(sk_c5,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 44[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 45[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c12) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 46[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 47[0:Inp] || -> equal(multiply(sk_c9,sk_c11),sk_c12) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 49[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 51[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 52[0:Inp] || -> equal(inverse(sk_c4),sk_c12) equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 53[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 54[0:Inp] || -> equal(inverse(sk_c5),sk_c11) equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 55[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 56[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 57[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 59[0:Inp] || -> equal(inverse(sk_c7),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 71[0:Inp] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),z) equal(inverse(x1),sk_c11) equal(inverse(x2),sk_c12) equal(inverse(x3),sk_c12) equal(inverse(sk_c12),sk_c11) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c12)** equal(multiply(y,z),sk_c11)** equal(multiply(v,sk_c11),sk_c12)** equal(multiply(x1,sk_c11),sk_c10)** equal(multiply(x2,sk_c12),sk_c11)** equal(multiply(z,sk_c12),sk_c11)** equal(multiply(x3,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.42/0.63 72[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.42/0.63 73[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.42/0.63 74[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.42/0.63 75[1:Spt:71.0,71.1,71.2,71.8,71.9,71.11] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)* equal(multiply(x,v),sk_c12)** equal(multiply(v,sk_c11),sk_c12)** -> .
% 0.42/0.63 77[2:Spt:9.1] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.42/0.63 79[3:Spt:19.1] || -> equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 81[3:SpL:79.0,75.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c10) equal(sk_c12,u) equal(multiply(v,sk_c10),sk_c12)** equal(multiply(sk_c10,sk_c11),sk_c12)** -> .
% 0.42/0.63 82[4:Spt:59.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 84[5:Spt:29.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 89[6:Spt:49.1] || -> equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 95[7:Spt:39.1] || -> equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 97[7:SpL:95.0,75.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.42/0.63 98[7:Rew:84.0,97.1] || equal(inverse(u),sk_c11)** equal(sk_c12,u) equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.42/0.63 99[7:Obv:98.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c11),sk_c12)** -> .
% 0.42/0.63 101[2:SpR:77.0,73.0] || -> equal(multiply(sk_c11,sk_c12),identity)**.
% 0.42/0.63 102[4:SpR:82.0,73.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.42/0.63 103[5:SpR:84.0,73.0] || -> equal(multiply(sk_c12,sk_c1),identity)**.
% 0.42/0.63 114[2:SpR:101.0,74.0] || -> equal(multiply(sk_c11,multiply(sk_c12,u)),multiply(identity,u))**.
% 0.42/0.63 117[0:SpR:73.0,74.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.42/0.63 120[2:Rew:72.0,114.0] || -> equal(multiply(sk_c11,multiply(sk_c12,u)),u)**.
% 0.42/0.63 122[0:Rew:72.0,117.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.42/0.63 132[5:SpR:103.0,120.0] || -> equal(multiply(sk_c11,identity),sk_c1)**.
% 0.42/0.63 136[5:SpR:132.0,74.0] || -> equal(multiply(sk_c11,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.42/0.63 139[5:Rew:72.0,136.0] || -> equal(multiply(sk_c1,u),multiply(sk_c11,u))**.
% 0.42/0.63 140[7:Rew:139.0,95.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.42/0.63 143[7:Rew:140.0,99.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.42/0.63 144[7:Obv:143.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c11),sk_c12)** -> .
% 0.42/0.63 150[0:SpR:122.0,122.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.42/0.63 152[3:SpR:79.0,122.0] || -> equal(multiply(inverse(sk_c11),sk_c12),sk_c10)**.
% 0.42/0.63 159[0:SpR:73.0,122.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.42/0.63 160[4:SpR:102.0,122.0] || -> equal(multiply(inverse(sk_c3),identity),sk_c2)**.
% 0.42/0.63 180[0:Rew:150.0,159.0] || -> equal(multiply(u,identity),u)**.
% 0.42/0.63 181[5:Rew:180.0,132.0] || -> equal(sk_c1,sk_c11)**.
% 0.42/0.63 182[4:Rew:180.0,160.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.42/0.63 184[5:Rew:181.0,84.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.42/0.63 206[4:SpR:182.0,73.0] || -> equal(multiply(sk_c2,sk_c3),identity)**.
% 0.42/0.63 209[6:Rew:89.0,206.0] || -> equal(identity,sk_c11)**.
% 0.42/0.63 210[6:Rew:209.0,72.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.63 212[6:Rew:209.0,101.0] || -> equal(multiply(sk_c11,sk_c12),sk_c11)**.
% 0.42/0.63 220[6:Rew:209.0,180.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.63 225[7:Rew:210.0,140.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 231[7:Rew:225.0,77.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 236[7:Rew:225.0,144.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c12,u) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.42/0.63 250[7:Rew:225.0,220.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 269[7:Rew:250.0,236.3,225.0,236.1,225.0,236.0] || equal(inverse(u),sk_c12)**+ equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.42/0.63 626[7:SpL:231.0,269.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c12)** equal(sk_c12,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 630[7:Obv:626.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.42/0.63 632[7:SpL:231.0,630.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 636[7:Obv:632.1] || -> .
