TSTP Solution File: GRP236-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP236-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:27 EDT 2022
% Result : Unsatisfiable 0.15s 0.42s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP236-1 : TPTP v8.1.0. Released v2.5.0.
% 0.05/0.10 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n022.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon Jun 13 09:29:48 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.42
% 0.15/0.42 SPASS V 3.9
% 0.15/0.42 SPASS beiseite: Proof found.
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 SPASS derived 848 clauses, backtracked 330 clauses, performed 11 splits and kept 602 clauses.
% 0.15/0.42 SPASS allocated 63693 KBytes.
% 0.15/0.42 SPASS spent 0:00:00.11 on the problem.
% 0.15/0.42 0:00:00.03 for the input.
% 0.15/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.42 0:00:00.01 for inferences.
% 0.15/0.42 0:00:00.00 for the backtracking.
% 0.15/0.42 0:00:00.05 for the reduction.
% 0.15/0.42
% 0.15/0.42
% 0.15/0.42 Here is a proof with depth 5, length 302 :
% 0.15/0.42 % SZS output start Refutation
% 0.15/0.42 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.15/0.42 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.15/0.42 3[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.15/0.42 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.42 5[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.15/0.42 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.15/0.42 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 8[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.15/0.42 9[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.15/0.42 10[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.15/0.42 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 13[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 14[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c3),sk_c7).
% 0.15/0.42 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 18[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.15/0.42 19[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.42 20[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.15/0.42 21[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 23[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.15/0.42 27[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,w),sk_c7)** equal(inverse(v),w) equal(multiply(w,sk_c8),sk_c7)** equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.15/0.42 28[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.15/0.42 29[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.15/0.42 30[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.15/0.42 31[0:Con:27.6] || equal(inverse(sk_c8),sk_c7) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,w),sk_c7)** equal(inverse(v),w) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.15/0.42 32[0:Rew:1.0,31.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,w),sk_c7)** equal(inverse(v),w) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.15/0.42 33[0:Obv:32.0] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(u,v),sk_c7)**+ equal(multiply(w,sk_c8),y)* equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** -> .
% 0.15/0.42 34[1:Spt:33.0,33.3,33.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.15/0.42 35[2:Spt:21.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.15/0.42 37[3:Spt:17.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.15/0.42 40[4:Spt:20.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.15/0.42 42[4:SpL:40.0,34.1] || equal(inverse(sk_c5),sk_c8) equal(sk_c6,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 43[4:Rew:35.0,42.0] || equal(sk_c8,sk_c8) equal(sk_c6,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 44[4:Obv:43.0] || equal(sk_c6,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 45[5:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.42 50[6:Spt:18.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.15/0.42 52[6:SpL:50.0,34.1] || equal(inverse(sk_c4),sk_c7) equal(sk_c8,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.15/0.42 53[6:Rew:37.0,52.0] || equal(sk_c8,sk_c7) equal(sk_c8,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.15/0.42 54[6:Obv:53.0] || equal(sk_c8,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.15/0.42 58[2:SpR:35.0,29.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.15/0.42 59[3:SpR:37.0,29.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.15/0.42 60[0:SpR:1.0,29.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.15/0.42 62[6:Rew:60.0,54.1] || equal(sk_c8,sk_c7)** equal(identity,sk_c7) -> .
% 0.15/0.42 64[2:SpL:58.0,34.1] || equal(inverse(sk_c8),sk_c5) equal(identity,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.15/0.42 70[2:SpR:58.0,30.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.15/0.42 71[6:SpR:50.0,30.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.15/0.42 73[0:SpR:29.0,30.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.15/0.42 75[2:Rew:28.0,70.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.15/0.42 76[0:Rew:28.0,73.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.15/0.42 83[0:SpR:60.0,30.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.15/0.42 85[1:SpL:60.0,34.1] || equal(inverse(sk_c7),sk_c8) equal(identity,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 86[0:Rew:28.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.15/0.42 89[4:SpR:40.0,75.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.15/0.42 91[5:Rew:45.0,89.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.42 95[5:Rew:91.0,1.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.15/0.42 97[5:Rew:91.0,45.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.15/0.42 100[5:Rew:91.0,59.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.15/0.42 101[5:Rew:91.0,60.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.15/0.42 108[6:Rew:91.0,62.0] || equal(sk_c7,sk_c7) equal(identity,sk_c7)** -> .
