TSTP Solution File: GRP299-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP299-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP299-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Mon Jun 13 08:15:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 549 clauses, backtracked 230 clauses, performed 9 splits and kept 451 clauses.
% 0.21/0.47 SPASS allocated 63547 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.04 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 4, length 195 :
% 0.21/0.47 % SZS output start Refutation
% 0.21/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 4[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 5[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 6[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 7[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 8[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 9[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 10[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 11[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 12[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 14[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.47 16[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 18[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.47 19[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.47 20[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.47 21[0:Inp] || -> equal(multiply(sk_c2,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.21/0.47 22[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.21/0.47 23[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.47 24[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.21/0.47 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_c5,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.47 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.47 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.47 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)** -> .
% 0.21/0.47 30[2:Spt:19.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.47 34[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 37[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 41[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 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)** -> .
% 0.21/0.47 44[5:Obv:43.1] || equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.47 45[5:Rew:37.0,44.0] || equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.47 46[5:Obv:45.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.47 48[4:SpR:37.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.21/0.47 59[4:SpR:48.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.21/0.47 61[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.47 63[4:Rew:26.0,59.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.21/0.47 64[0:Rew:26.0,61.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.47 68[5:SpR:41.0,63.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.47 70[5:Rew:34.0,68.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 71[5:Rew:70.0,30.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.47 76[5:MRR:71.0,46.0] || -> .
% 0.21/0.47 79[5:Spt:76.0,7.1,41.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.21/0.47 80[5:Spt:76.0,7.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 81[5:MRR:11.1,79.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.47 83[5:MRR:12.1,79.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.47 84[5:MRR:10.1,79.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.47 108[5:SpL:84.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 109[5:Obv:108.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 110[5:Rew:83.0,109.1,81.0,109.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.21/0.47 111[5:Obv:110.1] || -> .
% 0.21/0.47 112[4:Spt:111.0,13.0,37.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.21/0.47 113[4:Spt:111.0,13.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 114[4:MRR:17.1,112.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.47 116[4:MRR:18.0,112.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.47 117[4:MRR:16.0,112.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.47 134[4:SpL:117.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 135[4:Obv:134.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 136[4:Rew:116.0,135.1,114.0,135.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.21/0.47 137[4:Obv:136.1] || -> .
% 0.21/0.47 138[3:Spt:137.0,1.1,34.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.47 139[3:Spt:137.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 140[3:MRR:5.1,138.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.47 142[3:MRR:6.1,138.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.47 143[3:MRR:4.1,138.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.47 158[3:SpL:143.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 159[3:Obv:158.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 160[3:Rew:142.0,159.1,140.0,159.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.21/0.47 161[3:Obv:160.1] || -> .
% 0.21/0.47 162[2:Spt:161.0,19.1,30.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.21/0.47 163[2:Spt:161.0,19.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 164[2:MRR:23.1,162.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.47 166[2:MRR:24.1,162.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.47 167[2:MRR:22.1,162.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.47 182[2:SpL:167.0,29.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 183[2:Obv:182.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.47 184[2:Rew:166.0,183.1,164.0,183.0] || equal(sk_c4,sk_c4)* equal(sk_c6,sk_c6) -> .
% 0.21/0.47 185[2:Obv:184.1] || -> .
% 0.21/0.47 186[1:Spt:185.0,25.1,25.2,25.5,25.6,25.7,25.8,25.9] || 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_c5,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 190[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 191[2:Rew:190.0,186.6] || 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_c5,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.21/0.47 197[2:Obv:191.6] || 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_c5,sk_c7),sk_c6)** -> .
% 0.21/0.47 201[3:Spt:19.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.47 203[3:Rew:201.0,197.5] || 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) -> .
% 0.21/0.47 208[3:Obv:203.5] || 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)** -> .
% 0.21/0.47 212[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 213[4:SpR:212.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.21/0.47 215[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 218[4:SpR:213.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.21/0.48 220[4:Rew:26.0,218.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.21/0.48 223[5:SpR:215.0,220.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.48 224[5:Rew:190.0,223.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 225[5:Rew:224.0,190.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.48 226[5:Rew:224.0,201.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.48 228[5:Rew:224.0,208.4] || 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)** -> .
% 0.21/0.48 240[0:SpR:64.0,64.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.48 243[0:SpR:27.0,64.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.48 245[4:SpR:213.0,64.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.21/0.48 247[5:SpR:225.0,64.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.48 248[5:SpR:226.0,64.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.48 251[5:Rew:27.0,247.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 252[5:Rew:251.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 258[5:Rew:251.0,245.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.21/0.48 260[5:Rew:252.0,228.4] || 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) -> .