% 0.42/0.63 637[7:Spt:636.0,39.1,95.0] || equal(multiply(sk_c1,sk_c11),sk_c12)** -> .
% 0.42/0.63 638[7:Spt:636.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 640[6:Rew:210.0,212.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 641[6:Rew:640.0,181.0] || -> equal(sk_c1,sk_c12)**.
% 0.42/0.63 651[6:Rew:640.0,220.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 666[7:Rew:651.0,637.0,641.0,637.0,640.0,637.0] || equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 667[7:Obv:666.0] || -> .
% 0.42/0.63 720[6:Spt:667.0,49.1,89.0] || equal(multiply(sk_c2,sk_c3),sk_c11)** -> .
% 0.42/0.63 721[6:Spt:667.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 722[5:Rew:184.0,152.0] || -> equal(multiply(sk_c12,sk_c12),sk_c10)**.
% 0.42/0.63 723[6:Rew:206.0,720.0] || equal(identity,sk_c11)** -> .
% 0.42/0.63 726[4:Rew:206.0,46.1] || -> equal(inverse(sk_c6),sk_c9)** equal(identity,sk_c11).
% 0.42/0.63 727[6:MRR:726.1,723.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 728[4:Rew:206.0,44.1] || -> equal(inverse(sk_c5),sk_c11)** equal(identity,sk_c11).
% 0.42/0.63 729[6:MRR:728.1,723.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.42/0.63 735[4:Rew:206.0,47.1] || -> equal(multiply(sk_c9,sk_c11),sk_c12)** equal(identity,sk_c11).
% 0.42/0.63 736[6:MRR:735.1,723.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 737[4:Rew:206.0,45.1] || -> equal(multiply(sk_c6,sk_c9),sk_c12)** equal(identity,sk_c11).
% 0.42/0.63 738[6:MRR:737.1,723.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 739[4:Rew:206.0,43.1] || -> equal(multiply(sk_c5,sk_c11),sk_c10)** equal(identity,sk_c11).
% 0.42/0.63 740[6:MRR:739.1,723.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 761[6:SpR:729.0,122.0] || -> equal(multiply(sk_c11,multiply(sk_c5,u)),u)**.
% 0.42/0.63 776[2:SpR:101.0,122.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c12)**.
% 0.42/0.63 801[6:SpR:736.0,74.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),multiply(sk_c12,u))**.
% 0.42/0.63 809[6:SpR:738.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.42/0.63 811[6:Rew:727.0,809.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.42/0.63 813[6:SpR:740.0,122.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.42/0.63 815[6:Rew:79.0,813.0,729.0,813.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 819[6:Rew:815.0,723.0] || equal(identity,sk_c12)** -> .
% 0.42/0.63 821[6:Rew:815.0,101.0] || -> equal(multiply(sk_c12,sk_c12),identity)**.
% 0.42/0.63 826[6:Rew:815.0,736.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.42/0.63 827[6:Rew:815.0,740.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.42/0.63 828[6:Rew:815.0,120.0] || -> equal(multiply(sk_c12,multiply(sk_c12,u)),u)**.
% 0.42/0.63 832[6:Rew:815.0,801.0] || -> equal(multiply(sk_c9,multiply(sk_c12,u)),multiply(sk_c12,u))**.
% 0.42/0.63 846[6:Rew:815.0,761.0] || -> equal(multiply(sk_c12,multiply(sk_c5,u)),u)**.
% 0.42/0.63 848[6:Rew:722.0,821.0] || -> equal(identity,sk_c10)**.
% 0.42/0.63 856[6:Rew:848.0,819.0] || equal(sk_c10,sk_c12)** -> .
% 0.42/0.63 858[6:Rew:811.0,826.0] || -> equal(sk_c9,sk_c12)**.
% 0.42/0.63 876[6:Rew:828.0,832.0,858.0,832.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 880[6:Rew:876.0,846.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.42/0.63 893[6:Rew:880.0,827.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 894[6:MRR:893.0,856.0] || -> .
% 0.42/0.63 926[5:Spt:894.0,29.1,84.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.42/0.63 927[5:Spt:894.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 928[2:Rew:180.0,776.0] || -> equal(inverse(sk_c11),sk_c12)**.
% 0.42/0.63 929[3:Rew:928.0,152.0] || -> equal(multiply(sk_c12,sk_c12),sk_c10)**.
