TSTP Solution File: GRP364-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP364-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:47:02 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP364-1 : TPTP v8.1.0. Released v2.5.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 03:01:54 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 1042 clauses, backtracked 520 clauses, performed 14 splits and kept 1010 clauses.
% 0.21/0.51 SPASS allocated 63731 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.51 0:00:00.04 for the input.
% 0.21/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.00 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.07 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 4, length 456 :
% 0.21/0.51 % SZS output start Refutation
% 0.21/0.51 1[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.21/0.51 2[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.21/0.51 3[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 4[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.21/0.51 5[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.21/0.51 6[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 9[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 10[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 11[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c9,sk_c2),sk_c8).
% 0.21/0.51 12[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 15[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 16[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 17[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 18[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 21[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 22[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.21/0.51 23[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.21/0.51 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 25[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 26[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 27[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 28[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 29[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 30[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 31[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.21/0.51 32[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.51 33[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 34[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.21/0.51 35[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.21/0.51 36[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 37[0:Inp] || equal(multiply(sk_c7,sk_c9),sk_c8) equal(multiply(sk_c9,u),sk_c8)** equal(multiply(v,sk_c9),u)* equal(inverse(v),sk_c9) equal(multiply(w,sk_c7),sk_c9)** equal(inverse(w),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(sk_c9,y),sk_c8)** equal(multiply(z,sk_c9),y)* equal(inverse(z),sk_c9) -> .
% 0.21/0.51 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.51 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.51 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.51 41[0:Con:37.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(w,sk_c9),x)*+ equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8) -> .
% 0.21/0.51 42[1:Spt:41.2,41.3,41.6] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)*+ equal(multiply(sk_c9,v),sk_c8)** -> .
% 0.21/0.51 44[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.21/0.51 46[3:Spt:6.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.21/0.51 48[4:Spt:3.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 50[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.21/0.51 56[1:SpL:38.0,42.1] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.21/0.51 57[6:Spt:4.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.21/0.51 59[7:Spt:2.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.51 65[3:SpR:46.0,39.0] || -> equal(multiply(sk_c9,sk_c5),identity)**.
% 0.21/0.51 66[4:SpR:48.0,39.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.21/0.51 67[1:SpL:39.0,42.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.21/0.51 76[3:SpR:65.0,40.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.51 77[4:SpR:66.0,40.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.51 79[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.51 81[3:Rew:38.0,76.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),u)**.
% 0.21/0.51 82[4:Rew:38.0,77.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),u)**.
% 0.21/0.51 83[0:Rew:38.0,79.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.51 87[5:SpR:50.0,81.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.21/0.51 88[6:Rew:57.0,87.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 90[6:Rew:88.0,44.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.51 91[6:Rew:88.0,57.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.21/0.51 92[7:Rew:88.0,59.0] || -> equal(multiply(sk_c4,sk_c9),sk_c9)**.
% 0.21/0.51 94[6:Rew:88.0,67.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.21/0.51 96[6:Rew:88.0,56.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.21/0.51 113[7:SpR:92.0,82.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.21/0.51 114[7:Rew:90.0,113.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 116[7:Rew:114.0,48.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.51 119[7:Rew:114.0,66.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.51 121[7:Rew:114.0,88.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 122[7:Rew:114.0,90.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.51 131[7:Rew:114.0,94.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 140[7:Rew:114.0,131.0] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 172[0:SpR:83.0,83.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.51 175[0:SpR:39.0,83.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.51 181[7:SpR:122.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 200[7:Rew:39.0,181.0] || -> equal(identity,sk_c7)**.
% 0.21/0.51 201[7:Rew:200.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 203[7:Rew:200.0,119.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.21/0.51 204[7:Rew:200.0,140.1] || equal(inverse(inverse(sk_c7)),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 212[7:Rew:201.0,203.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.51 213[7:Rew:212.0,116.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 237[7:Rew:201.0,204.2,213.0,204.0,213.0,204.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.21/0.51 238[7:Obv:237.1] || equal(u,sk_c7)* -> .
% 0.21/0.51 239[7:UnC:238.0,121.0] || -> .
% 0.21/0.51 241[7:Spt:239.0,2.0,59.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.21/0.51 242[7:Spt:239.0,2.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 243[7:Rew:88.0,242.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.21/0.51 244[7:Rew:88.0,241.0] || equal(multiply(sk_c4,sk_c9),sk_c9)** -> .
