TSTP Solution File: GRP247-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP247-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:46:30 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP247-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 07:56:28 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 969 clauses, backtracked 269 clauses, performed 13 splits and kept 538 clauses.
% 0.21/0.49 SPASS allocated 63838 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.49 0:00:00.04 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.01 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.06 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 5, length 280 :
% 0.21/0.49 % SZS output start Refutation
% 0.21/0.49 1[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.21/0.49 2[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 5[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 7[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 8[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.49 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.49 11[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.49 12[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.21/0.49 14[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 17[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 18[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 19[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 20[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 21[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.49 22[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 23[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 24[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.21/0.49 25[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 26[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 28[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 29[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 30[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.21/0.49 32[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 34[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 35[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 36[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 37[0:Inp] || equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(v,sk_c8),sk_c7)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(w,sk_c7),sk_c9)** equal(multiply(x,sk_c9),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(y,sk_c8),sk_c7)** equal(inverse(y),sk_c8) equal(inverse(z),sk_c9) equal(multiply(z,sk_c8),sk_c9)** -> .
% 0.21/0.49 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.49 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.49 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.49 41[0:Con:37.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)**+ equal(multiply(v,sk_c7),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** -> .
% 0.21/0.49 42[1:Spt:41.3,41.7] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.21/0.49 47[2:Spt:20.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.49 55[3:Spt:25.1] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 57[3:SpL:55.0,42.1] || equal(inverse(sk_c4),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.21/0.49 58[3:Obv:57.1] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.49 59[3:Rew:47.0,58.0] || equal(sk_c9,sk_c9)* -> .
% 0.21/0.49 60[3:Obv:59.0] || -> .
% 0.21/0.49 61[3:Spt:60.0,25.1,55.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.21/0.49 62[3:Spt:60.0,25.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 64[3:MRR:7.1,61.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 67[3:MRR:1.0,61.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 74[3:SpL:67.0,42.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.21/0.49 75[3:Obv:74.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.21/0.49 76[3:Rew:64.0,75.0] || equal(sk_c9,sk_c9)* -> .
% 0.21/0.49 77[3:Obv:76.0] || -> .
% 0.21/0.49 78[2:Spt:77.0,20.0,47.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.49 79[2:Spt:77.0,20.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 81[2:MRR:8.0,78.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 84[2:MRR:2.0,78.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 91[2:SpL:84.0,42.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.21/0.49 92[2:Obv:91.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.21/0.49 93[2:Rew:81.0,92.0] || equal(sk_c9,sk_c9)* -> .
% 0.21/0.49 94[2:Obv:93.0] || -> .
% 0.21/0.49 95[1:Spt:94.0,41.0,41.1,41.2,41.4,41.5,41.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c7),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.21/0.49 97[2:Spt:26.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.49 99[3:Spt:29.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.21/0.49 101[4:Spt:22.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.49 103[5:Spt:19.1] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 106[2:SpR:97.0,39.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.21/0.49 107[3:SpR:99.0,39.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.21/0.49 108[4:SpR:101.0,39.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.49 110[6:Spt:24.1] || -> equal(multiply(sk_c6,sk_c8),sk_c9)**.
% 0.21/0.49 112[6:SpL:110.0,95.3] || equal(inverse(sk_c6),sk_c9) equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(sk_c9,sk_c9) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.21/0.49 113[6:Obv:112.3] || equal(inverse(sk_c6),sk_c9) equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.21/0.49 114[6:Rew:99.0,113.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.21/0.49 115[6:Obv:114.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.21/0.49 116[7:Spt:21.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.49 122[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.49 126[2:SpR:106.0,40.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.49 127[2:Rew:38.0,126.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),u)**.
% 0.21/0.49 128[0:Rew:38.0,122.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.49 138[5:SpR:103.0,127.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.49 143[0:SpR:128.0,128.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.49 146[0:SpR:39.0,128.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.49 148[7:SpR:116.0,128.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c8)**.
% 0.21/0.49 150[2:SpR:106.0,128.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c4)**.
% 0.21/0.49 151[3:SpR:107.0,128.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c6)**.
% 0.21/0.49 152[2:SpR:127.0,128.0] || -> equal(multiply(inverse(sk_c9),u),multiply(sk_c4,u))**.
% 0.21/0.49 153[5:SpR:138.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.49 160[7:Rew:101.0,148.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.49 162[3:Rew:150.0,151.0] || -> equal(sk_c6,sk_c4)**.