% 0.42/0.63 932[5:MRR:26.1,926.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 933[5:MRR:24.1,926.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.42/0.63 937[5:MRR:27.0,926.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 938[5:MRR:25.0,926.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 939[5:MRR:23.0,926.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 941[3:Rew:928.0,81.1] || equal(inverse(u),sk_c10)** equal(sk_c12,u) equal(inverse(v),sk_c10) equal(sk_c12,u) equal(multiply(v,sk_c10),sk_c12)** equal(multiply(sk_c10,sk_c11),sk_c12)** -> .
% 0.42/0.63 942[3:Obv:941.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c12,u) equal(multiply(v,sk_c10),sk_c12)** equal(multiply(sk_c10,sk_c11),sk_c12)** -> .
% 0.42/0.63 994[5:SpR:938.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.42/0.63 996[5:Rew:932.0,994.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.42/0.63 998[5:SpR:939.0,122.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.42/0.63 1000[5:Rew:79.0,998.0,933.0,998.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 1001[5:Rew:1000.0,77.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 1005[5:Rew:1000.0,101.0] || -> equal(multiply(sk_c12,sk_c12),identity)**.
% 0.42/0.63 1006[5:Rew:1000.0,937.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.42/0.63 1012[5:Rew:1000.0,942.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c12,u) equal(multiply(v,sk_c10),sk_c12)** equal(multiply(sk_c10,sk_c12),sk_c12)** -> .
% 0.42/0.63 1025[5:Rew:929.0,1005.0] || -> equal(identity,sk_c10)**.
% 0.42/0.63 1028[5:Rew:1025.0,180.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.42/0.63 1032[5:Rew:996.0,1006.0] || -> equal(sk_c9,sk_c12)**.
% 0.42/0.63 1042[5:Rew:1032.0,996.0] || -> equal(multiply(sk_c12,sk_c12),sk_c12)**.
% 0.42/0.63 1044[5:Rew:929.0,1042.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 1050[5:Rew:1044.0,1028.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 1084[5:Rew:1044.0,1012.4,1050.0,1012.4,1050.0,1012.3,1044.0,1012.3,1044.0,1012.1,1044.0,1012.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) equal(sk_c12,sk_c12) -> .
% 0.42/0.63 1085[5:Obv:1084.4] || equal(inverse(u),sk_c12)**+ equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.42/0.63 1485[5:SpL:1001.0,1085.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c12)** equal(sk_c12,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 1489[5:Obv:1485.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.42/0.63 1559[5:SpL:1001.0,1489.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 1563[5:Obv:1559.1] || -> .
% 0.42/0.63 1564[4:Spt:1563.0,59.1,82.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.42/0.63 1565[4:Spt:1563.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 1567[4:MRR:56.1,1564.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 1568[4:MRR:54.1,1564.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.42/0.63 1572[4:MRR:57.0,1564.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 1573[4:MRR:55.0,1564.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 1574[4:MRR:53.0,1564.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 1619[4:SpR:1573.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.42/0.63 1621[4:Rew:1567.0,1619.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.42/0.63 1623[4:SpR:1574.0,122.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.42/0.63 1625[4:Rew:79.0,1623.0,1568.0,1623.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 1626[4:Rew:1625.0,928.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 1629[4:Rew:1625.0,101.0] || -> equal(multiply(sk_c12,sk_c12),identity)**.
% 0.42/0.63 1631[4:Rew:1625.0,1572.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.42/0.63 1638[4:Rew:1625.0,942.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c12,u) equal(multiply(v,sk_c10),sk_c12)** equal(multiply(sk_c10,sk_c12),sk_c12)** -> .
% 0.42/0.63 1649[4:Rew:929.0,1629.0] || -> equal(identity,sk_c10)**.
% 0.42/0.63 1651[4:Rew:1649.0,180.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.42/0.63 1654[4:Rew:1621.0,1631.0] || -> equal(sk_c9,sk_c12)**.
% 0.42/0.63 1664[4:Rew:1654.0,1621.0] || -> equal(multiply(sk_c12,sk_c12),sk_c12)**.
% 0.42/0.63 1666[4:Rew:929.0,1664.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 1671[4:Rew:1666.0,1651.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 1704[4:Rew:1666.0,1638.4,1671.0,1638.4,1671.0,1638.3,1666.0,1638.3,1666.0,1638.1,1666.0,1638.0] || equal(inverse(u),sk_c12)** equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) equal(sk_c12,sk_c12) -> .
% 0.42/0.63 1705[4:Obv:1704.4] || equal(inverse(u),sk_c12)**+ equal(inverse(v),sk_c12)** equal(sk_c12,u) equal(v,sk_c12) -> .
% 0.42/0.63 1947[4:SpL:1626.0,1705.0] || equal(sk_c12,sk_c12) equal(inverse(u),sk_c12)** equal(sk_c12,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 1950[4:Obv:1947.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.42/0.63 1952[4:SpL:1626.0,1950.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 1955[4:Obv:1952.1] || -> .
