TSTP Solution File: GRP286-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP286-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:46:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP286-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 16:15:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 737 clauses, backtracked 303 clauses, performed 11 splits and kept 634 clauses.
% 0.19/0.47 SPASS allocated 63586 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.05 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 3, length 317 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.47 4[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 7[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 8[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 10[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 11[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 15[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.47 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.47 19[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 20[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 21[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 22[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 23[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 25[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 28[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 29[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 31[0:Inp] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c8),y)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 35[1:Spt:31.2,31.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.19/0.47 36[2:Spt:1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 38[2:SpL:36.0,35.1] || equal(inverse(sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 39[2:Obv:38.1] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.47 40[3:Spt:25.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 44[4:Spt:19.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 46[4:SpL:44.0,35.1] || equal(inverse(sk_c2),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 47[4:Obv:46.1] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.47 48[4:Rew:40.0,47.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 49[4:Obv:48.0] || -> .
% 0.19/0.47 50[4:Spt:49.0,19.1,44.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.19/0.47 51[4:Spt:49.0,19.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 52[4:MRR:24.1,50.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 53[4:MRR:21.1,50.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 54[4:MRR:23.1,50.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 55[4:MRR:22.1,50.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 56[4:MRR:20.1,50.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 63[4:SpL:56.0,35.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.19/0.47 64[4:Rew:53.0,63.0] || equal(sk_c7,sk_c7) equal(sk_c6,sk_c8)** -> .
% 0.19/0.47 65[4:Obv:64.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.47 71[4:SpR:52.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 72[4:SpR:53.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 86[4:SpR:71.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 88[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 90[4:SpR:72.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.47 93[4:Rew:32.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.47 95[4:Rew:32.0,90.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.47 96[0:Rew:32.0,88.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 103[4:SpR:54.0,93.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 104[4:Rew:55.0,103.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 106[4:Rew:104.0,36.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 112[4:Rew:104.0,56.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 123[4:Rew:104.0,95.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.19/0.47 151[4:SpR:112.0,123.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.47 152[4:Rew:106.0,151.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 153[4:MRR:152.0,65.0] || -> .
% 0.19/0.47 155[3:Spt:153.0,25.0,40.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.47 156[3:Spt:153.0,25.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 157[3:MRR:30.1,155.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 158[3:MRR:27.1,155.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 159[3:MRR:29.0,155.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 160[3:MRR:28.0,155.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 161[3:MRR:26.0,155.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 164[3:SpR:157.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 166[3:SpR:158.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 183[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 186[0:SpR:33.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 189[3:SpR:159.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 191[3:SpR:160.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c5)**.
% 0.19/0.47 192[3:SpR:164.0,96.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.19/0.47 194[3:SpR:166.0,96.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 197[3:Rew:160.0,189.0,157.0,189.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 199[3:Rew:197.0,158.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 200[3:Rew:197.0,39.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.19/0.47 204[3:Rew:197.0,161.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 217[3:Rew:197.0,191.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.47 218[3:Rew:33.0,217.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 219[3:Rew:218.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 221[3:Rew:218.0,164.0] || -> equal(multiply(sk_c8,sk_c4),sk_c5)**.
% 0.19/0.47 225[3:Rew:218.0,192.0] || -> equal(multiply(inverse(sk_c8),sk_c5),sk_c4)**.
% 0.19/0.47 229[3:Rew:225.0,194.0,197.0,194.0,218.0,194.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.47 231[3:Rew:229.0,159.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.19/0.47 233[3:Rew:229.0,221.0] || -> equal(multiply(sk_c8,sk_c3),sk_c5)**.
% 0.19/0.47 235[3:Rew:204.0,231.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.47 238[3:Rew:235.0,219.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 240[3:Rew:235.0,233.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 241[3:Rew:238.0,240.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.47 242[3:Rew:241.0,199.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 245[3:MRR:242.0,200.0] || -> .
% 0.19/0.47 269[2:Spt:245.0,1.1,36.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.47 270[2:Spt:245.0,1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 271[0:Rew:183.0,186.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 272[2:MRR:6.1,269.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 274[2:MRR:5.1,269.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 275[2:MRR:4.1,269.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 285[2:SpR:274.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 287[2:Rew:272.0,285.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 288[2:Rew:275.0,287.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 289[2:Rew:288.0,270.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 291[2:Rew:288.0,269.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.19/0.47 301[2:Rew:289.0,291.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 302[2:Obv:301.0] || -> .
% 0.19/0.47 306[1:Spt:302.0,31.0,31.1,31.3,31.4,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.47 307[1:EqR:306.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.47 309[2:Spt:1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 312[2:Rew:309.0,307.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(sk_c6,sk_c6) -> .
