TSTP Solution File: GRP278-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP278-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP278-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 00:59:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 667 clauses, backtracked 227 clauses, performed 9 splits and kept 553 clauses.
% 0.20/0.48 SPASS allocated 63520 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.04 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 315 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c1,sk_c6),sk_c5).
% 0.20/0.48 2[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.48 3[0:Inp] || -> equal(multiply(sk_c2,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c6),sk_c5).
% 0.20/0.48 4[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.48 5[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5)** equal(multiply(sk_c1,sk_c6),sk_c5).
% 0.20/0.48 6[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c2),sk_c6)** equal(inverse(sk_c1),sk_c6).
% 0.20/0.48 8[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c3),sk_c5)** equal(inverse(sk_c1),sk_c6).
% 0.20/0.48 10[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 11[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c2),sk_c6)** equal(inverse(sk_c4),sk_c5).
% 0.20/0.48 13[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c3),sk_c5)** equal(inverse(sk_c4),sk_c5).
% 0.20/0.48 15[0:Inp] || -> equal(inverse(sk_c4),sk_c5) equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 16[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c4),sk_c5).
% 0.20/0.48 17[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.20/0.48 18[0:Inp] || -> equal(multiply(sk_c2,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c4),sk_c5).
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.20/0.48 20[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5)** equal(multiply(sk_c6,sk_c4),sk_c5).
% 0.20/0.48 21[0:Inp] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(sk_c4),sk_c5) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(v,sk_c5),sk_c6)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c4),sk_c5) -> .
% 0.20/0.48 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 25[1:Spt:21.0,21.4] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c4),sk_c5)** -> .
% 0.20/0.48 26[2:Spt:11.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.48 28[3:Spt:16.1] || -> equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.20/0.48 30[3:SpL:28.0,25.1] || equal(inverse(sk_c6),sk_c5)** equal(sk_c5,sk_c5) -> .
% 0.20/0.48 31[3:Obv:30.1] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.20/0.48 32[4:Spt:6.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 34[5:Spt:1.1] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.48 37[1:SpL:22.0,25.1] || equal(inverse(identity),sk_c5)** equal(sk_c5,sk_c4) -> .
% 0.20/0.48 39[2:SpR:26.0,23.0] || -> equal(multiply(sk_c5,sk_c4),identity)**.
% 0.20/0.48 40[4:SpR:32.0,23.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.20/0.48 41[1:SpL:23.0,25.1] || equal(inverse(inverse(sk_c4)),sk_c5)** equal(sk_c5,identity) -> .
% 0.20/0.48 42[2:Rew:26.0,41.0] || equal(inverse(sk_c5),sk_c5)** equal(sk_c5,identity) -> .
% 0.20/0.48 51[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 54[0:Rew:22.0,51.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 56[4:SpR:40.0,24.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.20/0.48 58[4:Rew:22.0,56.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.20/0.48 64[5:SpR:34.0,58.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.48 69[0:SpR:54.0,54.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 72[2:SpR:39.0,54.0] || -> equal(multiply(inverse(sk_c5),identity),sk_c4)**.
% 0.20/0.48 75[0:SpR:23.0,54.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 77[4:SpR:40.0,54.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c1)**.
% 0.20/0.48 78[5:SpR:64.0,54.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.48 84[5:Rew:23.0,78.0] || -> equal(sk_c5,identity)**.
% 0.20/0.48 87[5:Rew:84.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 90[5:Rew:84.0,39.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.20/0.48 92[5:Rew:84.0,64.0] || -> equal(multiply(sk_c6,identity),sk_c6)**.
% 0.20/0.48 95[5:Rew:84.0,42.0] || equal(inverse(identity),identity)** equal(sk_c5,identity) -> .
% 0.20/0.48 101[5:Rew:22.0,90.0] || -> equal(identity,sk_c4)**.
% 0.20/0.48 102[5:Rew:101.0,22.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.48 104[5:Rew:101.0,40.0] || -> equal(multiply(sk_c6,sk_c1),sk_c4)**.
% 0.20/0.48 107[5:Rew:101.0,84.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 109[5:Rew:101.0,87.0] || -> equal(multiply(sk_c6,sk_c4),sk_c4)**.
% 0.20/0.48 112[5:Rew:101.0,92.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 113[5:Rew:112.0,109.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 114[5:Rew:113.0,101.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 115[5:Rew:113.0,107.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 118[5:Rew:113.0,102.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 119[5:Rew:113.0,104.0] || -> equal(multiply(sk_c6,sk_c1),sk_c6)**.
% 0.20/0.48 124[5:Rew:118.0,119.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.48 125[5:Rew:124.0,32.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 127[5:Rew:124.0,114.0] || -> equal(identity,sk_c1)**.
% 0.20/0.48 128[5:Rew:124.0,115.0] || -> equal(sk_c5,sk_c1)**.