% 0.42/0.63 1956[3:Spt:1955.0,19.1,79.0] || equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.42/0.63 1957[3:Spt:1955.0,19.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 1958[3:MRR:18.1,1956.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.42/0.63 1959[3:MRR:16.1,1956.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 1960[3:MRR:14.1,1956.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.42/0.63 1961[3:MRR:12.1,1956.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.42/0.63 1962[3:MRR:20.1,1956.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.42/0.63 1963[3:MRR:17.1,1956.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 1964[3:MRR:15.1,1956.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 1965[3:MRR:13.1,1956.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.42/0.63 1966[3:MRR:11.1,1956.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 1975[3:SpR:1959.0,122.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.42/0.63 1979[3:SpR:1961.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.42/0.63 1987[3:SpR:1962.0,122.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.42/0.63 1989[3:Rew:1958.0,1987.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.42/0.63 1990[3:SpR:1963.0,74.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),multiply(sk_c12,u))**.
% 0.42/0.63 1991[3:SpR:1963.0,122.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.42/0.63 1994[3:SpR:1964.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.42/0.63 1996[3:Rew:1959.0,1994.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.42/0.63 1998[3:SpR:1965.0,122.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c11)**.
% 0.42/0.63 2000[3:Rew:1960.0,1998.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.42/0.63 2001[3:Rew:2000.0,1956.0] || equal(sk_c11,sk_c12)** -> .
% 0.42/0.63 2012[3:SpR:1989.0,122.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c7)**.
% 0.42/0.63 2014[3:Rew:1957.0,2012.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.42/0.63 2016[3:SpR:1996.0,122.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.42/0.63 2018[3:Rew:73.0,2016.0] || -> equal(identity,sk_c12)**.
% 0.42/0.63 2020[3:Rew:2018.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2021[3:Rew:2018.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 2029[3:Rew:2020.0,1979.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.42/0.63 2032[3:Rew:2020.0,1990.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),u)**.
% 0.42/0.63 2036[3:Rew:2021.0,1966.0] || -> equal(sk_c4,sk_c11)**.
% 0.42/0.63 2037[3:Rew:2021.0,1991.0] || -> equal(inverse(sk_c9),sk_c11)**.
% 0.42/0.63 2041[3:Rew:2036.0,2029.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.63 2047[3:Rew:2041.0,2032.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.42/0.63 2049[3:Rew:2047.0,2014.0] || -> equal(sk_c7,sk_c9)**.
% 0.42/0.63 2050[3:Rew:2047.0,1975.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.42/0.63 2055[3:Rew:2049.0,1957.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.42/0.63 2060[3:Rew:2037.0,2055.0] || -> equal(sk_c9,sk_c11)**.
% 0.42/0.63 2062[3:Rew:2060.0,1964.0] || -> equal(multiply(sk_c6,sk_c11),sk_c12)**.
% 0.42/0.63 2072[3:Rew:2050.0,2062.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2073[3:MRR:2072.0,2001.0] || -> .
% 0.42/0.63 2085[2:Spt:2073.0,9.1,77.0] || equal(inverse(sk_c12),sk_c11)** -> .
% 0.42/0.63 2086[2:Spt:2073.0,9.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 2088[2:MRR:6.1,2085.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 2090[2:MRR:2.1,2085.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.42/0.63 2092[2:MRR:7.0,2085.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.42/0.63 2093[2:MRR:5.0,2085.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 2095[2:MRR:1.0,2085.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 2114[2:SpR:2093.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.42/0.63 2116[2:Rew:2088.0,2114.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.42/0.63 2122[2:SpR:2095.0,122.0] || -> equal(multiply(inverse(sk_c4),sk_c11),sk_c12)**.
% 0.42/0.63 2124[2:Rew:2090.0,2122.0] || -> equal(multiply(sk_c12,sk_c11),sk_c12)**.
% 0.42/0.63 2130[2:SpR:2116.0,122.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c12)**.
% 0.42/0.63 2132[2:Rew:73.0,2130.0] || -> equal(identity,sk_c12)**.
% 0.42/0.63 2133[2:Rew:2132.0,72.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2134[2:Rew:2132.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 2139[2:Rew:2133.0,2124.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2145[2:Rew:2139.0,2085.0] || equal(inverse(sk_c12),sk_c12)** -> .
% 0.42/0.63 2146[2:Rew:2139.0,2092.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.42/0.63 2157[2:Rew:2134.0,2146.0] || -> equal(sk_c9,sk_c12)**.
% 0.42/0.63 2159[2:Rew:2157.0,2088.0] || -> equal(inverse(sk_c6),sk_c12)**.
% 0.42/0.63 2161[2:Rew:2157.0,2093.0] || -> equal(multiply(sk_c6,sk_c12),sk_c12)**.
% 0.42/0.63 2181[2:Rew:2134.0,2161.0] || -> equal(sk_c6,sk_c12)**.
% 0.42/0.63 2182[2:Rew:2181.0,2159.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 2183[2:MRR:2182.0,2145.0] || -> .