% 0.21/0.51 245[0:Rew:172.0,175.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.51 246[6:Rew:88.0,32.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c9),sk_c9)**.
% 0.21/0.51 247[7:MRR:246.1,244.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 250[6:Rew:88.0,26.0] || -> equal(multiply(sk_c4,sk_c9),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 251[7:MRR:250.0,244.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 267[7:SpR:251.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 269[7:Rew:247.0,267.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.21/0.51 270[7:Rew:243.0,269.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 271[7:Rew:270.0,88.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 275[7:Rew:270.0,251.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.51 276[7:Rew:270.0,91.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.51 277[7:Rew:270.0,90.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.51 291[7:Rew:270.0,96.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 299[7:Rew:270.0,291.1,270.0,291.0] || equal(inverse(identity),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 316[7:SpR:276.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.51 318[7:Rew:39.0,316.0] || -> equal(identity,sk_c6)**.
% 0.21/0.51 319[7:Rew:318.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.51 320[7:Rew:318.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.21/0.51 322[7:Rew:318.0,299.0] || equal(inverse(sk_c6),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 323[7:Rew:318.0,245.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.51 332[7:SpR:277.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 334[7:Rew:320.0,332.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 338[7:Rew:334.0,319.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 339[7:Rew:334.0,323.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 344[7:Rew:334.0,322.0] || equal(inverse(sk_c7),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.21/0.51 356[7:Rew:339.0,275.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 359[7:Rew:356.0,247.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 373[7:Rew:338.0,344.2,359.0,344.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.21/0.51 374[7:Obv:373.1] || equal(u,sk_c7)* -> .
% 0.21/0.51 375[7:UnC:374.0,271.0] || -> .
% 0.21/0.51 378[6:Spt:375.0,4.0,57.0] || equal(multiply(sk_c9,sk_c6),sk_c8)** -> .
% 0.21/0.51 379[6:Spt:375.0,4.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 380[6:Rew:87.0,378.0] || equal(sk_c8,sk_c9)** -> .
% 0.21/0.51 381[5:Rew:87.0,34.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c8,sk_c9).
% 0.21/0.51 382[6:MRR:381.1,380.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 383[5:Rew:87.0,22.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c9).
% 0.21/0.51 384[6:MRR:383.1,380.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 385[5:Rew:87.0,28.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 386[6:MRR:385.0,380.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 387[5:Rew:87.0,16.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 388[6:MRR:387.0,380.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 389[5:Rew:87.0,10.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 390[6:MRR:389.0,380.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 392[6:SpR:379.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 398[6:SpR:382.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.51 400[6:SpR:384.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 403[6:SpR:386.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 405[6:Rew:379.0,403.0,382.0,403.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 407[6:Rew:405.0,380.0] || equal(sk_c9,sk_c7)** -> .
% 0.21/0.51 411[6:Rew:405.0,390.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 418[6:Rew:405.0,392.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 419[6:Rew:39.0,418.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 422[6:Rew:419.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 423[6:Rew:419.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 426[6:Rew:422.0,388.0] || -> equal(sk_c1,sk_c2)**.
% 0.21/0.51 429[6:Rew:426.0,400.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.21/0.51 435[6:Rew:423.0,411.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 446[6:Rew:423.0,429.0,435.0,429.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 447[6:Rew:446.0,398.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 448[6:Rew:447.0,386.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 449[6:MRR:448.0,407.0] || -> .
% 0.21/0.51 462[5:Spt:449.0,5.0,50.0] || equal(multiply(sk_c5,sk_c9),sk_c6)** -> .
% 0.21/0.51 463[5:Spt:449.0,5.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 464[5:MRR:35.1,462.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 465[5:MRR:23.1,462.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 466[5:MRR:29.0,462.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 467[5:MRR:17.0,462.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 468[5:MRR:11.0,462.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 470[5:SpR:463.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 478[5:SpR:465.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 481[5:SpR:466.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 483[5:Rew:463.0,481.0,464.0,481.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 488[5:Rew:483.0,468.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 490[5:Rew:483.0,67.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c7)** -> .
% 0.21/0.51 494[5:Rew:483.0,470.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 495[5:Rew:39.0,494.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 496[5:Rew:495.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 498[5:Rew:495.0,66.0] || -> equal(multiply(sk_c9,sk_c4),sk_c9)**.
% 0.21/0.51 502[5:Rew:496.0,488.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 503[5:Rew:496.0,478.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.51 506[5:Rew:502.0,467.0] || -> equal(multiply(sk_c1,sk_c9),sk_c7)**.