% 0.20/0.48 146[5:Rew:128.0,95.1,127.0,95.1,125.0,95.0,127.0,95.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 147[5:Obv:146.1] || -> .
% 0.20/0.48 154[5:Spt:147.0,1.1,34.0] || equal(multiply(sk_c1,sk_c6),sk_c5)** -> .
% 0.20/0.48 155[5:Spt:147.0,1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 156[0:Rew:69.0,75.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 157[4:Rew:156.0,77.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.20/0.48 158[2:Rew:156.0,72.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.20/0.48 159[4:Rew:157.0,31.0] || equal(sk_c5,sk_c1)** -> .
% 0.20/0.48 163[5:MRR:4.1,154.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 166[5:MRR:5.1,154.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 169[5:SpR:155.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 171[5:Rew:158.0,169.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.20/0.48 180[5:SpR:163.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c3,u)),u)**.
% 0.20/0.48 194[5:SpR:166.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 196[5:Rew:163.0,194.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 218[5:SpR:196.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 220[5:Rew:171.0,218.0,158.0,218.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 223[5:Rew:220.0,158.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 225[5:Rew:220.0,159.0] || equal(sk_c6,sk_c1)** -> .
% 0.20/0.48 227[5:Rew:220.0,28.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 228[5:Rew:220.0,166.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.20/0.48 244[5:Rew:220.0,180.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 246[5:Rew:157.0,223.0] || -> equal(sk_c4,sk_c1)**.
% 0.20/0.48 252[5:Rew:246.0,227.0] || -> equal(multiply(sk_c6,sk_c1),sk_c6)**.
% 0.20/0.48 253[5:Rew:40.0,252.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 255[5:Rew:253.0,22.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 259[5:Rew:246.0,228.0] || -> equal(multiply(sk_c3,sk_c1),sk_c6)**.
% 0.20/0.48 283[5:Rew:255.0,244.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 284[5:Rew:283.0,259.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.48 285[5:MRR:284.0,225.0] || -> .
% 0.20/0.48 298[4:Spt:285.0,6.0,32.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.20/0.48 299[4:Spt:285.0,6.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 300[4:MRR:9.1,298.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 302[4:MRR:10.0,298.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 305[4:SpR:299.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 307[4:Rew:158.0,305.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.20/0.48 312[4:SpR:300.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c3,u)),u)**.
% 0.20/0.48 325[4:SpR:302.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 327[4:Rew:300.0,325.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 337[4:SpR:327.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 339[4:Rew:307.0,337.0,158.0,337.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 341[4:Rew:339.0,158.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 344[4:Rew:339.0,28.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 345[4:Rew:339.0,39.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 346[4:Rew:339.0,31.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.48 347[4:Rew:339.0,302.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.20/0.48 361[4:Rew:339.0,312.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 363[4:Rew:344.0,345.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 364[4:Rew:363.0,22.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 368[4:Rew:341.0,346.0] || equal(sk_c4,sk_c6)** -> .
% 0.20/0.48 388[4:Rew:364.0,361.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 389[4:Rew:388.0,347.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 390[4:MRR:389.0,368.0] || -> .
% 0.20/0.48 399[3:Spt:390.0,16.1,28.0] || equal(multiply(sk_c6,sk_c4),sk_c5)** -> .
% 0.20/0.48 400[3:Spt:390.0,16.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 401[3:MRR:19.1,399.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 402[3:MRR:17.1,399.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 403[3:MRR:20.1,399.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 404[3:MRR:18.1,399.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 406[3:SpR:400.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 408[3:Rew:158.0,406.0] || -> equal(multiply(sk_c4,sk_c4),sk_c6)**.
% 0.20/0.48 423[3:SpR:403.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 425[3:Rew:401.0,423.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 427[3:SpR:404.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 429[3:Rew:402.0,427.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 435[3:SpR:425.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 437[3:Rew:408.0,435.0,158.0,435.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 438[3:Rew:437.0,400.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 439[3:Rew:437.0,26.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 442[3:Rew:437.0,39.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 451[3:Rew:437.0,37.1] || equal(inverse(identity),sk_c5)** equal(sk_c4,sk_c6) -> .
% 0.20/0.48 457[3:Rew:437.0,429.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 458[3:Rew:438.0,457.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 459[3:Rew:458.0,408.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 461[3:Rew:458.0,439.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 464[3:Rew:458.0,442.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.20/0.48 466[3:Rew:459.0,464.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 488[3:Rew:458.0,451.1,461.0,451.0,466.0,451.0,437.0,451.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 489[3:Obv:488.1] || -> .
% 0.20/0.48 493[2:Spt:489.0,11.0,26.0] || equal(inverse(sk_c4),sk_c5)** -> .