% 0.15/0.42 110[6:Rew:91.0,71.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.15/0.42 111[5:Rew:91.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.15/0.42 116[6:Obv:108.0] || equal(identity,sk_c7)** -> .
% 0.15/0.42 145[0:SpR:76.0,76.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.15/0.42 148[0:SpR:29.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.15/0.42 152[5:SpR:97.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.15/0.42 154[5:SpR:100.0,76.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.15/0.42 162[5:Rew:101.0,152.0,95.0,152.0] || -> equal(identity,sk_c6)**.
% 0.15/0.42 165[6:Rew:162.0,116.0] || equal(sk_c6,sk_c7)** -> .
% 0.15/0.42 168[5:Rew:162.0,101.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.15/0.42 181[5:Rew:95.0,154.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.15/0.42 182[5:Rew:162.0,181.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.15/0.42 183[5:Rew:97.0,182.0] || -> equal(sk_c4,sk_c7)**.
% 0.15/0.42 187[6:Rew:183.0,110.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.15/0.42 198[6:Rew:111.0,187.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.42 199[6:Rew:198.0,168.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.42 201[6:MRR:199.0,165.0] || -> .
% 0.15/0.42 205[6:Spt:201.0,18.1,50.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.15/0.42 206[6:Spt:201.0,18.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 207[6:Rew:91.0,205.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.15/0.42 208[6:Rew:168.0,207.0,183.0,207.0] || equal(sk_c6,sk_c7)** -> .
% 0.15/0.42 212[5:Rew:91.0,23.1,91.0,23.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.15/0.42 213[5:Rew:168.0,212.0,183.0,212.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.15/0.42 214[6:MRR:213.0,208.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.15/0.42 215[5:Rew:91.0,13.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 216[5:Rew:168.0,215.0,183.0,215.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 217[6:MRR:216.0,208.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 241[6:SpR:214.0,30.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.15/0.42 245[6:SpR:217.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.15/0.42 247[6:Rew:214.0,245.0,206.0,245.0] || -> equal(sk_c3,sk_c7)**.
% 0.15/0.42 253[6:Rew:247.0,241.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.15/0.42 259[6:Rew:111.0,253.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.42 260[6:Rew:259.0,168.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.42 266[6:MRR:260.0,208.0] || -> .
% 0.15/0.42 269[5:Spt:266.0,19.1,45.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.15/0.42 270[5:Spt:266.0,19.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 271[5:Rew:89.0,269.0] || equal(sk_c8,sk_c7)** -> .
% 0.15/0.42 272[0:Rew:145.0,148.0] || -> equal(multiply(u,identity),u)**.
% 0.15/0.42 273[4:Rew:89.0,4.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c7).
% 0.15/0.42 274[5:MRR:273.1,271.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.42 277[4:Rew:89.0,14.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 278[5:MRR:277.0,271.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 279[4:Rew:89.0,9.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 280[5:MRR:279.0,271.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 296[4:SpR:89.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.42 298[4:Rew:1.0,296.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.15/0.42 299[4:Rew:60.0,298.0] || -> equal(identity,sk_c6)**.
% 0.15/0.42 304[4:Rew:299.0,29.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.15/0.42 325[5:SpR:278.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.15/0.42 327[5:Rew:270.0,325.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.15/0.42 329[5:SpR:280.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.15/0.42 331[5:Rew:274.0,329.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.15/0.42 332[5:Rew:331.0,44.1] || equal(sk_c6,sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.15/0.42 333[5:Obv:332.1] || equal(sk_c6,sk_c7)** -> .
% 0.15/0.42 382[5:SpR:327.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.15/0.42 384[5:Rew:304.0,382.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.42 385[5:MRR:384.0,333.0] || -> .
% 0.15/0.42 386[4:Spt:385.0,20.1,40.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.15/0.42 387[4:Spt:385.0,20.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 390[4:MRR:15.0,386.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 392[2:Rew:1.0,64.0] || equal(sk_c5,sk_c7) equal(identity,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.15/0.42 402[2:SpR:58.0,76.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.15/0.42 404[2:Rew:1.0,402.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.15/0.42 405[2:Rew:272.0,404.0] || -> equal(sk_c5,sk_c7)**.