% 0.42/0.63 2204[1:Spt:2183.0,71.3,71.4,71.5,71.6,71.7,71.10,71.12,71.13,71.14,71.15,71.16] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(inverse(sk_c12),sk_c11) equal(multiply(u,v),sk_c11)**+ equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.42/0.63 2208[2:Spt:8.1] || -> equal(inverse(sk_c12),sk_c11)**.
% 0.42/0.63 2209[2:Rew:2208.0,2204.4] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(sk_c11,sk_c11) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.42/0.63 2212[2:Obv:2209.4] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.42/0.63 2215[2:SpR:2208.0,122.0] || -> equal(multiply(sk_c11,multiply(sk_c12,u)),u)**.
% 0.42/0.63 2217[3:Spt:18.1] || -> equal(multiply(sk_c11,sk_c10),sk_c12)**.
% 0.42/0.63 2220[3:Rew:2217.0,2212.9] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** equal(sk_c12,sk_c12) -> .
% 0.42/0.63 2221[3:Obv:2220.9] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** -> .
% 0.42/0.63 2227[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c12)**.
% 0.42/0.63 2228[4:SpR:2227.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c1,u)),u)**.
% 0.42/0.63 2230[5:Spt:59.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.42/0.63 2233[6:Spt:39.1] || -> equal(multiply(sk_c1,sk_c11),sk_c12)**.
% 0.42/0.63 2235[6:SpR:2233.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c12),sk_c11)**.
% 0.42/0.63 2237[6:Rew:2227.0,2235.0] || -> equal(multiply(sk_c12,sk_c12),sk_c11)**.
% 0.42/0.63 2238[7:Spt:49.1] || -> equal(multiply(sk_c2,sk_c3),sk_c11)**.
% 0.42/0.63 2240[7:SpR:2238.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c3)**.
% 0.42/0.63 2242[7:Rew:2230.0,2240.0] || -> equal(multiply(sk_c3,sk_c11),sk_c3)**.
% 0.42/0.63 2251[6:SpR:2237.0,122.0] || -> equal(multiply(inverse(sk_c12),sk_c11),sk_c12)**.
% 0.42/0.63 2253[6:Rew:2208.0,2251.0] || -> equal(multiply(sk_c11,sk_c11),sk_c12)**.
% 0.42/0.63 2255[7:SpR:2242.0,122.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c11)**.
% 0.42/0.63 2257[7:Rew:73.0,2255.0] || -> equal(identity,sk_c11)**.
% 0.42/0.63 2258[7:Rew:2257.0,72.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.42/0.63 2259[7:Rew:2257.0,180.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.42/0.63 2262[7:Rew:2258.0,2217.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 2264[7:Rew:2258.0,2215.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2265[7:Rew:2258.0,2253.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2271[7:Rew:2262.0,2221.5] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c12)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** -> .
% 0.42/0.63 2274[7:Rew:2265.0,2208.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 2283[7:Rew:2265.0,2259.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 2305[7:Rew:2283.0,2271.8,2265.0,2271.8,2283.0,2271.7,2265.0,2271.7,2283.0,2271.6,2265.0,2271.6,2283.0,2271.5,2265.0,2271.5,2265.0,2271.4,2265.0,2271.1] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(inverse(x),sk_c12)** equal(inverse(y),sk_c12)** equal(multiply(u,v),sk_c12)** equal(w,sk_c12) equal(x,sk_c12) equal(v,sk_c12) equal(y,sk_c12) -> .
% 0.42/0.63 2306[7:Con:2305.2] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(multiply(u,v),sk_c12)**+ equal(w,sk_c12) equal(v,sk_c12) -> .
% 0.42/0.63 2341[0:SpR:150.0,122.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.42/0.63 2361[7:SpL:2264.0,2306.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 2362[7:Obv:2361.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 2363[7:Rew:2274.0,2362.0] || equal(sk_c12,u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12)* -> .
% 0.42/0.63 2364[7:Obv:2363.0] || equal(inverse(u),sk_c12)** equal(u,sk_c12) equal(v,sk_c12)* -> .
% 0.42/0.63 2365[7:Con:2364.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.42/0.63 2394[7:SpL:2274.0,2365.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 2396[7:Obv:2394.1] || -> .
% 0.42/0.63 2397[7:Spt:2396.0,49.1,2238.0] || equal(multiply(sk_c2,sk_c3),sk_c11)** -> .
% 0.42/0.63 2398[7:Spt:2396.0,49.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 2400[7:MRR:46.1,2397.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 2405[7:MRR:45.1,2397.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 2426[7:SpR:2400.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.42/0.63 2464[7:SpR:2405.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.42/0.63 2468[7:Rew:2426.0,2464.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2469[7:Rew:2468.0,2237.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2486[7:Rew:2469.0,2397.0] || equal(multiply(sk_c2,sk_c3),sk_c12)** -> .