% 0.20/0.48 494[2:Spt:489.0,11.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 495[2:MRR:14.1,493.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 496[2:MRR:12.1,493.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 497[2:MRR:15.0,493.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 498[2:MRR:13.0,493.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 500[2:SpR:494.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 507[2:SpR:497.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 509[2:Rew:495.0,507.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 511[2:SpR:498.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 513[2:Rew:496.0,511.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 515[2:SpR:509.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 517[2:Rew:500.0,515.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 518[2:Rew:517.0,494.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 520[2:Rew:517.0,493.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.48 522[2:Rew:517.0,498.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.48 528[2:Rew:517.0,500.0] || -> equal(multiply(inverse(sk_c6),sk_c4),sk_c6)**.
% 0.20/0.48 533[2:Rew:517.0,513.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 534[2:Rew:518.0,533.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 536[2:Rew:534.0,520.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.48 538[2:Rew:23.0,528.0,534.0,528.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 540[2:Rew:538.0,156.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 545[2:Rew:540.0,522.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 547[2:Rew:545.0,496.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 549[2:MRR:547.0,536.0] || -> .
% 0.20/0.48 562[1:Spt:549.0,21.1,21.2,21.3,21.5,21.6,21.7,21.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c4),sk_c5) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c4),sk_c5) -> .
% 0.20/0.48 564[2:Spt:11.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.20/0.48 565[2:Rew:564.0,562.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(sk_c5,sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c4),sk_c5) -> .
% 0.20/0.48 567[2:Obv:565.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c4),sk_c5) -> .
% 0.20/0.48 569[2:SpR:564.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c4,u)),u)**.
% 0.20/0.48 571[3:Spt:16.1] || -> equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.20/0.48 573[3:Rew:571.0,567.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(sk_c5,sk_c5) -> .
% 0.20/0.48 574[3:Obv:573.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c6),sk_c4)** -> .
% 0.20/0.48 576[3:SpR:571.0,24.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(sk_c5,u))**.
% 0.20/0.48 579[4:Spt:6.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.48 580[4:SpR:579.0,54.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.20/0.48 588[5:Spt:1.1] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.20/0.48 590[5:SpR:588.0,54.0] || -> equal(multiply(inverse(sk_c1),sk_c5),sk_c6)**.
% 0.20/0.48 592[5:Rew:579.0,590.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.48 598[5:SpR:592.0,54.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.48 600[5:Rew:23.0,598.0] || -> equal(sk_c5,identity)**.
% 0.20/0.48 602[5:Rew:600.0,571.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 603[5:Rew:600.0,588.0] || -> equal(multiply(sk_c1,sk_c6),identity)**.
% 0.20/0.48 606[5:Rew:600.0,574.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(identity,sk_c6),sk_c4)** -> .
% 0.20/0.48 607[5:Rew:600.0,569.0] || -> equal(multiply(identity,multiply(sk_c4,u)),u)**.
% 0.20/0.48 609[5:Rew:600.0,576.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.48 612[5:Rew:22.0,607.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.48 615[5:Rew:22.0,609.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.48 616[5:Rew:612.0,615.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 617[5:Rew:616.0,602.0] || -> equal(identity,sk_c4)**.
% 0.20/0.48 618[5:Rew:616.0,580.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 619[5:Rew:617.0,156.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.20/0.48 621[5:Rew:617.0,23.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.20/0.48 623[5:Rew:617.0,600.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 625[5:Rew:617.0,603.0] || -> equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.20/0.48 626[5:Rew:618.0,625.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 629[5:Rew:626.0,617.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 630[5:Rew:626.0,623.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 632[5:Rew:626.0,619.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 633[5:Rew:626.0,621.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 636[5:Rew:629.0,606.4,632.0,606.4,626.0,606.4,632.0,606.3,630.0,606.3,632.0,606.2,630.0,606.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(sk_c6,sk_c6) -> .
% 0.20/0.48 637[5:Obv:636.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.20/0.48 638[5:Con:637.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.48 648[5:SpR:579.0,633.0] || -> equal(multiply(sk_c6,sk_c1),sk_c6)**.
% 0.20/0.48 649[5:Rew:616.0,648.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.48 650[5:Rew:649.0,579.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 658[5:Rew:649.0,638.0] || equal(inverse(u),sk_c1)** equal(u,sk_c6) -> .
% 0.20/0.48 661[5:Rew:649.0,658.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.48 694[5:SpL:650.0,661.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 696[5:Obv:694.1] || -> .
% 0.20/0.48 697[5:Spt:696.0,1.1,588.0] || equal(multiply(sk_c1,sk_c6),sk_c5)** -> .
