TSTP Solution File: GRP389-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP389-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:47:09 EDT 2022
% Result : Unsatisfiable 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP389-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 19:28:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.54
% 0.18/0.54 SPASS V 3.9
% 0.18/0.54 SPASS beiseite: Proof found.
% 0.18/0.54 % SZS status Theorem
% 0.18/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54 SPASS derived 1485 clauses, backtracked 437 clauses, performed 12 splits and kept 653 clauses.
% 0.18/0.54 SPASS allocated 64695 KBytes.
% 0.18/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.18/0.54 0:00:00.03 for the input.
% 0.18/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.54 0:00:00.01 for inferences.
% 0.18/0.54 0:00:00.00 for the backtracking.
% 0.18/0.54 0:00:00.11 for the reduction.
% 0.18/0.54
% 0.18/0.54
% 0.18/0.54 Here is a proof with depth 7, length 238 :
% 0.18/0.54 % SZS output start Refutation
% 0.18/0.54 3[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.54 4[0:Inp] || -> equal(inverse(sk_c5),sk_c10)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.54 5[0:Inp] || -> equal(inverse(sk_c6),sk_c11)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.54 7[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 8[0:Inp] || -> equal(inverse(sk_c7),sk_c8)** equal(inverse(sk_c10),sk_c9).
% 0.18/0.54 10[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.18/0.54 11[0:Inp] || -> equal(inverse(sk_c4),sk_c11) equal(inverse(sk_c1),sk_c11)**.
% 0.18/0.54 12[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.54 13[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c1),sk_c11)**.
% 0.18/0.54 14[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(inverse(sk_c1),sk_c11)**.
% 0.18/0.54 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.18/0.54 16[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 17[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c1),sk_c11)**.
% 0.18/0.54 23[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.18/0.54 24[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.18/0.54 25[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.18/0.54 26[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.18/0.54 34[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.18/0.54 35[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.18/0.54 36[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.18/0.54 37[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.18/0.54 38[0:Inp] || -> equal(inverse(sk_c4),sk_c11) equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 39[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.54 40[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 41[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 42[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.18/0.54 43[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 44[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 45[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.54 52[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.54 53[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.54 54[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.54 55[0:Inp] || equal(inverse(sk_c10),sk_c9) equal(inverse(u),sk_c11) equal(multiply(u,sk_c10),sk_c11)** equal(multiply(v,w),sk_c10)** equal(inverse(v),w) equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c11),sk_c10)** equal(inverse(x),sk_c11) equal(multiply(y,sk_c10),sk_c9)** equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(multiply(z,sk_c10),sk_c11)** equal(multiply(x1,x2),sk_c10)** equal(inverse(x1),x2) equal(multiply(x2,sk_c9),sk_c10)** -> .
% 0.18/0.54 56[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.54 57[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.54 58[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.54 59[0:Con:55.10] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c11) equal(inverse(y),sk_c11) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c10)**+ equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c11),sk_c10)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(y,sk_c10),sk_c11)** -> .
% 0.18/0.54 60[1:Spt:59.0,59.5,59.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)**+ equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.18/0.54 63[2:Spt:44.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 67[3:Spt:53.1] || -> equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.54 71[4:Spt:35.1] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.18/0.54 73[4:SpL:71.0,60.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c10,sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)** -> .
% 0.18/0.54 74[4:Obv:73.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c9),sk_c10)** -> .
% 0.18/0.54 75[4:Rew:67.0,74.1,63.0,74.0] || equal(sk_c3,sk_c3)* equal(sk_c10,sk_c10) -> .
% 0.18/0.54 76[4:Obv:75.1] || -> .
% 0.18/0.54 77[4:Spt:76.0,35.1,71.0] || equal(multiply(sk_c2,sk_c3),sk_c10)** -> .