% 0.15/0.42 409[2:Rew:405.0,392.2] || equal(sk_c5,sk_c7) equal(identity,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.15/0.42 415[2:Rew:60.0,409.2,405.0,409.0] || equal(sk_c7,sk_c7) equal(identity,sk_c7)** equal(identity,sk_c7)** -> .
% 0.15/0.42 416[2:Obv:415.1] || equal(identity,sk_c7)** -> .
% 0.15/0.42 436[0:SpR:60.0,76.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c8)**.
% 0.15/0.42 441[4:SpR:390.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.15/0.42 443[4:Rew:387.0,441.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.15/0.42 457[4:SpR:443.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.15/0.42 459[4:Rew:29.0,457.0] || -> equal(identity,sk_c7)**.
% 0.15/0.42 460[4:MRR:459.0,416.0] || -> .
% 0.15/0.42 461[3:Spt:460.0,17.0,37.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.15/0.42 462[3:Spt:460.0,17.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 465[3:MRR:12.0,461.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 475[3:SpR:465.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.15/0.42 477[3:Rew:462.0,475.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.15/0.42 483[3:SpR:477.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.15/0.42 485[3:Rew:29.0,483.0] || -> equal(identity,sk_c7)**.
% 0.15/0.42 486[3:MRR:485.0,416.0] || -> .
% 0.15/0.42 487[2:Spt:486.0,21.0,35.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.15/0.42 488[2:Spt:486.0,21.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 489[0:Rew:272.0,436.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.15/0.42 490[2:MRR:6.0,487.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.42 492[2:MRR:16.0,487.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 493[2:MRR:11.0,487.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 494[1:Rew:489.0,85.0] || equal(sk_c8,sk_c8) equal(identity,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 495[1:Obv:494.0] || equal(identity,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.15/0.42 506[2:SpR:492.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.15/0.42 508[2:Rew:488.0,506.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.15/0.42 510[2:SpR:493.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.15/0.42 512[2:Rew:490.0,510.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.15/0.42 513[2:Rew:512.0,495.1] || equal(identity,sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.15/0.42 514[2:Obv:513.1] || equal(identity,sk_c7)** -> .
% 0.15/0.42 516[0:SpR:29.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.15/0.42 522[0:Rew:272.0,516.0] || -> equal(inverse(inverse(u)),u)**.
% 0.15/0.42 526[2:SpR:508.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.15/0.42 528[2:Rew:29.0,526.0] || -> equal(identity,sk_c7)**.
% 0.15/0.42 529[2:MRR:528.0,514.0] || -> .
% 0.15/0.42 530[1:Spt:529.0,33.1,33.2,33.4,33.6,33.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.15/0.42 533[1:SpL:60.0,530.2] || equal(inverse(sk_c7),sk_c8) equal(inverse(u),sk_c8) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.42 536[1:Rew:489.0,533.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.42 537[1:Obv:536.0] || equal(inverse(u),sk_c8) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.42 538[2:Spt:17.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.15/0.42 542[3:Spt:6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.15/0.42 546[4:Spt:18.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.15/0.42 548[4:SpR:546.0,76.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.15/0.42 550[4:Rew:538.0,548.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.15/0.42 556[5:Spt:19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.42 558[5:SpR:556.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.42 560[5:Rew:1.0,558.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.15/0.42 561[6:Spt:5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.15/0.42 563[6:SpR:561.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.15/0.42 566[6:Rew:556.0,563.0,542.0,563.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.42 567[6:Rew:566.0,1.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.15/0.42 568[6:Rew:566.0,60.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.15/0.42 580[6:Rew:566.0,537.0] || equal(inverse(u),sk_c7) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.42 588[6:Rew:566.0,550.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.15/0.42 590[6:Rew:560.0,568.0] || -> equal(identity,sk_c6)**.
% 0.15/0.42 591[6:Rew:590.0,28.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.42 593[6:Rew:590.0,272.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.42 598[6:Rew:560.0,588.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.42 600[6:Rew:598.0,590.0] || -> equal(identity,sk_c7)**.