% 0.21/0.49 164[6:Rew:162.0,110.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.21/0.49 168[5:Rew:39.0,153.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 169[5:Rew:168.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 170[5:Rew:168.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.49 172[5:Rew:168.0,108.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.21/0.49 174[5:Rew:168.0,150.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c4)**.
% 0.21/0.49 176[7:Rew:169.0,160.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 181[7:Rew:176.0,115.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.21/0.49 182[5:Rew:169.0,172.0] || -> equal(sk_c5,sk_c8)**.
% 0.21/0.49 183[5:Rew:182.0,101.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 188[5:Rew:168.0,146.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.49 192[5:Rew:152.0,174.0] || -> equal(multiply(sk_c4,sk_c8),sk_c4)**.
% 0.21/0.49 193[6:Rew:164.0,192.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.49 194[6:Rew:193.0,97.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.49 203[5:Rew:143.0,188.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 206[7:Rew:203.0,181.3,176.0,181.3,203.0,181.2] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.49 227[5:SpR:170.0,128.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.49 231[5:Rew:203.0,227.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.49 243[5:SpR:231.0,170.0] || -> equal(multiply(u,inverse(u)),sk_c8)**.
% 0.21/0.49 423[7:SpL:194.0,206.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(u,sk_c8) -> .
% 0.21/0.49 426[7:Obv:423.2] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 442[7:SpL:183.0,426.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 445[7:Obv:442.1] || -> .
% 0.21/0.49 447[7:Spt:445.0,21.1,116.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.21/0.49 448[7:Spt:445.0,21.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 449[7:Rew:169.0,447.0,182.0,447.0] || equal(sk_c7,sk_c8)** -> .
% 0.21/0.49 456[5:Rew:203.0,15.1,182.0,15.0,203.0,15.0] || -> equal(sk_c7,sk_c8) equal(sk_c2,sk_c7)**.
% 0.21/0.49 457[7:MRR:456.0,449.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.49 458[7:Rew:457.0,448.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.49 499[7:SpR:458.0,243.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.21/0.49 506[7:Rew:203.0,499.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 507[7:MRR:506.0,449.0] || -> .
% 0.21/0.49 510[6:Spt:507.0,24.1,110.0] || equal(multiply(sk_c6,sk_c8),sk_c9)** -> .
% 0.21/0.49 511[6:Spt:507.0,24.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 512[6:Rew:203.0,510.0] || equal(sk_c6,sk_c9)** -> .
% 0.21/0.49 513[6:Rew:162.0,512.0] || equal(sk_c4,sk_c9)** -> .
% 0.21/0.49 516[5:Rew:203.0,12.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c6,sk_c9).
% 0.21/0.49 517[5:Rew:162.0,516.1] || -> equal(inverse(sk_c1),sk_c9)** equal(sk_c4,sk_c9).
% 0.21/0.49 518[6:MRR:517.1,513.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 519[5:Rew:203.0,30.1] || -> equal(inverse(sk_c3),sk_c9)** equal(sk_c6,sk_c9).
% 0.21/0.49 520[5:Rew:162.0,519.1] || -> equal(inverse(sk_c3),sk_c9)** equal(sk_c4,sk_c9).
% 0.21/0.49 521[6:MRR:520.1,513.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 525[5:Rew:203.0,36.0] || -> equal(sk_c6,sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 526[5:Rew:162.0,525.0] || -> equal(sk_c4,sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 527[6:MRR:526.0,513.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 528[5:Rew:203.0,18.1,203.0,18.0] || -> equal(sk_c6,sk_c9) equal(sk_c2,sk_c7)**.
% 0.21/0.49 529[5:Rew:162.0,528.0] || -> equal(sk_c4,sk_c9) equal(sk_c2,sk_c7)**.
% 0.21/0.49 530[6:MRR:529.0,513.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.49 531[6:Rew:530.0,511.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.49 544[5:SpR:97.0,231.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.49 551[6:SpR:518.0,231.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.21/0.49 555[6:Rew:544.0,551.0] || -> equal(sk_c4,sk_c1)**.
% 0.21/0.49 558[6:Rew:555.0,513.0] || equal(sk_c9,sk_c1)** -> .
% 0.21/0.49 563[6:Rew:555.0,544.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.21/0.49 566[6:SpR:521.0,231.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.21/0.49 570[6:Rew:563.0,566.0] || -> equal(sk_c3,sk_c1)**.
% 0.21/0.49 572[6:Rew:570.0,527.0] || -> equal(multiply(sk_c1,sk_c7),sk_c9)**.