% 0.42/0.63 2574[7:SpR:2468.0,180.0] || -> equal(identity,sk_c12)**.
% 0.42/0.63 2578[7:Rew:2574.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 2579[7:Rew:2574.0,73.0] || -> equal(multiply(inverse(u),u),sk_c12)**.
% 0.42/0.63 2614[7:SpR:2230.0,2579.0] || -> equal(multiply(sk_c3,sk_c2),sk_c12)**.
% 0.42/0.63 2644[7:SpR:2614.0,122.0] || -> equal(multiply(inverse(sk_c3),sk_c12),sk_c2)**.
% 0.42/0.63 2646[7:Rew:2578.0,2644.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.42/0.63 2650[7:SpR:2646.0,2579.0] || -> equal(multiply(sk_c2,sk_c3),sk_c12)**.
% 0.42/0.63 2652[7:MRR:2650.0,2486.0] || -> .
% 0.42/0.63 2653[6:Spt:2652.0,39.1,2233.0] || equal(multiply(sk_c1,sk_c11),sk_c12)** -> .
% 0.42/0.63 2654[6:Spt:2652.0,39.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 2656[6:MRR:36.1,2653.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 2658[6:MRR:32.1,2653.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.42/0.63 2661[6:MRR:35.1,2653.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 2663[6:MRR:31.1,2653.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 2677[6:SpR:2656.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.42/0.63 2682[6:SpR:2658.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.42/0.63 2695[6:SpR:2661.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.42/0.63 2699[6:Rew:2677.0,2695.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2700[6:Rew:2699.0,2682.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.42/0.63 2702[6:Rew:2699.0,2228.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.42/0.63 2708[6:Rew:2700.0,2663.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2714[6:Rew:2708.0,2653.0] || equal(multiply(sk_c1,sk_c12),sk_c12)** -> .
% 0.42/0.63 2739[6:Rew:2702.0,2714.0] || equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 2740[6:Obv:2739.0] || -> .
% 0.42/0.63 2764[5:Spt:2740.0,59.1,2230.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.42/0.63 2765[5:Spt:2740.0,59.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 2767[5:MRR:56.1,2764.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 2769[5:MRR:52.1,2764.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.42/0.63 2772[5:MRR:55.0,2764.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 2774[5:MRR:51.0,2764.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 2785[5:SpR:2767.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.42/0.63 2790[5:SpR:2769.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.42/0.63 2803[5:SpR:2772.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.42/0.63 2807[5:Rew:2785.0,2803.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 2808[5:Rew:2807.0,2790.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.42/0.63 2816[5:Rew:2808.0,2774.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 2817[5:Rew:2816.0,2208.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 2819[5:Rew:2816.0,2217.0] || -> equal(multiply(sk_c12,sk_c10),sk_c12)**.
% 0.42/0.63 2825[5:Rew:2816.0,2221.1] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** -> .
% 0.42/0.63 2831[5:Rew:2807.0,2819.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 2863[5:Rew:2816.0,2825.8,2816.0,2825.7,2816.0,2825.6,2816.0,2825.5,2831.0,2825.5,2816.0,2825.4] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c12)** equal(multiply(w,sk_c12),sk_c12)** equal(multiply(x,sk_c12),sk_c12)** equal(multiply(v,sk_c12),sk_c12)** equal(multiply(y,sk_c12),sk_c12)** -> .
% 0.42/0.63 2864[5:Con:2863.2] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(multiply(u,v),sk_c12)** equal(multiply(w,sk_c12),sk_c12)** equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.42/0.63 2907[5:SpR:2807.0,180.0] || -> equal(identity,sk_c12)**.
% 0.42/0.63 2910[5:Rew:2907.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.42/0.63 2917[5:Rew:2910.0,2864.3] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(multiply(u,v),sk_c12)** equal(w,sk_c12) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.42/0.63 2921[5:Rew:2910.0,2917.4] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(multiply(u,v),sk_c12)**+ equal(w,sk_c12) equal(v,sk_c12) -> .
% 0.42/0.63 3026[5:SpL:2807.0,2921.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 3028[5:Obv:3026.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.42/0.63 3029[5:Rew:2817.0,3028.0] || equal(sk_c12,u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12)* -> .
% 0.42/0.63 3030[5:Obv:3029.0] || equal(inverse(u),sk_c12)** equal(u,sk_c12) equal(v,sk_c12)* -> .
% 0.42/0.63 3031[5:Con:3030.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.42/0.63 3037[5:SpL:2817.0,3031.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.42/0.63 3039[5:Obv:3037.1] || -> .
% 0.42/0.63 3040[4:Spt:3039.0,29.1,2227.0] || equal(inverse(sk_c1),sk_c12)** -> .