% 0.18/0.54 78[4:Spt:76.0,35.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 82[4:MRR:36.1,77.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.54 83[4:MRR:34.1,77.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 95[4:SpL:83.0,60.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c10,sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 96[4:Obv:95.1] || equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 97[4:Rew:82.0,96.1,78.0,96.0] || equal(sk_c8,sk_c8)* equal(sk_c10,sk_c10) -> .
% 0.18/0.54 98[4:Obv:97.1] || -> .
% 0.18/0.54 99[3:Spt:98.0,53.1,67.0] || equal(multiply(sk_c3,sk_c9),sk_c10)** -> .
% 0.18/0.54 100[3:Spt:98.0,53.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 104[3:MRR:54.1,99.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.54 105[3:MRR:52.1,99.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 117[3:SpL:105.0,60.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c10,sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 118[3:Obv:117.1] || equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 119[3:Rew:104.0,118.1,100.0,118.0] || equal(sk_c8,sk_c8)* equal(sk_c10,sk_c10) -> .
% 0.18/0.54 120[3:Obv:119.1] || -> .
% 0.18/0.54 121[2:Spt:120.0,44.1,63.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.18/0.54 122[2:Spt:120.0,44.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 126[2:MRR:45.0,121.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.18/0.54 127[2:MRR:43.0,121.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 139[2:SpL:127.0,60.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c10,sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 140[2:Obv:139.1] || equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.18/0.54 141[2:Rew:126.0,140.1,122.0,140.0] || equal(sk_c8,sk_c8)* equal(sk_c10,sk_c10) -> .
% 0.18/0.54 142[2:Obv:141.1] || -> .
% 0.18/0.54 143[1:Spt:142.0,59.1,59.2,59.3,59.4,59.6,59.7,59.9] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.18/0.54 144[2:Spt:5.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.18/0.54 145[2:Rew:144.0,143.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(sk_c9,sk_c9) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.18/0.54 146[2:Obv:145.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.18/0.54 148[3:Spt:17.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.18/0.54 150[4:Spt:41.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.18/0.54 152[5:Spt:26.1] || -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.18/0.54 154[6:Spt:35.1] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.18/0.54 160[2:SpR:144.0,57.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.18/0.54 161[3:SpR:148.0,57.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.18/0.54 162[4:SpR:150.0,57.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.18/0.54 171[0:SpR:57.0,58.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.54 173[0:Rew:56.0,171.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.54 175[3:SpR:161.0,58.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.54 177[3:Rew:56.0,175.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.18/0.54 186[5:SpR:152.0,177.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.18/0.54 189[0:SpR:173.0,173.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.54 195[4:SpR:162.0,173.0] || -> equal(multiply(inverse(sk_c3),identity),sk_c2)**.
% 0.18/0.54 197[0:SpR:57.0,173.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.54 209[0:Rew:189.0,197.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.54 210[4:Rew:209.0,195.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.18/0.54 213[4:SpR:210.0,57.0] || -> equal(multiply(sk_c2,sk_c3),identity)**.
% 0.18/0.54 216[6:Rew:154.0,213.0] || -> equal(identity,sk_c10)**.
% 0.18/0.54 219[6:Rew:216.0,160.0] || -> equal(multiply(sk_c9,sk_c10),sk_c10)**.
% 0.18/0.54 223[6:Rew:216.0,209.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.54 229[6:Rew:223.0,152.0] || -> equal(sk_c1,sk_c11)**.
% 0.18/0.54 230[6:Rew:223.0,219.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.54 232[6:Rew:223.0,146.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11)** equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.18/0.54 233[6:Rew:229.0,148.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.18/0.54 237[6:Rew:230.0,144.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.54 259[6:Rew:223.0,232.3,230.0,232.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11)** equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)**+ equal(w,sk_c11) -> .
% 0.18/0.54 313[6:SpL:186.0,259.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c11),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c10) equal(sk_c10,sk_c10) equal(v,sk_c11) -> .
% 0.18/0.54 314[6:Obv:313.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c11),sk_c11)** equal(inverse(v),sk_c11)** equal(u,sk_c10) equal(v,sk_c11) -> .