% 0.19/0.47 313[2:Obv:312.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.19/0.47 317[2:SpR:309.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.47 319[3:Spt:13.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 322[3:Rew:319.0,313.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 323[3:Obv:322.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 327[3:SpR:319.0,96.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.19/0.47 329[4:Spt:30.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 330[4:SpR:329.0,96.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.47 332[5:Spt:18.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.47 338[6:Spt:24.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 340[6:SpR:338.0,96.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.19/0.47 342[6:Rew:329.0,340.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 343[7:Spt:12.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 345[7:SpR:343.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.19/0.47 347[7:Rew:309.0,345.0,332.0,345.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 349[7:Rew:347.0,319.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.19/0.47 350[7:Rew:347.0,338.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 351[7:Rew:347.0,317.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.47 356[7:Rew:347.0,342.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.47 357[7:Rew:349.0,356.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 358[7:Rew:357.0,329.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 361[7:Rew:357.0,323.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 366[7:Rew:357.0,350.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.19/0.47 367[7:Rew:33.0,351.0,357.0,351.0] || -> equal(identity,sk_c8)**.
% 0.19/0.47 368[7:Rew:367.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 371[7:Rew:367.0,271.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 373[7:Rew:371.0,366.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.47 375[7:Rew:373.0,358.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 385[7:Rew:371.0,361.5,368.0,361.5,357.0,361.5,371.0,361.4,357.0,361.4,371.0,361.3,357.0,361.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(v,sk_c8) equal(w,sk_c8) equal(u,sk_c8) -> .
% 0.19/0.47 386[7:Con:385.0] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 423[7:SpL:375.0,386.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 425[7:Obv:423.1] || -> .
% 0.19/0.47 426[7:Spt:425.0,12.1,343.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.19/0.47 427[7:Spt:425.0,12.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 428[7:MRR:9.1,426.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 429[7:MRR:11.1,426.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 430[7:MRR:10.1,426.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 431[7:MRR:8.1,426.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 445[7:SpR:429.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 447[7:Rew:427.0,445.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 448[7:Rew:430.0,447.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 450[7:Rew:448.0,428.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 452[7:Rew:448.0,319.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 454[7:Rew:448.0,342.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.47 457[7:Rew:448.0,426.0] || equal(multiply(sk_c1,sk_c8),sk_c8)** -> .
% 0.19/0.47 462[7:Rew:448.0,430.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 463[7:Rew:448.0,431.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 484[7:SpR:462.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.47 486[7:Rew:33.0,484.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 487[7:Rew:486.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 488[7:Rew:486.0,271.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 490[7:Rew:486.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 498[7:SpR:454.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.47 500[7:Rew:490.0,498.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 503[7:Rew:500.0,487.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 504[7:Rew:500.0,488.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 506[7:Rew:500.0,490.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.47 513[7:SpR:463.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 515[7:Rew:452.0,513.0,450.0,513.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 521[7:Rew:515.0,503.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 522[7:Rew:515.0,504.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 524[7:Rew:515.0,506.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.47 538[7:Rew:522.0,457.0] || equal(sk_c1,sk_c8)** -> .
% 0.19/0.47 569[7:SpR:332.0,524.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.19/0.47 571[7:Rew:521.0,569.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.47 572[7:MRR:571.0,538.0] || -> .
% 0.19/0.47 575[6:Spt:572.0,24.1,338.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.19/0.47 576[6:Spt:572.0,24.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 577[6:MRR:21.1,575.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 578[6:MRR:23.1,575.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 579[6:MRR:22.1,575.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 580[6:MRR:20.1,575.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 594[6:SpR:578.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 596[6:Rew:576.0,594.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 597[6:Rew:579.0,596.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 599[6:Rew:597.0,577.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 600[6:Rew:597.0,309.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 602[6:Rew:597.0,317.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.47 604[6:Rew:597.0,575.0] || equal(multiply(sk_c2,sk_c8),sk_c6)** -> .
% 0.19/0.47 605[6:Rew:597.0,330.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.47 608[6:Rew:597.0,579.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 609[6:Rew:597.0,580.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 629[6:SpR:608.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.47 631[6:Rew:33.0,629.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 633[6:Rew:631.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 634[6:Rew:631.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 640[6:SpR:609.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 642[6:Rew:600.0,640.0,599.0,640.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 644[6:Rew:642.0,602.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.47 645[6:Rew:642.0,604.0] || equal(multiply(sk_c2,sk_c8),sk_c8)** -> .
% 0.19/0.47 647[6:Rew:634.0,644.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.47 651[6:Rew:647.0,633.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 664[6:Rew:651.0,605.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.47 666[6:Rew:664.0,645.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 667[6:Obv:666.0] || -> .