% 0.42/0.63 3041[4:Spt:3039.0,29.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.42/0.63 3043[4:MRR:26.1,3040.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.42/0.63 3045[4:MRR:22.1,3040.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.42/0.63 3048[4:MRR:25.0,3040.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.42/0.63 3050[4:MRR:21.0,3040.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.42/0.63 3061[4:SpR:3043.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.42/0.63 3066[4:SpR:3045.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.42/0.63 3079[4:SpR:3048.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.42/0.63 3083[4:Rew:3061.0,3079.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.42/0.63 3084[4:Rew:3083.0,3066.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.42/0.63 3090[4:Rew:3084.0,3050.0] || -> equal(sk_c11,sk_c12)**.
% 0.42/0.63 3091[4:Rew:3090.0,2208.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.42/0.63 3093[4:Rew:3090.0,2217.0] || -> equal(multiply(sk_c12,sk_c10),sk_c12)**.
% 0.42/0.63 3099[4:Rew:3090.0,2221.1] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(x,sk_c12),sk_c11)** equal(multiply(v,sk_c12),sk_c11)** equal(multiply(y,sk_c11),sk_c12)** -> .
% 0.42/0.63 3105[4:Rew:3083.0,3093.0] || -> equal(sk_c10,sk_c12)**.
% 0.42/0.63 3137[4:Rew:3090.0,3099.8,3090.0,3099.7,3090.0,3099.6,3090.0,3099.5,3105.0,3099.5,3090.0,3099.4] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(inverse(x),sk_c12) equal(inverse(y),sk_c12) equal(multiply(u,v),sk_c12)** equal(multiply(w,sk_c12),sk_c12)** equal(multiply(x,sk_c12),sk_c12)** equal(multiply(v,sk_c12),sk_c12)** equal(multiply(y,sk_c12),sk_c12)** -> .
% 0.42/0.63 3138[4:Con:3137.2] || equal(inverse(u),v) equal(inverse(w),sk_c12) equal(multiply(u,v),sk_c12)** equal(multiply(w,sk_c12),sk_c12)** equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.48/0.64 3181[4:SpR:3083.0,180.0] || -> equal(identity,sk_c12)**.
% 0.48/0.64 3185[4:Rew:3181.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.64 3191[4:Rew:3185.0,3138.3] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(multiply(u,v),sk_c12)** equal(w,sk_c12) equal(multiply(v,sk_c12),sk_c12)** -> .
% 0.48/0.64 3195[4:Rew:3185.0,3191.4] || equal(inverse(u),v) equal(inverse(w),sk_c12)** equal(multiply(u,v),sk_c12)**+ equal(w,sk_c12) equal(v,sk_c12) -> .
% 0.48/0.64 3235[4:SpL:3083.0,3195.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(u,sk_c12) equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.48/0.64 3237[4:Obv:3235.2] || equal(inverse(sk_c12),u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12) -> .
% 0.48/0.64 3238[4:Rew:3091.0,3237.0] || equal(sk_c12,u)* equal(inverse(v),sk_c12)** equal(v,sk_c12) equal(u,sk_c12)* -> .
% 0.48/0.64 3239[4:Obv:3238.0] || equal(inverse(u),sk_c12)** equal(u,sk_c12) equal(v,sk_c12)* -> .
% 0.48/0.64 3240[4:Con:3239.2] || equal(inverse(u),sk_c12)** equal(u,sk_c12) -> .
% 0.48/0.64 3268[4:SpL:3091.0,3240.0] || equal(sk_c12,sk_c12)* equal(sk_c12,sk_c12)* -> .
% 0.48/0.64 3270[4:Obv:3268.1] || -> .
% 0.48/0.64 3271[3:Spt:3270.0,18.1,2217.0] || equal(multiply(sk_c11,sk_c10),sk_c12)** -> .
% 0.48/0.64 3272[3:Spt:3270.0,18.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.48/0.64 3273[3:MRR:16.1,3271.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.64 3274[3:MRR:14.1,3271.0] || -> equal(inverse(sk_c5),sk_c11)**.
% 0.48/0.64 3275[3:MRR:12.1,3271.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.64 3279[3:MRR:15.1,3271.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.64 3280[3:MRR:13.1,3271.0] || -> equal(multiply(sk_c5,sk_c11),sk_c10)**.
% 0.48/0.64 3281[3:MRR:11.1,3271.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.64 3286[3:SpR:3273.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.48/0.64 3292[3:SpR:3274.0,2341.0] || -> equal(multiply(sk_c5,multiply(sk_c11,u)),u)**.
% 0.48/0.64 3294[3:SpR:3275.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.48/0.64 3307[3:SpR:3279.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.48/0.64 3311[3:Rew:3286.0,3307.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.64 3312[3:Rew:3311.0,3294.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.48/0.64 3317[3:Rew:3312.0,3281.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.64 3321[3:Rew:3317.0,3271.0] || equal(multiply(sk_c12,sk_c10),sk_c12)** -> .
