TSTP Solution File: GRP297-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP297-1 : 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 11:46:44 EDT 2022
% Result : Unsatisfiable 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP297-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % 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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 20:29:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 550 clauses, backtracked 230 clauses, performed 9 splits and kept 450 clauses.
% 0.18/0.45 SPASS allocated 63551 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.45 0:00:00.04 for the input.
% 0.18/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.00 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.04 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 4, length 197 :
% 0.18/0.45 % SZS output start Refutation
% 0.18/0.45 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.18/0.45 4[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.18/0.45 5[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.18/0.45 6[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.18/0.45 7[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 8[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 9[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 10[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 11[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 12[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.45 14[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.45 16[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.45 17[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 18[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.45 19[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.18/0.45 20[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.45 21[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.18/0.45 22[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.18/0.45 23[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.45 24[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.18/0.45 25[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,v),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.18/0.45 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.45 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.45 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.45 29[1:Spt:25.0,25.3,25.4] || equal(inverse(u),v) equal(multiply(u,v),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.45 30[2:Spt:19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.45 34[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.18/0.45 37[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 41[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 43[5:SpL:41.0,29.1] || equal(inverse(sk_c1),sk_c7) equal(sk_c6,sk_c6) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.45 44[5:Obv:43.1] || equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.45 45[5:Rew:37.0,44.0] || equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.45 46[5:Obv:45.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.45 48[4:SpR:37.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.18/0.45 59[4:SpR:48.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.45 61[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.45 63[4:Rew:26.0,59.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.45 64[0:Rew:26.0,61.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.45 68[5:SpR:41.0,63.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.45 70[5:Rew:34.0,68.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.45 71[5:Rew:70.0,30.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.45 77[5:MRR:71.0,46.0] || -> .
% 0.18/0.45 81[5:Spt:77.0,7.1,41.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.18/0.45 82[5:Spt:77.0,7.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.45 83[5:MRR:11.1,81.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.45 85[5:MRR:12.1,81.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.45 86[5:MRR:10.1,81.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.45 110[5:SpL:86.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 111[5:Obv:110.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 112[5:Rew:85.0,111.1,83.0,111.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.18/0.45 113[5:Obv:112.1] || -> .
% 0.18/0.45 114[4:Spt:113.0,13.0,37.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.45 115[4:Spt:113.0,13.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.45 116[4:MRR:17.1,114.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.45 118[4:MRR:18.0,114.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.45 119[4:MRR:16.0,114.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.45 136[4:SpL:119.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 137[4:Obv:136.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 138[4:Rew:118.0,137.1,116.0,137.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.18/0.45 139[4:Obv:138.1] || -> .
% 0.18/0.45 140[3:Spt:139.0,1.1,34.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.18/0.45 141[3:Spt:139.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.45 142[3:MRR:5.1,140.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.45 144[3:MRR:6.1,140.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.45 145[3:MRR:4.1,140.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.45 160[3:SpL:145.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 161[3:Obv:160.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 162[3:Rew:144.0,161.1,142.0,161.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.18/0.45 163[3:Obv:162.1] || -> .
% 0.18/0.45 164[2:Spt:163.0,19.1,30.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.18/0.45 165[2:Spt:163.0,19.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.45 166[2:MRR:23.1,164.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.45 168[2:MRR:24.1,164.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.45 169[2:MRR:22.1,164.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.45 184[2:SpL:169.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 185[2:Obv:184.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.18/0.45 186[2:Rew:168.0,185.1,166.0,185.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.18/0.45 187[2:Obv:186.1] || -> .
% 0.18/0.45 188[1:Spt:187.0,25.1,25.2,25.5,25.6,25.7,25.8,25.9] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.18/0.45 192[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.18/0.45 193[2:Rew:192.0,188.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(sk_c5,sk_c5) -> .
% 0.18/0.45 199[2:Obv:193.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.18/0.45 203[3:Spt:19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.45 205[3:Rew:203.0,199.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(sk_c6,sk_c6) -> .
% 0.18/0.45 210[3:Obv:205.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.18/0.45 214[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.45 215[4:SpR:214.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.18/0.45 217[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.45 220[4:SpR:215.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.46 222[4:Rew:26.0,220.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.46 225[5:SpR:217.0,222.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.46 226[5:Rew:192.0,225.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 227[5:Rew:226.0,192.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.46 228[5:Rew:226.0,203.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.46 230[5:Rew:226.0,210.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.18/0.46 242[0:SpR:64.0,64.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.46 245[0:SpR:27.0,64.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.46 247[4:SpR:215.0,64.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.18/0.46 248[4:SpR:222.0,64.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c1,u))**.
% 0.18/0.46 249[5:SpR:227.0,64.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.18/0.46 250[5:SpR:228.0,64.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.46 253[5:Rew:27.0,249.0] || -> equal(identity,sk_c6)**.
% 0.18/0.46 254[5:Rew:253.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.46 260[5:Rew:253.0,247.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.18/0.46 262[5:Rew:254.0,230.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.18/0.46 267[5:Rew:250.0,260.0] || -> equal(sk_c1,sk_c7)**.