% 0.21/0.48 265[5:Rew:248.0,258.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.48 266[5:Rew:265.0,212.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 271[5:Rew:251.0,243.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.21/0.48 275[5:Rew:240.0,271.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 279[5:Obv:260.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.21/0.48 280[5:Rew:275.0,279.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)**+ -> .
% 0.21/0.48 320[5:SpL:226.0,280.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.21/0.48 323[5:Obv:320.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 324[5:Rew:266.0,323.1] || equal(inverse(u),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.48 325[5:Obv:324.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 367[5:SpL:266.0,325.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 370[5:Obv:367.1] || -> .
% 0.21/0.48 372[5:Spt:370.0,7.1,215.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.21/0.48 373[5:Spt:370.0,7.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 375[5:MRR:11.1,372.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.48 376[5:MRR:8.1,372.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 377[0:Rew:240.0,243.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.48 379[5:MRR:10.1,372.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.48 380[5:MRR:9.1,372.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 409[4:SpR:213.0,64.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.21/0.48 411[4:Rew:377.0,409.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.48 417[5:SpR:379.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.21/0.48 419[5:Rew:375.0,417.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.21/0.48 421[5:SpR:380.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.21/0.48 423[5:Rew:376.0,421.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.48 432[5:SpR:419.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.21/0.48 434[5:Rew:27.0,432.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 440[5:Rew:434.0,377.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 455[5:Rew:440.0,380.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.48 459[5:Rew:455.0,376.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 461[5:Rew:411.0,459.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.48 464[5:Rew:461.0,372.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.48 470[5:Rew:423.0,464.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.48 471[5:Obv:470.0] || -> .
% 0.21/0.48 478[4:Spt:471.0,13.0,212.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.21/0.48 479[4:Spt:471.0,13.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 480[4:MRR:17.1,478.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.48 481[4:MRR:14.1,478.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 483[4:MRR:16.0,478.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.48 484[4:MRR:15.0,478.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 489[4:Rew:479.0,208.4] || 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) -> .
% 0.21/0.48 490[4:Obv:489.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.21/0.48 510[4:SpR:483.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.21/0.48 512[4:Rew:480.0,510.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.21/0.48 514[4:SpR:484.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.21/0.48 516[4:Rew:481.0,514.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.48 518[4:SpR:512.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.21/0.48 520[4:Rew:27.0,518.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 522[4:Rew:520.0,377.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 539[4:Rew:522.0,484.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.48 541[4:Rew:522.0,490.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)**+ -> .
% 0.21/0.48 543[4:Rew:539.0,481.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 613[4:SpL:516.0,541.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.21/0.48 616[4:Obv:613.3] || equal(inverse(u),sk_c7)** equal(inverse(sk_c7),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 617[4:Rew:543.0,616.1] || equal(inverse(u),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.48 618[4:Obv:617.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 737[4:SpL:543.0,618.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 740[4:Obv:737.1] || -> .
% 0.21/0.48 742[3:Spt:740.0,19.1,201.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.21/0.48 743[3:Spt:740.0,19.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 745[3:MRR:23.1,742.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.48 746[3:MRR:20.1,742.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 748[3:MRR:22.1,742.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.48 749[3:MRR:21.1,742.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 772[3:SpR:748.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.21/0.48 774[3:Rew:745.0,772.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.21/0.48 776[3:SpR:749.0,64.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.21/0.48 778[3:Rew:746.0,776.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.48 780[3:SpR:774.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.21/0.48 782[3:Rew:27.0,780.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 783[3:Rew:782.0,377.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 788[3:Rew:783.0,190.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 795[3:Rew:788.0,742.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.21/0.48 801[3:Rew:778.0,795.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.48 802[3:Obv:801.0] || -> .
% 0.21/0.48 806[2:Spt:802.0,1.1,190.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.48 807[2:Spt:802.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 808[2:MRR:5.1,806.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.48 811[2:MRR:4.1,806.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.21/0.48 824[2:SpR:811.0,64.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.21/0.48 826[2:Rew:808.0,824.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.21/0.48 832[2:SpR:826.0,64.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.21/0.48 834[2:Rew:27.0,832.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 835[2:Rew:834.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 836[2:Rew:834.0,377.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 839[2:Rew:835.0,807.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 844[2:Rew:839.0,806.0] || equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.21/0.48 850[2:Rew:836.0,844.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 851[2:Obv:850.0] || -> .
% 0.21/0.48 % SZS output end Refutation
% 0.21/0.48 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
% 0.21/0.48
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