% 0.21/0.49 582[6:SpR:531.0,231.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.49 586[6:Rew:183.0,582.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 591[6:Rew:586.0,572.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.49 594[6:Rew:203.0,591.0] || -> equal(sk_c9,sk_c1)**.
% 0.21/0.49 595[6:MRR:594.0,558.0] || -> .
% 0.21/0.49 605[5:Spt:595.0,19.1,103.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.21/0.49 606[5:Spt:595.0,19.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 610[5:MRR:7.1,605.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 612[0:Rew:143.0,146.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.49 620[5:MRR:1.0,605.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 646[2:SpR:106.0,128.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c4)**.
% 0.21/0.49 648[2:Rew:612.0,646.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.49 658[5:SpR:620.0,128.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.49 660[5:Rew:610.0,658.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.49 670[5:SpR:660.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.49 672[5:Rew:648.0,670.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.49 673[5:MRR:672.0,605.0] || -> .
% 0.21/0.49 674[4:Spt:673.0,22.0,101.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.49 675[4:Spt:673.0,22.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 676[4:MRR:10.0,674.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 677[4:MRR:28.0,674.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 678[4:MRR:34.0,674.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 679[4:MRR:16.0,674.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 680[4:MRR:4.0,674.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 688[4:SpR:678.0,128.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.49 690[4:Rew:677.0,688.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.49 692[4:SpR:679.0,128.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.21/0.49 694[4:Rew:675.0,692.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.49 696[4:SpR:680.0,128.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.49 698[4:Rew:676.0,696.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.49 704[4:SpR:694.0,128.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.49 706[4:Rew:39.0,704.0] || -> equal(identity,sk_c7)**.
% 0.21/0.49 709[4:Rew:706.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.49 712[4:Rew:706.0,612.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.49 717[4:Rew:712.0,678.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.49 719[4:Rew:712.0,95.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.21/0.49 720[4:Rew:717.0,677.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.49 739[4:SpR:698.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.49 741[4:Rew:690.0,739.0,720.0,739.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 742[4:Rew:741.0,679.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.21/0.49 746[4:Rew:741.0,712.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 747[4:Rew:741.0,709.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.49 751[4:Rew:741.0,719.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.21/0.49 755[4:Rew:746.0,742.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.49 756[4:Rew:755.0,675.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 766[4:Rew:746.0,751.5,746.0,751.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c8) -> .
% 0.21/0.49 767[4:Con:766.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.49 786[4:SpR:676.0,747.0] || -> equal(multiply(sk_c9,sk_c1),sk_c8)**.
% 0.21/0.49 793[4:SpR:786.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c1)**.
% 0.21/0.49 795[4:Rew:720.0,793.0] || -> equal(multiply(sk_c9,sk_c8),sk_c1)**.
% 0.21/0.49 796[4:Rew:746.0,795.0] || -> equal(sk_c9,sk_c1)**.
% 0.21/0.49 797[4:Rew:796.0,676.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.49 809[4:Rew:796.0,767.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.49 812[4:Rew:796.0,809.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c8)** equal(u,sk_c1) equal(v,sk_c8) -> .
% 0.21/0.49 958[4:SpL:797.0,812.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c8)** equal(sk_c1,sk_c1) equal(u,sk_c8) -> .
% 0.21/0.49 961[4:Obv:958.2] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 978[4:SpL:756.0,961.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 981[4:Obv:978.1] || -> .
% 0.21/0.49 983[3:Spt:981.0,29.0,99.0] || equal(inverse(sk_c6),sk_c9)** -> .
% 0.21/0.49 984[3:Spt:981.0,29.1] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.49 985[3:MRR:11.0,983.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.49 986[3:MRR:23.0,983.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 987[3:MRR:35.0,983.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.49 988[3:MRR:17.0,983.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.49 989[3:MRR:5.0,983.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.49 1006[3:SpR:987.0,128.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.49 1008[3:Rew:984.0,1006.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.49 1010[3:SpR:988.0,128.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.21/0.49 1012[3:Rew:986.0,1010.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.49 1014[3:SpR:989.0,128.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.50 1016[3:Rew:985.0,1014.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.50 1022[3:SpR:1012.0,128.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.50 1024[3:Rew:39.0,1022.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1026[3:Rew:1024.0,612.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1030[3:Rew:1024.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.50 1032[3:Rew:1026.0,987.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.50 1034[3:Rew:1026.0,95.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.21/0.50 1035[3:Rew:1032.0,984.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.50 1055[3:SpR:1016.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.50 1057[3:Rew:1008.0,1055.0,1035.0,1055.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 1058[3:Rew:1057.0,988.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.21/0.50 1061[3:Rew:1057.0,1026.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.50 1065[3:Rew:1057.0,1030.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.50 1067[3:Rew:1057.0,1034.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.21/0.50 1068[3:Rew:1061.0,1058.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.50 1069[3:Rew:1068.0,986.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 1082[3:Rew:1061.0,1067.5,1061.0,1067.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c8) -> .