% 0.15/0.42 605[6:Rew:598.0,591.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.42 606[6:Rew:598.0,593.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.15/0.42 622[6:Rew:605.0,580.3,566.0,580.3,606.0,580.2,566.0,580.2,600.0,580.1] || equal(inverse(u),sk_c7)** equal(sk_c7,v)* equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.42 623[6:Obv:622.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.42 624[6:Con:623.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.15/0.42 643[0:SpR:522.0,76.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.15/0.42 691[6:SpL:567.0,624.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.15/0.42 693[6:Obv:691.1] || -> .
% 0.15/0.42 694[6:Spt:693.0,5.1,561.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.15/0.42 695[6:Spt:693.0,5.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.42 696[6:MRR:20.1,694.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.42 698[6:MRR:15.0,694.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.42 699[6:MRR:10.0,694.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.42 701[6:SpR:695.0,522.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.15/0.42 704[6:Rew:1.0,701.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.42 706[6:Rew:704.0,699.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.42 707[6:Rew:560.0,706.0] || -> equal(sk_c8,sk_c6)**.
% 0.15/0.42 708[6:Rew:707.0,542.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.42 711[6:Rew:707.0,1.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.15/0.42 715[6:Rew:707.0,60.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.15/0.42 719[6:Rew:707.0,694.0] || equal(multiply(sk_c5,sk_c6),sk_c6)** -> .
% 0.15/0.43 743[6:SpR:696.0,643.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.15/0.43 746[6:SpR:708.0,522.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.15/0.43 749[6:Rew:711.0,746.0] || -> equal(sk_c5,sk_c7)**.
% 0.15/0.43 752[6:Rew:749.0,719.0] || equal(multiply(sk_c7,sk_c6),sk_c6)** -> .
% 0.15/0.43 754[6:Rew:715.0,752.0] || equal(identity,sk_c6)** -> .
% 0.15/0.43 787[6:SpR:698.0,30.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.15/0.43 791[6:Rew:743.0,787.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.43 792[6:Rew:791.0,560.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.43 795[6:Rew:791.0,715.0] || -> equal(identity,sk_c6)**.
% 0.15/0.43 801[6:Rew:792.0,754.0] || equal(identity,sk_c7)** -> .
% 0.15/0.43 810[6:Rew:792.0,795.0] || -> equal(identity,sk_c7)**.
% 0.15/0.43 815[6:Rew:810.0,801.0] || equal(sk_c7,sk_c7)* -> .
% 0.15/0.43 816[6:Obv:815.0] || -> .
% 0.15/0.43 845[5:Spt:816.0,19.1,556.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.15/0.43 846[5:Spt:816.0,19.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.43 847[5:MRR:4.1,845.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.43 849[5:MRR:14.0,845.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.43 850[5:MRR:9.0,845.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.43 853[5:SpR:846.0,643.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.15/0.43 860[5:SpR:847.0,522.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.15/0.43 863[5:Rew:1.0,860.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.43 865[5:Rew:863.0,850.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.43 874[2:SpR:538.0,522.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.15/0.43 877[2:Rew:1.0,874.0] || -> equal(sk_c4,sk_c7)**.
% 0.15/0.43 909[5:SpR:849.0,30.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.15/0.43 913[5:Rew:853.0,909.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.43 918[5:Rew:913.0,865.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.43 920[5:Rew:913.0,60.0] || -> equal(sk_c8,identity)**.
% 0.15/0.43 921[5:Rew:918.0,1.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.15/0.43 930[5:Rew:918.0,537.0] || equal(inverse(u),sk_c7) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.43 933[5:Rew:918.0,920.0] || -> equal(identity,sk_c7)**.
% 0.15/0.43 934[5:Rew:933.0,272.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.15/0.43 959[5:Rew:913.0,930.3,918.0,930.3,934.0,930.2,918.0,930.2,933.0,930.1] || equal(inverse(u),sk_c7)** equal(sk_c7,v)* equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 960[5:Obv:959.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 961[5:Con:960.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.15/0.43 1003[5:SpL:921.0,961.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.15/0.43 1004[5:Obv:1003.1] || -> .