% 0.48/0.64 3322[3:Rew:3317.0,3292.0] || -> equal(multiply(sk_c5,multiply(sk_c12,u)),u)**.
% 0.48/0.64 3323[3:Rew:3317.0,3280.0] || -> equal(multiply(sk_c5,sk_c12),sk_c10)**.
% 0.48/0.64 3340[3:Rew:3311.0,3321.0] || equal(sk_c10,sk_c12)** -> .
% 0.48/0.64 3343[3:Rew:3311.0,3322.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.48/0.64 3344[3:Rew:3343.0,3323.0] || -> equal(sk_c10,sk_c12)**.
% 0.48/0.64 3345[3:MRR:3344.0,3340.0] || -> .
% 0.48/0.64 3359[2:Spt:3345.0,8.1,2208.0] || equal(inverse(sk_c12),sk_c11)** -> .
% 0.48/0.64 3360[2:Spt:3345.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.48/0.64 3361[2:MRR:6.1,3359.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.48/0.64 3363[2:MRR:2.1,3359.0] || -> equal(inverse(sk_c4),sk_c12)**.
% 0.48/0.64 3364[2:MRR:9.1,3359.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.48/0.64 3365[2:MRR:10.0,3359.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.48/0.64 3366[2:MRR:7.0,3359.0] || -> equal(multiply(sk_c9,sk_c11),sk_c12)**.
% 0.48/0.64 3367[2:MRR:5.0,3359.0] || -> equal(multiply(sk_c6,sk_c9),sk_c12)**.
% 0.48/0.64 3369[2:MRR:1.0,3359.0] || -> equal(multiply(sk_c4,sk_c12),sk_c11)**.
% 0.48/0.64 3374[2:SpR:3361.0,2341.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.48/0.64 3379[2:SpR:3363.0,122.0] || -> equal(multiply(sk_c12,multiply(sk_c4,u)),u)**.
% 0.48/0.64 3390[2:SpR:3366.0,122.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c11)**.
% 0.48/0.64 3392[2:SpR:3367.0,74.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c12,u))**.
% 0.48/0.64 3393[2:SpR:3367.0,122.0] || -> equal(multiply(inverse(sk_c6),sk_c12),sk_c9)**.
% 0.48/0.64 3395[2:Rew:3361.0,3393.0] || -> equal(multiply(sk_c9,sk_c12),sk_c9)**.
% 0.48/0.64 3396[2:Rew:3374.0,3392.0] || -> equal(multiply(sk_c12,u),u)**.
% 0.48/0.64 3397[2:Rew:3396.0,3379.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.48/0.64 3400[2:Rew:3397.0,3369.0] || -> equal(sk_c11,sk_c12)**.
% 0.48/0.64 3402[2:Rew:3400.0,3359.0] || equal(inverse(sk_c12),sk_c12)** -> .
% 0.48/0.64 3403[2:Rew:3400.0,3366.0] || -> equal(multiply(sk_c9,sk_c12),sk_c12)**.
% 0.48/0.64 3407[2:Rew:3400.0,3390.0] || -> equal(multiply(inverse(sk_c9),sk_c12),sk_c12)**.
% 0.48/0.64 3408[2:Rew:3395.0,3403.0] || -> equal(sk_c9,sk_c12)**.
% 0.48/0.64 3410[2:Rew:3408.0,3364.0] || -> equal(inverse(sk_c7),sk_c12)**.
% 0.48/0.64 3411[2:Rew:3408.0,3365.0] || -> equal(multiply(sk_c8,sk_c12),sk_c7)**.
% 0.48/0.64 3420[2:Rew:73.0,3407.0,3408.0,3407.0] || -> equal(identity,sk_c12)**.
% 0.48/0.64 3421[2:Rew:3420.0,180.0] || -> equal(multiply(u,sk_c12),u)**.
% 0.48/0.64 3427[2:Rew:3421.0,3411.0] || -> equal(sk_c7,sk_c8)**.
% 0.48/0.64 3430[2:Rew:3427.0,3360.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.48/0.64 3433[2:Rew:3427.0,3410.0] || -> equal(inverse(sk_c8),sk_c12)**.
% 0.48/0.64 3436[2:Rew:3430.0,3433.0] || -> equal(sk_c8,sk_c12)**.
% 0.48/0.64 3438[2:Rew:3436.0,3430.0] || -> equal(inverse(sk_c12),sk_c12)**.
% 0.48/0.64 3439[2:MRR:3438.0,3402.0] || -> .
% 0.48/0.64 % SZS output end Refutation
% 0.48/0.64 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_10 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_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_29 prove_this_31 prove_this_32 prove_this_35 prove_this_36 prove_this_39 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_49 prove_this_51 prove_this_52 prove_this_53 prove_this_54 prove_this_55 prove_this_56 prove_this_57 prove_this_59 prove_this_71 left_identity left_inverse associativity
% 0.48/0.64
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