% 0.18/0.54 315[6:Rew:233.0,314.1] || equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(inverse(v),sk_c11)** equal(u,sk_c10) equal(v,sk_c11) -> .
% 0.18/0.54 316[6:Obv:315.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c11)** equal(u,sk_c10) equal(v,sk_c11) -> .
% 0.18/0.54 1277[6:SpL:237.0,316.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c11)** equal(sk_c10,sk_c10) equal(u,sk_c11) -> .
% 0.18/0.54 1283[6:Obv:1277.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.18/0.54 1284[6:SpL:233.0,1283.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.18/0.54 1290[6:Obv:1284.1] || -> .
% 0.18/0.54 1292[6:Spt:1290.0,35.1,154.0] || equal(multiply(sk_c2,sk_c3),sk_c10)** -> .
% 0.18/0.54 1293[6:Spt:1290.0,35.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 1294[6:Rew:213.0,1292.0] || equal(identity,sk_c10)** -> .
% 0.18/0.54 1305[4:Rew:213.0,34.1] || -> equal(multiply(sk_c7,sk_c8),sk_c10)** equal(identity,sk_c10).
% 0.18/0.54 1306[6:MRR:1305.1,1294.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 1352[3:SpR:161.0,173.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.18/0.54 1354[3:Rew:209.0,1352.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.18/0.54 1360[6:SpR:1306.0,173.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.18/0.54 1362[6:Rew:1293.0,1360.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.18/0.54 1364[2:SpR:160.0,173.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.18/0.54 1366[2:Rew:209.0,1364.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.18/0.54 1388[6:SpR:1362.0,173.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.18/0.54 1390[6:Rew:57.0,1388.0] || -> equal(identity,sk_c10)**.
% 0.18/0.54 1391[6:MRR:1390.0,1294.0] || -> .
% 0.18/0.54 1392[5:Spt:1391.0,26.1,152.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.18/0.54 1393[5:Spt:1391.0,26.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 1397[5:MRR:23.1,1392.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.18/0.54 1406[5:MRR:25.1,1392.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 1407[5:MRR:24.1,1392.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.18/0.54 1422[5:SpR:1406.0,173.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.18/0.54 1424[5:Rew:1393.0,1422.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.18/0.54 1438[5:SpR:1424.0,173.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.18/0.54 1440[5:Rew:57.0,1438.0] || -> equal(identity,sk_c10)**.
% 0.18/0.54 1446[5:Rew:1440.0,209.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.54 1465[5:Rew:1446.0,1407.0] || -> equal(sk_c6,sk_c11)**.
% 0.18/0.54 1466[5:Rew:1446.0,1392.0] || equal(sk_c1,sk_c11)** -> .
% 0.18/0.54 1467[5:Rew:1465.0,1397.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.18/0.54 1469[5:Rew:1354.0,1467.0] || -> equal(sk_c1,sk_c11)**.
% 0.18/0.54 1470[5:MRR:1469.0,1466.0] || -> .
% 0.18/0.54 1488[4:Spt:1470.0,41.1,150.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.18/0.54 1489[4:Spt:1470.0,41.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.18/0.54 1490[4:MRR:40.1,1488.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.18/0.54 1491[4:MRR:38.1,1488.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.18/0.54 1492[4:MRR:44.1,1488.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 1494[4:MRR:43.0,1488.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 1495[4:MRR:42.0,1488.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.18/0.54 1496[4:MRR:39.0,1488.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.54 1497[4:MRR:37.0,1488.0] || -> equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.18/0.54 1524[4:SpR:1494.0,173.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.18/0.54 1526[4:Rew:1492.0,1524.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.18/0.54 1532[4:SpR:1496.0,173.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.18/0.54 1534[4:Rew:1490.0,1532.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.54 1543[4:SpR:1526.0,173.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.18/0.54 1545[4:Rew:57.0,1543.0] || -> equal(identity,sk_c10)**.