% 0.15/0.43 1005[4:Spt:1004.0,18.1,546.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.15/0.43 1006[4:Spt:1004.0,18.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.43 1007[4:Rew:877.0,1005.0] || equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.15/0.43 1010[2:Rew:877.0,3.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.43 1011[4:MRR:1010.1,1007.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.43 1022[2:Rew:877.0,8.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.43 1023[4:MRR:1022.0,1007.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.43 1037[4:SpR:1011.0,522.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.15/0.43 1040[4:Rew:1.0,1037.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.43 1042[4:Rew:1040.0,1023.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.43 1043[4:MRR:1042.0,1007.0] || -> .
% 0.15/0.43 1046[3:Spt:1043.0,6.0,542.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.15/0.43 1047[3:Spt:1043.0,6.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.43 1048[3:MRR:21.0,1046.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.43 1050[3:MRR:16.0,1046.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.43 1051[3:MRR:11.0,1046.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.43 1053[3:SpR:1047.0,522.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.15/0.43 1056[3:Rew:1.0,1053.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.43 1058[3:Rew:1056.0,1051.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.43 1064[3:SpR:1048.0,643.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.15/0.43 1084[3:SpR:1050.0,30.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.15/0.43 1088[3:Rew:1064.0,1084.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.43 1089[3:Rew:1088.0,60.0] || -> equal(sk_c8,identity)**.
% 0.15/0.43 1092[3:Rew:1088.0,1058.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.43 1094[3:Rew:1089.0,489.0] || -> equal(inverse(sk_c7),identity)**.
% 0.15/0.43 1102[3:Rew:1089.0,537.0] || equal(inverse(u),identity) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.43 1105[3:Rew:1089.0,1092.0] || -> equal(identity,sk_c7)**.
% 0.15/0.43 1107[3:Rew:1105.0,272.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.15/0.43 1110[3:Rew:1105.0,1089.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.43 1111[3:Rew:1105.0,1094.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.15/0.43 1132[3:Rew:1088.0,1102.3,1110.0,1102.3,1107.0,1102.2,1110.0,1102.2,1105.0,1102.1,1105.0,1102.0] || equal(inverse(u),sk_c7)** equal(sk_c7,v)* equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 1133[3:Obv:1132.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 1134[3:Con:1133.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.15/0.43 1186[3:SpL:1111.0,1134.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.15/0.43 1187[3:Obv:1186.1] || -> .
% 0.15/0.43 1188[2:Spt:1187.0,17.0,538.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.15/0.43 1189[2:Spt:1187.0,17.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.15/0.43 1190[2:MRR:2.0,1188.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.43 1192[2:MRR:12.0,1188.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.15/0.43 1193[2:MRR:7.0,1188.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.15/0.43 1196[2:SpR:1189.0,643.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.15/0.43 1207[2:SpR:1190.0,522.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.15/0.43 1210[2:Rew:1.0,1207.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.43 1212[2:Rew:1210.0,1193.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.15/0.43 1234[2:SpR:1192.0,30.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.15/0.43 1238[2:Rew:1196.0,1234.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.15/0.43 1239[2:Rew:1238.0,60.0] || -> equal(sk_c8,identity)**.
% 0.15/0.43 1242[2:Rew:1238.0,1212.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.43 1244[2:Rew:1239.0,1.0] || -> equal(inverse(identity),sk_c7)**.
% 0.15/0.43 1252[2:Rew:1239.0,537.0] || equal(inverse(u),identity) equal(identity,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.15/0.43 1255[2:Rew:1239.0,1242.0] || -> equal(identity,sk_c7)**.
% 0.15/0.43 1256[2:Rew:1255.0,272.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.15/0.43 1260[2:Rew:1255.0,1239.0] || -> equal(sk_c8,sk_c7)**.
% 0.15/0.43 1261[2:Rew:1255.0,1244.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.15/0.43 1282[2:Rew:1238.0,1252.3,1260.0,1252.3,1256.0,1252.2,1260.0,1252.2,1255.0,1252.1,1255.0,1252.0] || equal(inverse(u),sk_c7)** equal(sk_c7,v)* equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 1283[2:Obv:1282.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(v,sk_c7)* -> .
% 0.15/0.43 1284[2:Con:1283.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.15/0.43 1336[2:SpL:1261.0,1284.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.15/0.43 1337[2:Obv:1336.1] || -> .
% 0.15/0.43 % SZS output end Refutation
% 0.15/0.43 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_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_23 prove_this_27 left_identity left_inverse associativity
% 0.15/0.43
%------------------------------------------------------------------------------