% 0.21/0.50 1083[3:Con:1082.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.50 1110[3:SpR:985.0,1065.0] || -> equal(multiply(sk_c9,sk_c1),sk_c8)**.
% 0.21/0.50 1117[3:SpR:1110.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c1)**.
% 0.21/0.50 1119[3:Rew:1061.0,1117.0,1035.0,1117.0] || -> equal(sk_c9,sk_c1)**.
% 0.21/0.50 1120[3:Rew:1119.0,985.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.50 1132[3:Rew:1119.0,1083.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.50 1135[3:Rew:1119.0,1132.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c8)** equal(u,sk_c1) equal(v,sk_c8) -> .
% 0.21/0.50 1272[3:SpL:1120.0,1135.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c8)** equal(sk_c1,sk_c1) equal(u,sk_c8) -> .
% 0.21/0.50 1275[3:Obv:1272.2] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.50 1292[3:SpL:1069.0,1275.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 1295[3:Obv:1292.1] || -> .
% 0.21/0.50 1297[2:Spt:1295.0,26.0,97.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.50 1298[2:Spt:1295.0,26.1] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.21/0.50 1299[2:MRR:8.0,1297.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 1300[2:MRR:20.0,1297.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 1301[2:MRR:32.0,1297.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.21/0.50 1302[2:MRR:14.0,1297.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 1303[2:MRR:2.0,1297.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 1311[2:SpR:1301.0,128.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.21/0.50 1313[2:Rew:1298.0,1311.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.21/0.50 1315[2:SpR:1302.0,128.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.21/0.50 1317[2:Rew:1300.0,1315.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.50 1319[2:SpR:1303.0,128.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.50 1321[2:Rew:1299.0,1319.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.50 1323[2:SpR:1313.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c9)**.
% 0.21/0.50 1329[2:SpR:1317.0,128.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.50 1331[2:Rew:39.0,1329.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1333[2:Rew:1331.0,612.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1334[2:Rew:1331.0,39.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.50 1342[2:Rew:1333.0,1323.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.50 1343[2:Rew:1333.0,95.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.21/0.50 1358[2:SpR:1321.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.50 1360[2:Rew:1313.0,1358.0,1342.0,1358.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 1361[2:Rew:1360.0,1302.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.21/0.50 1365[2:Rew:1360.0,1333.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.50 1366[2:Rew:1360.0,1334.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.50 1370[2:Rew:1360.0,1343.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c9) equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.21/0.50 1374[2:Rew:1365.0,1361.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.50 1375[2:Rew:1374.0,1300.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 1385[2:Rew:1365.0,1370.5,1365.0,1370.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c8) -> .
% 0.21/0.50 1386[2:Con:1385.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.50 1413[2:SpR:1299.0,1366.0] || -> equal(multiply(sk_c9,sk_c1),sk_c8)**.
% 0.21/0.50 1420[2:SpR:1413.0,128.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c1)**.
% 0.21/0.50 1422[2:Rew:1365.0,1420.0,1342.0,1420.0] || -> equal(sk_c9,sk_c1)**.
% 0.21/0.50 1423[2:Rew:1422.0,1299.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.50 1434[2:Rew:1422.0,1386.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c8)** equal(u,sk_c9) equal(v,sk_c8) -> .
% 0.21/0.50 1437[2:Rew:1422.0,1434.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c8)** equal(u,sk_c1) equal(v,sk_c8) -> .
% 0.21/0.50 1494[2:SpL:1423.0,1437.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c8)** equal(sk_c1,sk_c1) equal(u,sk_c8) -> .
% 0.21/0.50 1497[2:Obv:1494.2] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.50 1498[2:SpL:1375.0,1497.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 1501[2:Obv:1498.1] || -> .
% 0.21/0.50 % SZS output end Refutation
% 0.21/0.50 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_10 prove_this_11 prove_this_12 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_28 prove_this_29 prove_this_30 prove_this_32 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.21/0.50
%------------------------------------------------------------------------------