% 0.18/0.54 1548[4:Rew:1545.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.54 1549[4:Rew:1545.0,209.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.54 1551[4:Rew:1545.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.18/0.54 1552[4:Rew:1548.0,1534.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.54 1561[4:Rew:1552.0,1366.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.54 1565[4:Rew:1552.0,146.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.18/0.54 1568[4:Rew:1549.0,1495.0] || -> equal(sk_c6,sk_c11)**.
% 0.18/0.54 1569[4:Rew:1568.0,1489.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.18/0.54 1571[4:Rew:1354.0,1569.0] || -> equal(sk_c1,sk_c11)**.
% 0.18/0.54 1572[4:Rew:1571.0,148.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.18/0.54 1593[4:Rew:1549.0,1565.5,1549.0,1565.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11)** equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.18/0.54 1635[4:SpR:1491.0,1551.0] || -> equal(multiply(sk_c11,sk_c4),sk_c10)**.
% 0.18/0.54 1642[4:SpR:1635.0,173.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c4)**.
% 0.18/0.54 1644[4:Rew:1549.0,1642.0,1572.0,1642.0] || -> equal(sk_c11,sk_c4)**.
% 0.18/0.54 1645[4:Rew:1644.0,1491.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.18/0.54 1646[4:Rew:1644.0,1497.0] || -> equal(multiply(sk_c4,sk_c4),sk_c10)**.
% 0.18/0.54 1655[4:Rew:1644.0,1593.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c11)** equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.18/0.54 1658[4:Rew:1644.0,1655.5,1644.0,1655.4,1644.0,1655.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c4)** equal(u,sk_c10) equal(multiply(v,sk_c4),sk_c10)**+ equal(w,sk_c4) -> .
% 0.18/0.54 1698[4:SpL:1646.0,1658.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(sk_c10,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.54 1699[4:Obv:1698.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.54 1700[4:Rew:1645.0,1699.1] || equal(inverse(u),sk_c10)** equal(sk_c4,sk_c4) equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.54 1701[4:Obv:1700.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.54 2006[4:SpL:1561.0,1701.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c4)** equal(sk_c10,sk_c10) equal(u,sk_c4) -> .
% 0.18/0.54 2009[4:Obv:2006.2] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.18/0.54 2012[4:SpL:1645.0,2009.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.18/0.54 2015[4:Obv:2012.1] || -> .
% 0.18/0.54 2016[3:Spt:2015.0,17.1,148.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.18/0.54 2017[3:Spt:2015.0,17.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.54 2018[3:MRR:14.1,2016.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.18/0.54 2019[3:MRR:13.1,2016.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.18/0.54 2020[3:MRR:11.1,2016.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.18/0.54 2023[3:MRR:16.0,2016.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.54 2024[3:MRR:15.0,2016.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.18/0.54 2025[3:MRR:12.0,2016.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.54 2026[3:MRR:10.0,2016.0] || -> equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.18/0.54 2056[3:SpR:2023.0,173.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.18/0.55 2058[3:Rew:2017.0,2056.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.18/0.55 2064[3:SpR:2025.0,173.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.18/0.55 2066[3:Rew:2019.0,2064.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.55 2072[3:SpR:2058.0,173.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.18/0.55 2074[3:Rew:57.0,2072.0] || -> equal(identity,sk_c10)**.
% 0.18/0.55 2076[3:Rew:2074.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.55 2077[3:Rew:2074.0,209.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.55 2078[3:Rew:2074.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.18/0.55 2080[3:Rew:2076.0,2066.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.55 2089[3:Rew:2080.0,144.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 2093[3:Rew:2080.0,146.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.18/0.55 2096[3:Rew:2077.0,2024.0] || -> equal(sk_c6,sk_c11)**.