% 0.21/0.51 508[5:Rew:496.0,498.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.51 509[5:Rew:508.0,48.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 515[5:Rew:503.0,506.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 518[5:Rew:515.0,495.0] || -> equal(identity,sk_c7)**.
% 0.21/0.51 519[5:Rew:515.0,496.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 522[5:Rew:515.0,509.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 538[5:Rew:519.0,490.2,515.0,490.2,518.0,490.1,522.0,490.0,522.0,490.0,515.0,490.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.21/0.51 539[5:Obv:538.1] || equal(u,sk_c7)* -> .
% 0.21/0.51 540[5:UnC:539.0,83.0] || -> .
% 0.21/0.51 543[4:Spt:540.0,3.0,48.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.51 544[4:Spt:540.0,3.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 545[4:MRR:33.0,543.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 546[4:MRR:21.0,543.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 547[4:MRR:27.0,543.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 548[4:MRR:15.0,543.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 549[4:MRR:9.0,543.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 551[4:SpR:544.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 555[4:SpR:545.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.51 557[4:SpR:546.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 574[4:SpR:547.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 576[4:Rew:544.0,574.0,545.0,574.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 581[4:Rew:576.0,549.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 584[4:Rew:576.0,56.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c7)** -> .
% 0.21/0.51 587[4:Rew:576.0,551.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 589[4:Rew:39.0,587.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 590[4:Rew:589.0,65.0] || -> equal(multiply(sk_c9,sk_c5),sk_c9)**.
% 0.21/0.51 591[4:Rew:589.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 592[4:Rew:589.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 595[4:Rew:591.0,548.0] || -> equal(sk_c1,sk_c2)**.
% 0.21/0.51 597[4:Rew:595.0,557.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.21/0.51 599[4:Rew:592.0,590.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 600[4:Rew:592.0,581.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 602[4:Rew:599.0,46.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 610[4:Rew:592.0,597.0,600.0,597.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 611[4:Rew:610.0,555.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 612[4:Rew:611.0,547.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 614[4:Rew:612.0,589.0] || -> equal(identity,sk_c7)**.
% 0.21/0.51 618[4:Rew:612.0,602.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 628[4:Rew:610.0,584.2,612.0,584.2,612.0,584.1,618.0,584.0,614.0,584.0,612.0,584.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.21/0.51 629[4:Obv:628.1] || equal(u,sk_c7)* -> .
% 0.21/0.51 630[4:UnC:629.0,545.0] || -> .
% 0.21/0.51 633[3:Spt:630.0,6.0,46.0] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.21/0.51 634[3:Spt:630.0,6.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 635[3:MRR:36.0,633.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 636[3:MRR:24.0,633.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 637[3:MRR:30.0,633.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 638[3:MRR:18.0,633.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 639[3:MRR:12.0,633.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 641[3:SpR:634.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 645[3:SpR:636.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 651[3:SpR:637.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 653[3:Rew:634.0,651.0,635.0,651.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 659[3:Rew:653.0,639.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 661[3:Rew:653.0,67.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c7)** -> .
% 0.21/0.51 665[3:Rew:653.0,641.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 666[3:Rew:39.0,665.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 667[3:Rew:666.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 668[3:Rew:666.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 671[3:Rew:667.0,659.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 672[3:Rew:667.0,645.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.51 673[3:Rew:671.0,638.0] || -> equal(multiply(sk_c1,sk_c9),sk_c7)**.
% 0.21/0.51 674[3:Rew:672.0,673.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 677[3:Rew:674.0,637.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.51 679[3:Rew:674.0,666.0] || -> equal(identity,sk_c7)**.
% 0.21/0.51 680[3:Rew:674.0,667.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 681[3:Rew:674.0,668.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 683[3:Rew:681.0,677.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 684[3:Rew:683.0,635.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 695[3:Rew:680.0,661.2,674.0,661.2,679.0,661.1,684.0,661.0,684.0,661.0,674.0,661.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.21/0.51 696[3:Obv:695.1] || equal(u,sk_c7)* -> .
% 0.21/0.51 697[3:UnC:696.0,83.0] || -> .
% 0.21/0.51 700[2:Spt:697.0,1.0,44.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.21/0.51 701[2:Spt:697.0,1.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 702[2:MRR:31.1,700.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 704[2:MRR:25.0,700.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 708[2:SpR:701.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 715[2:SpR:704.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 717[2:Rew:701.0,715.0,702.0,715.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 719[2:Rew:717.0,700.0] || equal(multiply(sk_c9,sk_c7),sk_c7)** -> .
