TSTP Solution File: GRP275-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP275-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:38 EDT 2022
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP275-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 01:14:54 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 764 clauses, backtracked 303 clauses, performed 12 splits and kept 599 clauses.
% 0.22/0.50 SPASS allocated 63640 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.50 0:00:00.04 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.01 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.06 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 4, length 260 :
% 0.22/0.50 % SZS output start Refutation
% 0.22/0.50 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.22/0.50 4[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.22/0.50 5[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 6[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.22/0.50 7[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 8[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.22/0.50 9[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.50 10[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 11[0:Inp] || -> equal(inverse(sk_c4),sk_c5)** equal(inverse(sk_c1),sk_c8).
% 0.22/0.50 12[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 13[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 14[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 15[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 16[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 17[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 19[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 20[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 21[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.50 22[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 23[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 24[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 25[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 27[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 28[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 29[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 30[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 31[0:Inp] || equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)** equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,y),sk_c7)** equal(inverse(x),y) equal(multiply(y,sk_c8),sk_c7)** -> .
% 0.22/0.50 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.50 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.50 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.50 35[0:Con:31.6] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.22/0.50 36[1:Spt:35.0,35.3,35.4] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.22/0.50 41[2:Spt:19.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 43[3:Spt:7.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 47[4:Spt:25.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 52[5:Spt:1.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 54[5:SpL:52.0,36.1] || equal(inverse(sk_c1),sk_c8) equal(sk_c7,sk_c7) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.22/0.50 55[5:Obv:54.1] || equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.22/0.50 56[5:Rew:43.0,55.0] || equal(sk_c8,sk_c8) equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.22/0.50 57[5:Obv:56.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.22/0.50 59[2:SpR:41.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.22/0.50 68[2:SpR:59.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.22/0.50 70[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.50 73[2:Rew:32.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.22/0.50 74[0:Rew:32.0,70.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.50 84[4:SpR:47.0,73.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.22/0.50 86[5:MRR:84.0,57.0] || -> .
% 0.22/0.50 89[5:Spt:86.0,1.1,52.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.22/0.50 90[5:Spt:86.0,1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 92[5:MRR:5.1,89.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 94[5:MRR:6.1,89.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 95[5:MRR:4.1,89.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 120[5:SpL:95.0,36.1] || equal(inverse(sk_c4),sk_c5) equal(sk_c7,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 121[5:Obv:120.1] || equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 122[5:Rew:94.0,121.1,92.0,121.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.22/0.50 123[5:Obv:122.1] || -> .
% 0.22/0.50 124[4:Spt:123.0,25.1,47.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.22/0.50 125[4:Spt:123.0,25.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 126[4:MRR:29.1,124.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 128[4:MRR:30.1,124.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 129[4:MRR:28.1,124.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 144[4:SpL:129.0,36.1] || equal(inverse(sk_c4),sk_c5) equal(sk_c7,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 145[4:Obv:144.1] || equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 146[4:Rew:128.0,145.1,126.0,145.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.22/0.50 147[4:Obv:146.1] || -> .
% 0.22/0.50 148[3:Spt:147.0,7.0,43.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 149[3:Spt:147.0,7.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 150[3:MRR:11.1,148.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 152[3:MRR:12.0,148.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 153[3:MRR:10.0,148.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 168[3:SpL:153.0,36.1] || equal(inverse(sk_c4),sk_c5) equal(sk_c7,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 169[3:Obv:168.1] || equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 170[3:Rew:152.0,169.1,150.0,169.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.22/0.50 171[3:Obv:170.1] || -> .
% 0.22/0.50 172[2:Spt:171.0,19.0,41.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.22/0.50 173[2:Spt:171.0,19.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 174[2:MRR:23.1,172.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 176[2:MRR:24.0,172.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.22/0.50 177[2:MRR:22.0,172.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 192[2:SpL:177.0,36.1] || equal(inverse(sk_c4),sk_c5) equal(sk_c7,sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 193[2:Obv:192.1] || equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.22/0.50 194[2:Rew:176.0,193.1,174.0,193.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.22/0.50 195[2:Obv:194.1] || -> .