% 0.18/0.46 268[5:Rew:267.0,214.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.46 273[5:Rew:253.0,245.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.18/0.46 277[5:Rew:242.0,273.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.46 281[5:Obv:262.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.46 282[5:Rew:277.0,281.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)**+ -> .
% 0.18/0.46 322[5:SpL:228.0,282.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.18/0.46 325[5:Obv:322.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.46 326[5:Rew:268.0,325.1] || equal(inverse(u),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) -> .
% 0.18/0.46 327[5:Obv:326.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.46 369[5:SpL:268.0,327.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.18/0.46 372[5:Obv:369.1] || -> .
% 0.18/0.46 374[5:Spt:372.0,7.1,217.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.18/0.46 375[5:Spt:372.0,7.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.46 377[5:MRR:11.1,374.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.46 378[5:MRR:8.1,374.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.46 379[0:Rew:242.0,245.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.46 381[5:MRR:10.1,374.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.46 382[5:MRR:9.1,374.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 401[3:SpR:203.0,64.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.18/0.46 403[4:Rew:248.0,401.0] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.18/0.46 417[5:SpR:381.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.18/0.46 419[5:Rew:377.0,417.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.18/0.46 421[5:SpR:382.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.18/0.46 423[5:Rew:378.0,421.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.46 436[5:SpR:419.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.18/0.46 438[5:Rew:27.0,436.0] || -> equal(identity,sk_c6)**.
% 0.18/0.46 440[5:Rew:438.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.46 444[5:Rew:438.0,379.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.46 446[5:Rew:440.0,375.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 457[5:Rew:446.0,403.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.18/0.46 467[5:Rew:444.0,457.0] || -> equal(sk_c1,sk_c7)**.
% 0.18/0.46 469[5:Rew:467.0,374.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.46 473[5:Rew:423.0,469.0] || equal(sk_c6,sk_c6)* -> .
% 0.18/0.46 474[5:Obv:473.0] || -> .
% 0.18/0.46 483[4:Spt:474.0,13.0,214.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.46 484[4:Spt:474.0,13.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.46 485[4:MRR:17.1,483.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.46 486[4:MRR:14.1,483.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.46 488[4:MRR:16.0,483.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.46 489[4:MRR:15.0,483.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 494[4:Rew:484.0,210.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.18/0.46 495[4:Obv:494.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.46 515[4:SpR:488.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.18/0.46 517[4:Rew:485.0,515.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.18/0.46 519[4:SpR:489.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.18/0.46 521[4:Rew:486.0,519.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.46 523[4:SpR:517.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.18/0.46 525[4:Rew:27.0,523.0] || -> equal(identity,sk_c6)**.
% 0.18/0.46 527[4:Rew:525.0,379.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.46 544[4:Rew:527.0,489.0] || -> equal(sk_c2,sk_c7)**.
% 0.18/0.46 547[4:Rew:527.0,495.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)**+ -> .
% 0.18/0.46 548[4:Rew:544.0,486.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.46 618[4:SpL:521.0,547.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.18/0.46 621[4:Obv:618.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.46 622[4:Rew:548.0,621.1] || equal(inverse(u),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) -> .
% 0.18/0.46 623[4:Obv:622.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.46 742[4:SpL:548.0,623.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.18/0.46 745[4:Obv:742.1] || -> .
% 0.18/0.46 747[3:Spt:745.0,19.1,203.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.18/0.46 748[3:Spt:745.0,19.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.46 750[3:MRR:23.1,747.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.46 751[3:MRR:20.1,747.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.46 753[3:MRR:22.1,747.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.46 754[3:MRR:21.1,747.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 777[3:SpR:753.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.18/0.46 779[3:Rew:750.0,777.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.18/0.46 781[3:SpR:754.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.18/0.46 783[3:Rew:751.0,781.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.46 785[3:SpR:779.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.18/0.46 787[3:Rew:27.0,785.0] || -> equal(identity,sk_c6)**.
% 0.18/0.46 788[3:Rew:787.0,379.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.46 793[3:Rew:788.0,192.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 800[3:Rew:793.0,747.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.18/0.46 806[3:Rew:783.0,800.0] || equal(sk_c6,sk_c6)* -> .
% 0.18/0.46 807[3:Obv:806.0] || -> .
% 0.18/0.46 811[2:Spt:807.0,1.1,192.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.18/0.46 812[2:Spt:807.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.46 813[2:MRR:5.1,811.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.18/0.46 816[2:MRR:4.1,811.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.18/0.46 829[2:SpR:816.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.18/0.46 831[2:Rew:813.0,829.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.18/0.46 837[2:SpR:831.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.18/0.46 839[2:Rew:27.0,837.0] || -> equal(identity,sk_c6)**.
% 0.18/0.46 840[2:Rew:839.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.46 841[2:Rew:839.0,379.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.46 844[2:Rew:840.0,812.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 849[2:Rew:844.0,811.0] || equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.18/0.46 855[2:Rew:841.0,849.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.46 856[2:Obv:855.0] || -> .
% 0.18/0.46 % SZS output end Refutation
% 0.18/0.46 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_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 left_identity left_inverse associativity
% 0.18/0.46
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