% 0.21/0.51 726[2:Rew:717.0,708.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 728[2:Rew:39.0,726.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 730[2:Rew:728.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 736[2:UnC:730.0,719.0] || -> .
% 0.21/0.51 742[1:Spt:736.0,41.0,41.1,41.4,41.5,41.7,41.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c7),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8) -> .
% 0.21/0.51 744[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.21/0.51 745[2:Rew:744.0,742.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c9)** equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.21/0.51 747[2:Obv:745.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c9)** equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.21/0.51 750[2:SpR:744.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.21/0.51 752[3:Spt:3.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 754[3:Rew:752.0,747.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.21/0.51 755[3:Obv:754.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 758[3:SpR:752.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.51 760[4:Spt:36.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.21/0.51 763[5:Spt:33.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 769[6:Spt:35.1] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.21/0.51 770[6:SpR:769.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),multiply(sk_c6,u))**.
% 0.21/0.51 771[6:SpR:769.0,83.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.21/0.51 773[6:Rew:760.0,771.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.21/0.51 774[6:Rew:773.0,10.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 775[6:Rew:773.0,16.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 776[6:Rew:773.0,28.0] || -> equal(sk_c8,sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 777[6:Rew:773.0,22.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c9).
% 0.21/0.51 778[6:Rew:773.0,34.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c8,sk_c9).
% 0.21/0.51 780[6:Rew:778.1,32.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c9),sk_c9)**.
% 0.21/0.51 783[6:Rew:776.0,26.0] || -> equal(multiply(sk_c4,sk_c9),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 785[6:SpR:773.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c6)**.
% 0.21/0.51 787[6:Rew:39.0,785.0] || -> equal(identity,sk_c6)**.
% 0.21/0.51 788[6:Rew:787.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.51 789[6:Rew:787.0,245.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.51 790[6:Rew:787.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.21/0.51 792[6:Rew:788.0,770.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),u)**.
% 0.21/0.51 814[6:SpR:790.0,83.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.21/0.51 815[6:SpR:790.0,789.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.51 817[6:SpR:760.0,790.0] || -> equal(multiply(sk_c9,sk_c5),sk_c6)**.
% 0.21/0.51 818[6:SpR:763.0,790.0] || -> equal(multiply(sk_c9,sk_c4),sk_c6)**.
% 0.21/0.51 820[6:Rew:789.0,814.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.51 823[7:Spt:777.1] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 824[7:Rew:823.0,744.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.51 825[7:Rew:823.0,752.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.21/0.51 832[7:Rew:823.0,755.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 841[6:SpR:817.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c6),sk_c5)**.
% 0.21/0.51 843[6:Rew:789.0,841.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.21/0.51 851[6:SpR:818.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c6),sk_c4)**.
% 0.21/0.51 853[6:Rew:789.0,851.0,843.0,851.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.51 855[6:Rew:853.0,769.0] || -> equal(multiply(sk_c4,sk_c9),sk_c6)**.
% 0.21/0.51 857[6:Rew:853.0,843.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.51 859[6:Rew:853.0,792.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),u)**.
% 0.21/0.51 863[6:Rew:855.0,783.0] || -> equal(sk_c6,sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 865[6:Rew:855.0,780.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c9).
% 0.21/0.51 868[8:Spt:865.1] || -> equal(sk_c6,sk_c9)**.
% 0.21/0.51 870[8:Rew:868.0,788.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 871[8:Rew:868.0,789.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 873[8:Rew:868.0,815.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 876[8:Rew:857.0,873.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.51 877[8:Rew:876.0,763.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 884[8:Rew:870.0,824.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 891[8:Rew:884.0,832.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 897[8:Rew:884.0,877.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 899[8:Rew:884.0,871.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 908[8:Rew:899.0,891.3,884.0,891.3,899.0,891.2,884.0,891.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 909[8:Con:908.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 932[8:SpL:897.0,909.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 934[8:Obv:932.1] || -> .
% 0.21/0.51 935[8:Spt:934.0,865.1,868.0] || equal(sk_c6,sk_c9)** -> .