% 0.22/0.50 196[1:Spt:195.0,35.1,35.2,35.5,35.6,35.7,35.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.22/0.50 200[2:Spt:13.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.50 201[2:Rew:200.0,196.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.22/0.50 207[2:Obv:201.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.50 211[3:Spt:7.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 213[3:Rew:211.0,207.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.22/0.50 218[3:Obv:213.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.22/0.50 222[4:Spt:23.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 223[4:SpR:222.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.22/0.50 225[5:Spt:11.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 226[5:SpR:225.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.22/0.50 228[4:SpR:223.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.22/0.50 230[4:Rew:32.0,228.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.22/0.50 231[6:Spt:29.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.50 234[7:Spt:5.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 245[0:SpR:74.0,74.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.50 247[0:SpR:32.0,74.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.22/0.50 248[0:SpR:33.0,74.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.50 250[2:SpR:200.0,74.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.22/0.50 251[4:SpR:223.0,74.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.22/0.50 252[5:SpR:226.0,74.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.22/0.50 253[4:SpR:230.0,74.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c2,u))**.
% 0.22/0.50 254[3:SpR:211.0,74.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.50 259[5:Rew:251.0,252.0] || -> equal(sk_c2,sk_c1)**.
% 0.22/0.50 262[6:Rew:259.0,231.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 270[5:Rew:259.0,253.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c1,u))**.
% 0.22/0.50 272[5:Rew:270.0,250.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.22/0.50 273[6:Rew:262.0,272.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.50 274[6:Rew:273.0,200.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.50 276[6:Rew:273.0,225.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.22/0.50 277[7:Rew:273.0,234.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.22/0.50 278[6:Rew:273.0,226.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.22/0.50 281[6:Rew:273.0,218.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.22/0.50 288[6:Rew:273.0,262.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.22/0.50 292[0:Rew:245.0,248.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.50 297[6:Rew:273.0,281.3,273.0,281.2,273.0,281.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.22/0.50 316[6:SpR:278.0,74.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c1)**.
% 0.22/0.50 318[6:Rew:292.0,316.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.22/0.50 321[6:SpR:318.0,33.0] || -> equal(multiply(sk_c1,sk_c6),identity)**.
% 0.22/0.50 324[7:Rew:277.0,321.0] || -> equal(identity,sk_c7)**.
% 0.22/0.50 330[7:Rew:324.0,292.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.50 336[7:Rew:330.0,297.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.22/0.50 337[7:Rew:330.0,288.0] || -> equal(sk_c6,sk_c1)**.
% 0.22/0.50 339[7:Rew:337.0,276.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.22/0.50 340[7:Rew:337.0,274.0] || -> equal(multiply(sk_c1,sk_c1),sk_c7)**.
% 0.22/0.50 351[7:Rew:337.0,336.3,337.0,336.2,337.0,336.1,337.0,336.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1) equal(u,sk_c1) equal(multiply(v,sk_c1),sk_c7)**+ -> .
% 0.22/0.50 407[7:SpL:340.0,351.3] || equal(inverse(u),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(sk_c7,sk_c7) -> .
% 0.22/0.50 411[7:Obv:407.3] || equal(inverse(u),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) -> .
% 0.22/0.50 412[7:Rew:339.0,411.1] || equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.22/0.50 413[7:Obv:412.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.22/0.50 445[7:SpL:339.0,413.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.22/0.50 448[7:Obv:445.1] || -> .
% 0.22/0.50 450[7:Spt:448.0,5.1,234.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.22/0.50 451[7:Spt:448.0,5.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 452[7:Rew:321.0,450.0,273.0,450.0] || equal(identity,sk_c7)** -> .
% 0.22/0.50 457[6:Rew:321.0,4.1,273.0,4.1] || -> equal(multiply(sk_c4,sk_c5),sk_c7)** equal(identity,sk_c7).
% 0.22/0.50 458[7:MRR:457.1,452.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 491[7:SpR:458.0,74.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.22/0.50 493[7:Rew:451.0,491.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.22/0.50 503[7:SpR:493.0,74.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.22/0.50 505[7:Rew:33.0,503.0] || -> equal(identity,sk_c7)**.
% 0.22/0.50 506[7:MRR:505.0,452.0] || -> .
% 0.22/0.50 507[6:Spt:506.0,29.1,231.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.22/0.50 508[6:Spt:506.0,29.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 509[6:Rew:259.0,507.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.22/0.50 510[6:Rew:272.0,509.0] || equal(sk_c8,sk_c6)** -> .
