TSTP Solution File: GRP300-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP300-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:46:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP300-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 17:20:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 278 clauses, backtracked 147 clauses, performed 9 splits and kept 289 clauses.
% 0.20/0.45 SPASS allocated 63309 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 3, length 138 :
% 0.20/0.45 % SZS output start Refutation
% 0.20/0.45 1[0:Inp] || -> equal(multiply(sk_c5,sk_c4),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.20/0.45 2[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.20/0.45 3[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.20/0.45 4[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.20/0.45 5[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.20/0.45 6[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.20/0.45 8[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 9[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 10[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 13[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.20/0.45 14[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.45 15[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.45 16[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.45 20[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c5)** equal(multiply(sk_c4,sk_c6),sk_c5).
% 0.20/0.45 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.45 22[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.45 25[0:Inp] || equal(multiply(sk_c6,sk_c5),sk_c4) equal(multiply(u,sk_c6),sk_c5)** equal(inverse(u),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6) equal(multiply(v,sk_c6),sk_c5)** equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c4) equal(multiply(w,sk_c4),sk_c5)** equal(inverse(w),sk_c4) -> .
% 0.20/0.45 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.45 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.45 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.45 29[0:Con:25.5] || equal(inverse(u),sk_c4) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.20/0.45 30[1:Spt:29.1,29.4] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.45 37[2:Spt:16.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.45 39[3:Spt:10.1] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 41[3:SpL:39.0,30.1] || equal(inverse(sk_c1),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.45 42[3:Obv:41.1] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.20/0.45 43[3:Rew:37.0,42.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.45 44[3:Obv:43.0] || -> .
% 0.20/0.45 45[3:Spt:44.0,10.1,39.0] || equal(multiply(sk_c1,sk_c6),sk_c5)** -> .
% 0.20/0.45 46[3:Spt:44.0,10.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.45 48[3:MRR:9.1,45.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.45 50[3:MRR:8.1,45.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.45 57[3:SpL:50.0,30.1] || equal(inverse(sk_c2),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.45 58[3:Obv:57.1] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.20/0.45 59[3:Rew:48.0,58.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.45 60[3:Obv:59.0] || -> .
% 0.20/0.45 61[2:Spt:60.0,16.1,37.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.20/0.45 62[2:Spt:60.0,16.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.45 64[2:MRR:15.1,61.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.45 66[2:MRR:14.0,61.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.45 73[2:SpL:66.0,30.1] || equal(inverse(sk_c2),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.45 74[2:Obv:73.1] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.20/0.45 75[2:Rew:64.0,74.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.45 76[2:Obv:75.0] || -> .
% 0.20/0.45 77[1:Spt:76.0,29.0,29.2,29.3,29.5,29.6,29.7] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(sk_c5,sk_c4),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.20/0.45 78[2:Spt:4.1] || -> equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.20/0.45 79[2:Rew:78.0,77.5] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)** equal(sk_c4,sk_c4) -> .
% 0.20/0.45 80[2:Obv:79.5] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c5)** -> .
% 0.20/0.45 82[3:Spt:22.1] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.45 83[3:Rew:82.0,80.4] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.45 84[3:Obv:83.4] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6)** -> .
% 0.20/0.45 86[4:Spt:16.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.45 88[5:Spt:10.1] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.45 92[4:SpR:86.0,27.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.20/0.45 98[3:SpR:82.0,28.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.45 101[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.45 103[0:Rew:26.0,101.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.45 106[0:SpR:103.0,103.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.45 108[2:SpR:78.0,103.0] || -> equal(multiply(inverse(sk_c6),sk_c4),sk_c5)**.
% 0.20/0.45 109[4:SpR:92.0,103.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c1)**.
% 0.20/0.45 110[3:SpR:82.0,103.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c6)**.
% 0.20/0.45 111[5:SpR:88.0,103.0] || -> equal(multiply(inverse(sk_c1),sk_c5),sk_c6)**.
% 0.20/0.45 112[0:SpR:26.0,103.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.20/0.45 113[0:SpR:27.0,103.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.45 116[5:Rew:78.0,111.0,86.0,111.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.45 119[5:Rew:116.0,84.1] || equal(inverse(u),sk_c4) equal(inverse(sk_c6),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6)** -> .
% 0.20/0.45 122[5:Rew:116.0,108.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.45 123[5:Rew:116.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.45 124[5:Rew:27.0,122.0] || -> equal(identity,sk_c5)**.
% 0.20/0.45 125[5:Rew:124.0,26.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.45 126[5:Rew:124.0,27.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.45 128[5:Rew:124.0,109.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c1)**.
% 0.20/0.45 131[5:Rew:123.0,128.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.45 132[5:Rew:131.0,86.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.45 144[5:Rew:116.0,119.3,125.0,119.3,116.0,119.2,132.0,119.1,116.0,119.0] || equal(inverse(u),sk_c6) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(sk_c6,sk_c6) -> .