% 0.20/0.48 698[5:Spt:696.0,1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 699[5:MRR:4.1,697.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 700[5:MRR:2.1,697.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 701[5:MRR:5.1,697.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 702[5:MRR:3.1,697.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 708[5:SpR:698.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 719[5:SpR:701.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 721[5:Rew:699.0,719.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 726[5:SpR:702.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 728[5:Rew:700.0,726.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 729[5:SpR:721.0,24.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.20/0.48 730[5:SpR:721.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 732[5:Rew:708.0,730.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 733[5:Rew:732.0,698.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 741[5:Rew:732.0,697.0] || equal(multiply(sk_c1,sk_c6),sk_c6)** -> .
% 0.20/0.48 742[5:Rew:732.0,569.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.48 751[5:Rew:732.0,728.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 752[5:Rew:733.0,751.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 759[5:Rew:752.0,742.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.48 760[5:Rew:759.0,729.0,732.0,729.0,752.0,729.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 764[5:Rew:760.0,580.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 765[5:UnC:764.0,741.0] || -> .
% 0.20/0.48 772[4:Spt:765.0,6.0,579.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.20/0.48 773[4:Spt:765.0,6.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 774[4:MRR:9.1,772.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 775[4:MRR:7.1,772.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 776[4:MRR:10.0,772.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 777[4:MRR:8.0,772.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 778[4:Rew:773.0,574.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(sk_c4,sk_c4) -> .
% 0.20/0.48 779[4:Obv:778.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.20/0.48 783[4:SpR:773.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 795[4:SpR:776.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 797[4:Rew:774.0,795.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 799[4:SpR:777.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 801[4:Rew:775.0,799.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 802[4:SpR:797.0,24.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.20/0.48 803[4:SpR:797.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 805[4:Rew:783.0,803.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 806[4:Rew:805.0,773.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 807[4:Rew:805.0,564.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 814[4:Rew:805.0,569.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.48 818[4:Rew:805.0,779.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.20/0.48 823[4:Rew:805.0,801.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 824[4:Rew:806.0,823.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 825[4:Rew:824.0,807.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 831[4:Rew:824.0,814.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.48 832[4:Rew:831.0,802.0,805.0,802.0,824.0,802.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 839[4:Rew:805.0,818.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.20/0.48 840[4:Con:839.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.48 862[4:SpR:832.0,156.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 865[4:Rew:862.0,156.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 868[4:Rew:865.0,840.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.48 896[4:SpL:825.0,868.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 897[4:Obv:896.1] || -> .
% 0.20/0.48 898[3:Spt:897.0,16.1,571.0] || equal(multiply(sk_c6,sk_c4),sk_c5)** -> .
% 0.20/0.48 899[3:Spt:897.0,16.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 900[3:MRR:19.1,898.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 901[3:MRR:17.1,898.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 902[3:MRR:20.1,898.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 903[3:MRR:18.1,898.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 905[3:SpR:899.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 914[3:SpR:902.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 916[3:Rew:900.0,914.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 918[3:SpR:903.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 920[3:Rew:901.0,918.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 925[3:SpR:916.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 927[3:Rew:905.0,925.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 928[3:Rew:927.0,899.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 934[3:Rew:927.0,898.0] || equal(multiply(sk_c6,sk_c4),sk_c6)** -> .
% 0.20/0.48 941[3:Rew:927.0,920.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 942[3:Rew:928.0,941.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 944[3:Rew:942.0,928.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 946[3:Rew:944.0,934.0,942.0,934.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 947[3:Obv:946.0] || -> .
% 0.20/0.48 956[2:Spt:947.0,11.0,564.0] || equal(inverse(sk_c4),sk_c5)** -> .
% 0.20/0.48 957[2:Spt:947.0,11.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.20/0.48 958[2:MRR:14.1,956.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.20/0.48 959[2:MRR:12.1,956.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.48 960[2:MRR:15.0,956.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.20/0.48 961[2:MRR:13.0,956.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 963[2:SpR:957.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.20/0.48 970[2:SpR:960.0,54.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.20/0.48 972[2:Rew:958.0,970.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.20/0.48 974[2:SpR:961.0,54.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 976[2:Rew:959.0,974.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 978[2:SpR:972.0,54.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.20/0.48 980[2:Rew:963.0,978.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.48 981[2:Rew:980.0,957.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.48 983[2:Rew:980.0,956.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.48 985[2:Rew:980.0,961.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.48 987[2:Rew:980.0,963.0] || -> equal(multiply(inverse(sk_c6),sk_c4),sk_c6)**.
% 0.20/0.48 992[2:Rew:980.0,976.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 993[2:Rew:981.0,992.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 995[2:Rew:993.0,983.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.48 997[2:Rew:23.0,987.0,993.0,987.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 999[2:Rew:997.0,156.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 1004[2:Rew:999.0,985.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 1006[2:Rew:1004.0,959.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 1008[2:MRR:1006.0,995.0] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 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_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 left_identity left_inverse associativity
% 0.20/0.48
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