% 0.22/0.50 517[5:Rew:259.0,28.1] || -> equal(multiply(sk_c4,sk_c5),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.22/0.50 518[5:Rew:272.0,517.1] || -> equal(multiply(sk_c4,sk_c5),sk_c7)** equal(sk_c8,sk_c6).
% 0.22/0.50 519[6:MRR:518.1,510.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 520[5:Rew:259.0,27.1] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.22/0.50 521[5:Rew:272.0,520.1] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(sk_c8,sk_c6).
% 0.22/0.50 522[6:MRR:521.1,510.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.50 549[6:SpR:519.0,74.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.22/0.50 551[6:Rew:508.0,549.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.22/0.50 557[6:SpR:551.0,74.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.22/0.50 559[6:Rew:33.0,557.0] || -> equal(identity,sk_c7)**.
% 0.22/0.50 562[6:Rew:559.0,292.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.50 564[6:Rew:559.0,247.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.22/0.50 575[6:Rew:562.0,522.0] || -> equal(sk_c8,sk_c3)**.
% 0.22/0.50 576[6:Rew:562.0,272.0] || -> equal(sk_c6,sk_c1)**.
% 0.22/0.50 581[6:Rew:575.0,510.0] || equal(sk_c3,sk_c6)** -> .
% 0.22/0.50 585[6:Rew:575.0,254.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c3)**.
% 0.22/0.50 592[6:Rew:576.0,581.0] || equal(sk_c3,sk_c1)** -> .
% 0.22/0.50 594[6:Rew:564.0,585.0,576.0,585.0] || -> equal(sk_c3,sk_c1)**.
% 0.22/0.50 595[6:MRR:594.0,592.0] || -> .
% 0.22/0.50 613[5:Spt:595.0,11.1,225.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 614[5:Spt:595.0,11.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 615[4:Rew:292.0,251.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.50 616[4:Rew:615.0,250.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.22/0.50 618[5:MRR:8.1,613.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.22/0.50 621[5:MRR:10.0,613.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 622[5:MRR:9.0,613.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.50 651[5:SpR:621.0,74.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.22/0.50 653[5:Rew:614.0,651.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.22/0.50 659[5:SpR:653.0,74.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.22/0.50 661[5:Rew:33.0,659.0] || -> equal(identity,sk_c7)**.
% 0.22/0.50 663[5:Rew:661.0,292.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.50 669[5:Rew:663.0,622.0] || -> equal(sk_c8,sk_c3)**.
% 0.22/0.50 670[5:Rew:663.0,616.0] || -> equal(sk_c2,sk_c6)**.
% 0.22/0.50 673[5:Rew:663.0,218.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.22/0.50 674[5:Rew:669.0,618.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.22/0.50 676[5:Rew:669.0,615.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.22/0.50 678[5:Rew:669.0,200.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.22/0.50 694[5:Rew:674.0,676.0,670.0,676.0] || -> equal(sk_c3,sk_c6)**.
% 0.22/0.50 695[5:Rew:694.0,669.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.50 697[5:Rew:694.0,674.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.22/0.50 701[5:Rew:694.0,678.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.50 717[5:Rew:695.0,673.3,695.0,673.2,695.0,673.1,695.0,673.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)**+ -> .
% 0.22/0.50 801[5:SpL:701.0,717.3] || equal(inverse(u),sk_c6)** equal(inverse(sk_c6),sk_c6)** equal(u,sk_c6) equal(sk_c7,sk_c7) -> .
% 0.22/0.50 804[5:Obv:801.3] || equal(inverse(u),sk_c6)** equal(inverse(sk_c6),sk_c6)** equal(u,sk_c6) -> .
% 0.22/0.50 805[5:Rew:697.0,804.1] || equal(inverse(u),sk_c6)** equal(sk_c6,sk_c6) equal(u,sk_c6) -> .
% 0.22/0.50 806[5:Obv:805.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.22/0.50 847[5:SpL:697.0,806.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.22/0.50 850[5:Obv:847.1] || -> .
% 0.22/0.50 852[4:Spt:850.0,23.1,222.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.22/0.50 853[4:Spt:850.0,23.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.50 854[4:MRR:20.1,852.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.22/0.50 856[4:MRR:22.0,852.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.50 857[4:MRR:21.0,852.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.51 872[4:SpR:856.0,74.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.22/0.51 874[4:Rew:853.0,872.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.22/0.51 880[4:SpR:874.0,74.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.22/0.51 882[4:Rew:33.0,880.0] || -> equal(identity,sk_c7)**.