% 0.18/0.55 2097[3:Rew:2096.0,2018.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.18/0.55 2115[3:Rew:2077.0,2093.5,2077.0,2093.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11)** equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.18/0.55 2147[3:SpR:2020.0,2078.0] || -> equal(multiply(sk_c11,sk_c4),sk_c10)**.
% 0.18/0.55 2158[3:SpR:2147.0,173.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c4)**.
% 0.18/0.55 2160[3:Rew:2077.0,2158.0,2097.0,2158.0] || -> equal(sk_c11,sk_c4)**.
% 0.18/0.55 2161[3:Rew:2160.0,2020.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.18/0.55 2163[3:Rew:2160.0,2026.0] || -> equal(multiply(sk_c4,sk_c4),sk_c10)**.
% 0.18/0.55 2171[3:Rew:2160.0,2115.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c11)** equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** equal(w,sk_c11) -> .
% 0.18/0.55 2174[3:Rew:2160.0,2171.5,2160.0,2171.4,2160.0,2171.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c4) equal(inverse(w),sk_c4)** equal(u,sk_c10) equal(multiply(v,sk_c4),sk_c10)**+ equal(w,sk_c4) -> .
% 0.18/0.55 2203[3:SpL:2163.0,2174.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(sk_c10,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.55 2204[3:Obv:2203.4] || equal(inverse(u),sk_c10)** equal(inverse(sk_c4),sk_c4)** equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.55 2205[3:Rew:2161.0,2204.1] || equal(inverse(u),sk_c10)** equal(sk_c4,sk_c4) equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.55 2206[3:Obv:2205.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c4)** equal(u,sk_c10) equal(v,sk_c4) -> .
% 0.18/0.55 2490[3:SpL:2089.0,2206.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c4)** equal(sk_c10,sk_c10) equal(u,sk_c4) -> .
% 0.18/0.55 2493[3:Obv:2490.2] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.18/0.55 2496[3:SpL:2161.0,2493.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.18/0.55 2499[3:Obv:2496.1] || -> .
% 0.18/0.55 2500[2:Spt:2499.0,5.1,144.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.18/0.55 2501[2:Spt:2499.0,5.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.18/0.55 2502[2:MRR:4.1,2500.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.18/0.55 2504[2:MRR:8.1,2500.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.55 2507[2:MRR:7.0,2500.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.18/0.55 2509[2:MRR:3.0,2500.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.18/0.55 2531[2:SpR:2507.0,173.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.18/0.55 2533[2:Rew:2504.0,2531.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.18/0.55 2539[2:SpR:2509.0,173.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.18/0.55 2541[2:Rew:2502.0,2539.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.55 2547[2:SpR:2533.0,173.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.18/0.55 2549[2:Rew:57.0,2547.0] || -> equal(identity,sk_c10)**.
% 0.18/0.55 2550[2:Rew:2549.0,209.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.18/0.55 2551[2:Rew:2549.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.18/0.55 2554[2:Rew:2550.0,2509.0] || -> equal(sk_c5,sk_c9)**.
% 0.18/0.55 2557[2:Rew:2554.0,2502.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.18/0.55 2563[2:Rew:2551.0,2541.0] || -> equal(sk_c9,sk_c10)**.
% 0.18/0.55 2567[2:Rew:2563.0,2500.0] || equal(inverse(sk_c10),sk_c10)** -> .
% 0.18/0.55 2571[2:Rew:2563.0,2557.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 2572[2:Rew:2571.0,2567.0] || equal(sk_c10,sk_c10)* -> .
% 0.18/0.55 2573[2:Obv:2572.0] || -> .
% 0.18/0.55 % SZS output end Refutation
% 0.18/0.55 Formulae used in the proof : prove_this_3 prove_this_4 prove_this_5 prove_this_7 prove_this_8 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_23 prove_this_24 prove_this_25 prove_this_26 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_52 prove_this_53 prove_this_54 prove_this_55 left_identity left_inverse associativity
% 0.18/0.55
%------------------------------------------------------------------------------