TSTP Solution File: GRP298-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP298-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:44 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP298-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 05:09:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 345 clauses, backtracked 178 clauses, performed 9 splits and kept 350 clauses.
% 0.18/0.43 SPASS allocated 63344 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 145 :
% 0.18/0.43 % SZS output start Refutation
% 0.18/0.43 1[0:Inp] || -> equal(multiply(sk_c2,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.43 2[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.43 3[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.43 4[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.43 5[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.43 6[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.43 7[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.43 9[0:Inp] || -> equal(multiply(sk_c2,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 10[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 11[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.43 18[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.43 19[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.43 25[0:Inp] || -> equal(multiply(sk_c2,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.18/0.43 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 27[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 28[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 29[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.18/0.43 33[0:Inp] || equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(inverse(v),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7) 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_c6),sk_c7)** -> .
% 0.18/0.43 34[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.43 35[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.43 36[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.43 37[0:Con:33.4] || 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(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.18/0.43 38[1:Spt:37.1,37.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.18/0.43 45[2:Spt:19.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.43 47[3:Spt:11.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 49[3:SpL:47.0,38.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 50[3:Obv:49.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 51[3:Rew:45.0,50.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 52[3:Obv:51.0] || -> .
% 0.18/0.43 53[3:Spt:52.0,11.1,47.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.18/0.43 54[3:Spt:52.0,11.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.43 57[3:MRR:10.1,53.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.43 61[3:MRR:9.1,53.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.43 70[3:SpL:61.0,38.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 71[3:Obv:70.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.18/0.43 72[3:Rew:57.0,71.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 73[3:Obv:72.0] || -> .
% 0.18/0.43 74[2:Spt:73.0,19.0,45.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 75[2:Spt:73.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.43 78[2:MRR:18.1,74.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.43 82[2:MRR:17.0,74.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.43 91[2:SpL:82.0,38.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 92[2:Obv:91.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.18/0.43 93[2:Rew:78.0,92.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 94[2:Obv:93.0] || -> .
% 0.18/0.43 95[1:Spt:94.0,37.0,37.2,37.4,37.5,37.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.18/0.43 96[2:Spt:3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.43 97[2:Rew:96.0,95.4] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.18/0.43 98[2:Obv:97.4] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.43 100[3:Spt:27.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 101[3:Rew:100.0,98.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 102[3:Obv:101.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.18/0.43 104[4:Spt:19.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.43 106[5:Spt:11.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 110[4:SpR:104.0,35.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.18/0.43 115[4:SpR:110.0,36.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.43 119[0:SpR:35.0,36.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.43 120[4:Rew:34.0,115.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.43 121[0:Rew:34.0,119.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.43 125[5:SpR:106.0,120.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.43 126[5:Rew:96.0,125.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.43 127[5:Rew:126.0,96.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.43 128[5:Rew:126.0,100.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.43 129[5:Rew:126.0,102.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.18/0.43 133[5:Rew:128.0,129.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 134[5:Obv:133.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.43 141[0:SpR:121.0,121.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.43 143[4:SpR:110.0,121.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.18/0.43 145[5:SpR:127.0,121.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.18/0.43 146[5:SpR:128.0,121.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.43 149[0:SpR:35.0,121.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.43 152[5:Rew:35.0,145.0] || -> equal(identity,sk_c7)**.
% 0.18/0.43 156[5:Rew:152.0,143.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c1)**.
% 0.18/0.43 162[5:Rew:146.0,156.0] || -> equal(sk_c1,sk_c8)**.
% 0.18/0.43 163[5:Rew:162.0,104.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.43 168[5:Rew:152.0,149.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.18/0.43 172[5:Rew:141.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.43 173[5:Rew:172.0,134.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.43 209[5:SpL:163.0,173.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 211[5:Obv:209.1] || -> .
% 0.18/0.43 213[5:Spt:211.0,11.1,106.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.18/0.43 214[5:Spt:211.0,11.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.43 215[0:Rew:141.0,149.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.43 216[4:Rew:215.0,143.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.18/0.43 220[5:MRR:10.1,213.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.43 224[5:MRR:9.1,213.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.43 245[3:SpR:100.0,121.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.43 248[2:SpR:96.0,121.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.18/0.43 250[4:Rew:216.0,248.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.43 265[5:SpR:224.0,121.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.18/0.43 267[5:Rew:96.0,265.0,220.0,265.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.43 279[5:Rew:267.0,250.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 280[5:MRR:279.0,213.0] || -> .
% 0.18/0.43 282[4:Spt:280.0,19.0,104.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 283[4:Spt:280.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.43 286[4:MRR:18.1,282.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.44 290[4:MRR:17.0,282.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.44 291[4:Rew:283.0,102.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.44 292[4:Obv:291.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.44 320[4:SpR:290.0,121.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.18/0.44 322[4:Rew:96.0,320.0,286.0,320.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.44 327[4:Rew:322.0,245.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.44 328[4:Rew:322.0,248.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.18/0.44 335[4:Rew:35.0,328.0] || -> equal(identity,sk_c7)**.
% 0.18/0.44 339[4:Rew:335.0,215.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.44 343[4:Rew:339.0,327.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.44 344[4:Rew:339.0,292.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.44 420[4:SpL:343.0,344.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.44 421[4:Obv:420.1] || -> .
% 0.18/0.44 422[3:Spt:421.0,27.1,100.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.44 423[3:Spt:421.0,27.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.44 425[3:MRR:28.1,422.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.44 426[3:MRR:26.1,422.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.44 429[3:MRR:29.1,422.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.18/0.44 430[3:MRR:25.1,422.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.44 451[3:SpR:429.0,121.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.18/0.44 453[3:Rew:425.0,451.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.44 455[3:SpR:430.0,121.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.18/0.44 457[3:Rew:96.0,455.0,426.0,455.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.44 462[3:Rew:457.0,422.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.18/0.44 478[3:Rew:453.0,462.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.44 479[3:Obv:478.0] || -> .
% 0.18/0.44 487[2:Spt:479.0,3.1,96.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.18/0.44 488[2:Spt:479.0,3.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.18/0.44 489[2:MRR:7.1,487.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.18/0.44 490[2:MRR:4.1,487.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.44 491[2:MRR:2.1,487.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.44 493[2:MRR:6.1,487.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.18/0.44 494[2:MRR:5.1,487.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.18/0.44 495[2:MRR:1.1,487.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.18/0.44 497[2:SpR:488.0,121.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.18/0.44 509[2:SpR:493.0,121.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c5)**.
% 0.18/0.44 511[2:Rew:489.0,509.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.18/0.44 517[2:SpR:495.0,121.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.18/0.44 519[2:Rew:491.0,517.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.44 520[2:Rew:519.0,487.0] || equal(sk_c6,sk_c8)** -> .
% 0.18/0.44 522[2:SpR:511.0,121.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.18/0.44 524[2:Rew:35.0,522.0] || -> equal(identity,sk_c7)**.
% 0.18/0.44 526[2:Rew:524.0,215.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.44 534[2:Rew:526.0,494.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.44 536[2:Rew:526.0,497.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.18/0.44 537[2:Rew:534.0,490.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.44 539[2:Rew:536.0,537.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.44 540[2:MRR:539.0,520.0] || -> .
% 0.18/0.44 % SZS output end Refutation
% 0.18/0.44 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_9 prove_this_10 prove_this_11 prove_this_17 prove_this_18 prove_this_19 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_33 left_identity left_inverse associativity
% 0.18/0.44
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