% 0.22/0.51 883[4:Rew:882.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.51 884[4:Rew:882.0,292.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.51 889[4:Rew:883.0,211.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.51 895[4:Rew:889.0,854.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.51 896[4:Rew:889.0,200.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.51 899[4:Rew:889.0,857.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.22/0.51 902[4:Rew:889.0,218.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.22/0.51 907[4:Rew:884.0,899.0] || -> equal(sk_c3,sk_c6)**.
% 0.22/0.51 908[4:Rew:907.0,895.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.22/0.51 919[4:Rew:889.0,902.3,884.0,902.2,889.0,902.2,889.0,902.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)**+ -> .
% 0.22/0.51 1005[4:SpL:896.0,919.3] || equal(inverse(u),sk_c6)** equal(inverse(sk_c6),sk_c6)** equal(u,sk_c6) equal(sk_c7,sk_c7) -> .
% 0.22/0.51 1008[4:Obv:1005.3] || equal(inverse(u),sk_c6)** equal(inverse(sk_c6),sk_c6)** equal(u,sk_c6) -> .
% 0.22/0.51 1009[4:Rew:908.0,1008.1] || equal(inverse(u),sk_c6)** equal(sk_c6,sk_c6) equal(u,sk_c6) -> .
% 0.22/0.51 1010[4:Obv:1009.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.22/0.51 1038[4:SpL:908.0,1010.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.22/0.51 1041[4:Obv:1038.1] || -> .
% 0.22/0.51 1043[3:Spt:1041.0,7.1,211.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.51 1044[3:Spt:1041.0,7.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 1045[3:MRR:19.1,1043.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 1046[3:MRR:1.0,1043.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.51 1047[3:MRR:25.0,1043.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.22/0.51 1056[3:SpR:1046.0,74.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.22/0.51 1058[3:Rew:1044.0,1056.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.22/0.51 1067[3:SpR:1058.0,74.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.22/0.51 1069[3:Rew:33.0,1067.0] || -> equal(identity,sk_c7)**.
% 0.22/0.51 1070[3:Rew:1069.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.51 1071[3:Rew:1069.0,292.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.51 1074[3:Rew:1070.0,1043.0] || equal(sk_c8,sk_c6)** -> .
% 0.22/0.51 1078[3:Rew:1071.0,1047.0] || -> equal(sk_c8,sk_c2)**.
% 0.22/0.51 1079[3:Rew:1071.0,250.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.22/0.51 1081[3:Rew:1078.0,1045.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.22/0.51 1087[3:Rew:1078.0,1074.0] || equal(sk_c2,sk_c6)** -> .
% 0.22/0.51 1088[3:Rew:1078.0,1079.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.22/0.51 1089[3:Rew:1088.0,1081.0] || -> equal(sk_c2,sk_c6)**.
% 0.22/0.51 1093[3:Rew:1089.0,1087.0] || equal(sk_c6,sk_c6)* -> .
% 0.22/0.51 1094[3:Obv:1093.0] || -> .
% 0.22/0.51 1104[2:Spt:1094.0,13.1,200.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.22/0.51 1105[2:Spt:1094.0,13.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 1106[2:MRR:17.1,1104.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.22/0.51 1107[2:MRR:14.1,1104.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.22/0.51 1109[2:MRR:16.1,1104.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.22/0.51 1110[2:MRR:15.1,1104.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.22/0.51 1122[2:SpR:1109.0,74.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.22/0.51 1124[2:Rew:1106.0,1122.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.22/0.51 1126[2:SpR:1110.0,74.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.22/0.51 1128[2:Rew:1107.0,1126.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.22/0.51 1130[2:SpR:1124.0,74.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.22/0.51 1132[2:Rew:33.0,1130.0] || -> equal(identity,sk_c7)**.
% 0.22/0.51 1133[2:Rew:1132.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.51 1137[2:Rew:1133.0,1105.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.51 1145[2:Rew:1137.0,1104.0] || equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.22/0.51 1149[2:Rew:1137.0,1128.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.51 1152[2:Rew:1149.0,1145.0] || equal(sk_c7,sk_c7)* -> .
% 0.22/0.51 1153[2:Obv:1152.0] || -> .
% 0.22/0.51 % SZS output end Refutation
% 0.22/0.51 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_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.22/0.51
%------------------------------------------------------------------------------