% 0.19/0.47 676[5:Spt:667.0,18.1,332.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.47 677[5:Spt:667.0,18.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 678[5:MRR:15.1,676.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 679[5:MRR:17.0,676.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 680[5:MRR:16.0,676.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 681[5:MRR:14.0,676.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 695[5:SpR:679.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 697[5:Rew:677.0,695.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 698[5:Rew:680.0,697.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 700[5:Rew:698.0,678.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 701[5:Rew:698.0,319.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 703[5:Rew:698.0,327.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.47 708[5:Rew:698.0,680.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 709[5:Rew:698.0,681.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 711[5:Rew:698.0,323.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 714[5:Rew:698.0,711.5,698.0,711.4,698.0,711.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.19/0.47 715[5:Con:714.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.19/0.47 729[5:SpR:708.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.47 731[5:Rew:33.0,729.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 732[5:Rew:731.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 733[5:Rew:731.0,271.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 735[5:Rew:731.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 740[5:SpR:709.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 742[5:Rew:701.0,740.0,700.0,740.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 744[5:Rew:742.0,703.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.47 746[5:Rew:735.0,744.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.47 749[5:Rew:746.0,732.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 750[5:Rew:746.0,733.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 756[5:Rew:749.0,715.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.47 760[5:Rew:750.0,709.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.47 762[5:Rew:760.0,700.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 769[5:Con:756.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.47 770[5:Rew:750.0,769.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 840[5:SpL:762.0,770.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 842[5:Obv:840.1] || -> .
% 0.19/0.47 843[4:Spt:842.0,30.1,329.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.47 844[4:Spt:842.0,30.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 845[4:MRR:27.1,843.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 846[4:MRR:29.0,843.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 847[4:MRR:28.0,843.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 848[4:MRR:26.0,843.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 860[4:SpR:846.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 862[4:Rew:844.0,860.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 863[4:Rew:847.0,862.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 864[4:Rew:863.0,845.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 865[4:Rew:863.0,309.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 868[4:Rew:863.0,317.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.19/0.47 872[4:Rew:863.0,847.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 873[4:Rew:863.0,848.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.19/0.47 875[4:Rew:863.0,323.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 878[4:Rew:863.0,875.5,863.0,875.4,863.0,875.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.19/0.47 879[4:Con:878.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.19/0.47 891[4:SpR:872.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c5)**.
% 0.19/0.47 893[4:Rew:33.0,891.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 894[4:Rew:893.0,271.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 895[4:Rew:893.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 896[4:Rew:893.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 902[4:SpR:873.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c8)**.
% 0.19/0.47 904[4:Rew:865.0,902.0,864.0,902.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 906[4:Rew:904.0,868.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.47 908[4:Rew:896.0,906.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.47 911[4:Rew:908.0,894.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 912[4:Rew:908.0,895.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 915[4:Rew:911.0,873.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.47 918[4:Rew:911.0,879.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.47 920[4:Rew:915.0,864.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 930[4:Rew:912.0,918.3,911.0,918.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(v,sk_c8) equal(u,sk_c8) -> .
% 0.19/0.47 931[4:Con:930.0] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 990[4:SpL:920.0,931.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 992[4:Obv:990.1] || -> .
% 0.19/0.47 993[3:Spt:992.0,13.1,319.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.47 994[3:Spt:992.0,13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.47 995[3:MRR:25.1,993.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 996[3:MRR:7.0,993.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.47 997[3:MRR:19.0,993.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.47 998[3:SpR:994.0,96.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.19/0.47 1000[3:SpR:995.0,96.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.47 1006[3:SpR:996.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.19/0.47 1008[3:Rew:309.0,1006.0,994.0,1006.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 1010[3:Rew:1008.0,317.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.47 1011[3:Rew:1008.0,993.0] || equal(multiply(sk_c7,sk_c8),sk_c8)** -> .
% 0.19/0.47 1013[3:Rew:1008.0,997.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 1014[3:Rew:33.0,1010.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 1015[3:Rew:1014.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1016[3:Rew:1014.0,271.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1019[3:Rew:1015.0,1000.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.47 1020[3:Rew:1016.0,1013.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.47 1022[3:Rew:1020.0,1019.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 1023[3:Rew:1022.0,998.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 1024[3:Rew:1023.0,996.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 1029[3:Rew:1022.0,1011.0,1024.0,1011.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 1030[3:Obv:1029.0] || -> .
% 0.19/0.47 1035[2:Spt:1030.0,1.1,309.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.19/0.47 1036[2:Spt:1030.0,1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 1037[2:MRR:6.1,1035.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 1039[2:MRR:5.1,1035.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 1040[2:MRR:4.1,1035.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 1050[2:SpR:1039.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 1052[2:Rew:1037.0,1050.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 1053[2:Rew:1040.0,1052.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 1054[2:Rew:1053.0,1036.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.19/0.47 1056[2:Rew:1053.0,1035.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.19/0.47 1062[2:Rew:1054.0,1056.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 1063[2:Obv:1062.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 Formulae used in the proof : prove_this_1 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_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 left_identity left_inverse associativity
% 0.19/0.47
%------------------------------------------------------------------------------