% 0.21/0.51 936[8:Spt:934.0,865.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 939[8:MRR:863.0,935.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 942[8:SpR:936.0,820.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.21/0.51 987[8:SpR:939.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.21/0.51 988[8:SpR:939.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 990[8:Rew:936.0,988.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.21/0.51 991[8:Rew:825.0,990.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 993[8:Rew:991.0,935.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.51 994[8:Rew:991.0,763.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.51 995[8:Rew:991.0,857.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.51 996[8:Rew:991.0,818.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.21/0.51 1002[8:Rew:991.0,859.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.21/0.51 1011[8:Rew:942.0,995.0] || -> equal(sk_c3,sk_c4)**.
% 0.21/0.51 1022[8:Rew:1002.0,987.0,1011.0,987.0,991.0,987.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1025[8:Rew:1022.0,996.0] || -> equal(sk_c6,sk_c4)**.
% 0.21/0.51 1027[8:Rew:1025.0,815.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.21/0.51 1032[8:Rew:1025.0,993.0] || equal(sk_c4,sk_c7)** -> .
% 0.21/0.51 1034[8:Rew:994.0,1027.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.51 1043[8:Rew:1034.0,1032.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1044[8:Obv:1043.0] || -> .
% 0.21/0.51 1056[7:Spt:1044.0,777.1,823.0] || equal(sk_c8,sk_c9)** -> .
% 0.21/0.51 1057[7:Spt:1044.0,777.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 1060[7:MRR:774.0,1056.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 1061[7:MRR:775.0,1056.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 1065[7:SpR:1057.0,820.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.21/0.51 1067[7:Rew:857.0,1065.0] || -> equal(sk_c1,sk_c4)**.
% 0.21/0.51 1069[7:Rew:1067.0,1061.0] || -> equal(multiply(sk_c4,sk_c9),sk_c2)**.
% 0.21/0.51 1070[7:Rew:855.0,1069.0] || -> equal(sk_c2,sk_c6)**.
% 0.21/0.51 1071[7:Rew:1070.0,1060.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.21/0.51 1072[7:Rew:789.0,1071.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 1073[7:MRR:1072.0,1056.0] || -> .
% 0.21/0.51 1075[6:Spt:1073.0,35.1,769.0] || equal(multiply(sk_c5,sk_c9),sk_c6)** -> .
% 0.21/0.51 1076[6:Spt:1073.0,35.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 1077[6:MRR:23.1,1075.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 1078[6:MRR:29.0,1075.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 1079[6:MRR:17.0,1075.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 1080[6:MRR:11.0,1075.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 1087[6:SpR:1077.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 1093[6:SpR:1078.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 1095[6:Rew:752.0,1093.0,1076.0,1093.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1098[6:Rew:1095.0,758.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 1103[6:Rew:1095.0,755.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 1106[6:Rew:1095.0,1080.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 1107[6:Rew:39.0,1098.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 1108[6:Rew:1107.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 1109[6:Rew:1107.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 1112[6:Rew:1108.0,1106.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 1113[6:Rew:1108.0,1087.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.51 1116[6:Rew:1112.0,1079.0] || -> equal(multiply(sk_c1,sk_c9),sk_c7)**.
% 0.21/0.51 1118[6:Rew:1113.0,1116.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 1122[6:Rew:1118.0,1078.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.51 1125[6:Rew:1118.0,1109.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1127[6:Rew:1125.0,1122.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 1128[6:Rew:1127.0,1076.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 1139[6:Rew:1125.0,1103.3,1118.0,1103.3,1125.0,1103.2,1118.0,1103.2,1118.0,1103.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 1140[6:Con:1139.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 1198[6:SpL:1128.0,1140.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1199[6:Obv:1198.1] || -> .
% 0.21/0.51 1200[5:Spt:1199.0,33.0,763.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.51 1201[5:Spt:1199.0,33.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 1202[5:MRR:21.0,1200.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 1203[5:MRR:27.0,1200.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 1204[5:MRR:15.0,1200.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 1205[5:MRR:9.0,1200.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 1206[5:SpR:1201.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.51 1210[5:SpR:1202.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 1219[5:SpR:1203.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 1221[5:Rew:752.0,1219.0,1201.0,1219.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1225[5:Rew:1221.0,758.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 1230[5:Rew:1221.0,1205.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 1231[5:Rew:1221.0,755.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 1233[5:Rew:39.0,1225.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 1234[5:Rew:1233.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 1235[5:Rew:1233.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 1238[5:Rew:1234.0,1204.0] || -> equal(sk_c1,sk_c2)**.