% 0.20/0.45 145[5:Obv:144.3] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.45 181[5:SpL:126.0,145.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.45 188[5:Obv:181.1] || equal(inverse(inverse(sk_c6)),sk_c6)** -> .
% 0.20/0.45 189[5:Rew:132.0,188.0,132.0,188.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.45 190[5:Obv:189.0] || -> .
% 0.20/0.45 191[5:Spt:190.0,10.1,88.0] || equal(multiply(sk_c1,sk_c6),sk_c5)** -> .
% 0.20/0.45 192[5:Spt:190.0,10.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.45 194[5:Rew:192.0,109.0] || -> equal(multiply(sk_c4,identity),sk_c1)**.
% 0.20/0.45 197[0:Rew:106.0,113.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.45 198[5:Rew:197.0,194.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.45 199[5:Rew:198.0,86.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.45 201[5:Rew:198.0,191.0] || equal(multiply(sk_c4,sk_c6),sk_c5)** -> .
% 0.20/0.45 203[5:Rew:199.0,110.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.45 204[5:Rew:78.0,203.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.45 206[5:Rew:204.0,82.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.45 220[5:Rew:206.0,201.0,204.0,201.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.45 221[5:Obv:220.0] || -> .
% 0.20/0.45 230[4:Spt:221.0,16.1,86.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.20/0.45 231[4:Spt:221.0,16.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.45 237[4:MRR:13.0,230.0] || -> equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.20/0.45 238[4:Rew:237.0,84.3,231.0,84.1] || equal(inverse(u),sk_c4) equal(sk_c4,sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(sk_c6,sk_c6) -> .
% 0.20/0.46 239[4:Obv:238.3] || equal(inverse(u),sk_c4) equal(multiply(u,sk_c4),sk_c5)** -> .
% 0.20/0.46 240[4:SpR:231.0,103.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.46 242[4:Rew:98.0,240.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.46 243[4:Rew:242.0,237.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.46 246[4:Rew:243.0,231.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.46 253[4:Rew:243.0,239.0] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c4),sk_c5)** -> .
% 0.20/0.46 257[4:Rew:243.0,253.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.46 297[4:SpR:242.0,197.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 302[4:Rew:297.0,27.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.46 352[4:SpL:302.0,257.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.46 358[4:Obv:352.1] || equal(inverse(inverse(sk_c6)),sk_c6)** -> .
% 0.20/0.46 359[4:Rew:246.0,358.0,246.0,358.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 360[4:Obv:359.0] || -> .
% 0.20/0.46 361[3:Spt:360.0,22.1,82.0] || equal(multiply(sk_c4,sk_c6),sk_c5)** -> .
% 0.20/0.46 362[3:Spt:360.0,22.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.46 363[3:Rew:362.0,108.0] || -> equal(multiply(sk_c4,sk_c4),sk_c5)**.
% 0.20/0.46 365[3:MRR:21.1,361.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 367[3:MRR:20.1,361.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 387[3:SpR:367.0,103.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 389[3:Rew:78.0,387.0,365.0,387.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.46 393[3:Rew:389.0,363.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 395[3:Rew:389.0,361.0] || equal(multiply(sk_c6,sk_c6),sk_c5)** -> .
% 0.20/0.46 404[3:Rew:393.0,395.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.46 405[3:Obv:404.0] || -> .
% 0.20/0.46 411[2:Spt:405.0,4.1,78.0] || equal(multiply(sk_c6,sk_c5),sk_c4)** -> .
% 0.20/0.46 412[2:Spt:405.0,4.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.46 413[2:MRR:6.1,411.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.20/0.46 414[2:MRR:3.1,411.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 415[2:MRR:5.1,411.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.46 416[2:MRR:2.1,411.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 417[2:MRR:1.1,411.0] || -> equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.20/0.46 425[2:SpR:415.0,103.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.46 427[2:Rew:413.0,425.0] || -> equal(multiply(sk_c4,sk_c5),sk_c4)**.
% 0.20/0.46 429[2:SpR:416.0,103.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 431[2:Rew:414.0,429.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.46 432[2:Rew:431.0,411.0] || equal(sk_c4,sk_c6)** -> .
% 0.20/0.46 434[2:SpR:417.0,103.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c4)**.
% 0.20/0.46 437[2:SpR:427.0,103.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c5)**.
% 0.20/0.46 439[2:Rew:27.0,437.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 443[2:Rew:439.0,112.0] || -> equal(multiply(inverse(sk_c5),u),u)**.
% 0.20/0.46 449[2:Rew:443.0,434.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.46 450[2:MRR:449.0,432.0] || -> .
% 0.20/0.46 % SZS output end Refutation
% 0.20/0.46 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_8 prove_this_9 prove_this_10 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_20 prove_this_21 prove_this_22 prove_this_25 left_identity left_inverse associativity
% 0.20/0.46
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