% 0.21/0.51 1239[5:Rew:1238.0,1202.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.21/0.51 1240[5:Rew:1238.0,1210.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.21/0.51 1241[5:Rew:1235.0,1230.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 1244[5:Rew:1241.0,1239.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.21/0.51 1245[5:Rew:1235.0,1240.0,1241.0,1240.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1246[5:Rew:1245.0,1206.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 1247[5:Rew:1246.0,1203.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 1251[5:Rew:1247.0,1234.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1253[5:Rew:1247.0,1244.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 1263[5:Rew:1251.0,1231.3,1247.0,1231.3,1251.0,1231.2,1247.0,1231.2,1247.0,1231.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 1264[5:Con:1263.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 1306[5:SpL:1253.0,1264.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1307[5:Obv:1306.1] || -> .
% 0.21/0.51 1308[4:Spt:1307.0,36.0,760.0] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.21/0.51 1309[4:Spt:1307.0,36.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.51 1310[4:MRR:24.0,1308.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 1311[4:MRR:30.0,1308.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.51 1312[4:MRR:18.0,1308.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.21/0.51 1313[4:MRR:12.0,1308.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.21/0.51 1316[4:SpR:1310.0,83.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 1325[4:SpR:1311.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.51 1327[4:Rew:752.0,1325.0,1309.0,1325.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1330[4:Rew:1327.0,758.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.51 1336[4:Rew:1327.0,1313.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.21/0.51 1337[4:Rew:1327.0,755.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c7),sk_c9)** -> .
% 0.21/0.51 1339[4:Rew:39.0,1330.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 1340[4:Rew:1339.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 1341[4:Rew:1339.0,245.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 1344[4:Rew:1340.0,1336.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.51 1345[4:Rew:1340.0,1316.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.51 1346[4:Rew:1344.0,1312.0] || -> equal(multiply(sk_c1,sk_c9),sk_c7)**.
% 0.21/0.51 1347[4:Rew:1345.0,1346.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 1350[4:Rew:1347.0,1311.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.51 1353[4:Rew:1347.0,1341.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1355[4:Rew:1353.0,1350.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 1356[4:Rew:1355.0,1309.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 1367[4:Rew:1353.0,1337.3,1347.0,1337.3,1353.0,1337.2,1347.0,1337.2,1347.0,1337.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 1368[4:Con:1367.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 1414[4:SpL:1356.0,1368.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1416[4:Obv:1414.1] || -> .
% 0.21/0.51 1417[3:Spt:1416.0,3.1,752.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.21/0.51 1418[3:Spt:1416.0,3.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 1419[3:MRR:6.1,1417.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.21/0.51 1420[3:MRR:2.1,1417.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.51 1421[3:MRR:4.1,1417.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.21/0.51 1422[3:MRR:5.1,1417.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.21/0.51 1431[3:SpR:1420.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.21/0.51 1433[3:Rew:744.0,1431.0,1418.0,1431.0] || -> equal(sk_c9,sk_c7)**.
% 0.21/0.51 1435[3:Rew:1433.0,1419.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.51 1438[3:Rew:1433.0,750.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.51 1440[3:Rew:1433.0,1417.0] || equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.21/0.51 1442[3:Rew:1433.0,1421.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.21/0.51 1443[3:Rew:1433.0,1422.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 1446[3:Rew:39.0,1438.0] || -> equal(identity,sk_c8)**.
% 0.21/0.51 1448[3:Rew:1446.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 1471[3:SpR:1443.0,83.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.21/0.51 1473[3:Rew:1442.0,1471.0,1435.0,1471.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1478[3:Rew:1473.0,1448.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1479[3:Rew:1473.0,1440.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.21/0.51 1495[3:Rew:1478.0,1479.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1496[3:Obv:1495.0] || -> .
% 0.21/0.51 1503[2:Spt:1496.0,1.0,744.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.21/0.52 1504[2:Spt:1496.0,1.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.52 1505[2:MRR:31.1,1503.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.52 1507[2:MRR:25.0,1503.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.52 1511[2:SpR:1504.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.21/0.52 1518[2:SpR:1507.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.52 1520[2:Rew:1504.0,1518.0,1505.0,1518.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.52 1522[2:Rew:1520.0,1503.0] || equal(multiply(sk_c9,sk_c7),sk_c7)** -> .
% 0.21/0.52 1524[2:Rew:1520.0,1511.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.21/0.52 1526[2:Rew:39.0,1524.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1527[2:Rew:1526.0,38.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1531[2:UnC:1527.0,1522.0] || -> .
% 0.21/0.52 % SZS output end Refutation
% 0.21/0.52 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.21/0.52
%------------------------------------------------------------------------------