TSTP Solution File: GRP304-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP304-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:46:46 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP304-1 : TPTP v8.1.0. Released v2.5.0.
% 0.05/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 13 13:55:41 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.37
% 0.13/0.37 SPASS V 3.9
% 0.13/0.37 SPASS beiseite: Proof found.
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 SPASS derived 745 clauses, backtracked 259 clauses, performed 9 splits and kept 581 clauses.
% 0.13/0.37 SPASS allocated 63556 KBytes.
% 0.13/0.37 SPASS spent 0:00:00.08 on the problem.
% 0.13/0.37 0:00:00.03 for the input.
% 0.13/0.37 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.37 0:00:00.00 for inferences.
% 0.13/0.37 0:00:00.00 for the backtracking.
% 0.13/0.37 0:00:00.03 for the reduction.
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 Here is a proof with depth 4, length 317 :
% 0.13/0.37 % SZS output start Refutation
% 0.13/0.37 1[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.13/0.37 2[0:Inp] || -> equal(multiply(sk_c2,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5).
% 0.13/0.37 3[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.13/0.37 4[0:Inp] || -> equal(multiply(sk_c7,sk_c4),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.13/0.37 5[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c4)** equal(multiply(sk_c6,sk_c7),sk_c5).
% 0.13/0.37 6[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.13/0.37 7[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 8[0:Inp] || -> equal(inverse(sk_c2),sk_c7)** equal(inverse(sk_c7),sk_c5).
% 0.13/0.37 9[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 10[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 11[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c7),sk_c5).
% 0.13/0.37 12[0:Inp] || -> equal(multiply(sk_c2,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 13[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 14[0:Inp] || -> equal(multiply(sk_c7,sk_c4),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 15[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c4) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 16[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 17[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 18[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(inverse(sk_c1),sk_c6)**.
% 0.13/0.37 19[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 20[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 21[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c6)**.
% 0.13/0.37 22[0:Inp] || equal(multiply(sk_c7,sk_c6),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(multiply(v,sk_c7),sk_c6)** equal(inverse(v),sk_c7) equal(multiply(sk_c7,w),sk_c6)** equal(multiply(x,sk_c7),w)* equal(inverse(x),sk_c7) -> .
% 0.13/0.37 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.13/0.37 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.13/0.37 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.13/0.37 26[0:Rew:1.0,22.0] || equal(sk_c5,sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(multiply(v,sk_c7),sk_c6)** equal(inverse(v),sk_c7) equal(multiply(sk_c7,w),sk_c6)** equal(multiply(x,sk_c7),w)* equal(inverse(x),sk_c7) -> .
% 0.13/0.37 27[0:Obv:26.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c7),x)*+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.37 28[1:Spt:27.0,27.4,27.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),v)*+ equal(multiply(sk_c7,v),sk_c6)** -> .
% 0.13/0.37 30[2:Spt:11.1] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.13/0.37 32[3:Spt:6.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.13/0.37 36[4:Spt:21.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.13/0.37 38[5:Spt:16.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 41[1:SpL:23.0,28.1] || equal(inverse(identity),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c6)** -> .
% 0.13/0.37 43[2:SpR:30.0,24.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.13/0.37 44[4:SpR:36.0,24.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.13/0.37 52[2:SpR:43.0,25.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.13/0.37 53[0:SpR:1.0,25.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.13/0.37 56[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.13/0.37 58[2:Rew:23.0,52.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.13/0.37 59[0:Rew:23.0,56.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.13/0.37 61[4:SpR:44.0,25.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.13/0.37 63[4:Rew:23.0,61.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.13/0.37 72[5:SpR:38.0,63.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.13/0.37 73[5:Rew:32.0,72.0] || -> equal(sk_c5,sk_c6)**.
% 0.13/0.37 74[5:Rew:73.0,30.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.13/0.37 75[5:Rew:73.0,32.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.13/0.37 77[5:Rew:73.0,43.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.13/0.37 85[5:Rew:75.0,77.0] || -> equal(identity,sk_c6)**.
% 0.13/0.37 86[5:Rew:85.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.13/0.37 87[5:Rew:85.0,24.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.13/0.37 89[5:Rew:85.0,41.0] || equal(inverse(sk_c6),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c6)** -> .
% 0.13/0.37 91[5:Rew:86.0,75.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.37 99[5:Rew:91.0,74.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.37 102[5:Rew:91.0,86.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.37 107[5:Rew:91.0,87.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.13/0.37 121[5:Rew:102.0,89.2,91.0,89.2,99.0,89.0,91.0,89.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.13/0.37 122[5:Obv:121.1] || equal(u,sk_c7)* -> .
% 0.13/0.37 123[5:UnC:122.0,107.0] || -> .
% 0.13/0.37 126[5:Spt:123.0,16.1,38.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.13/0.37 127[5:Spt:123.0,16.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.37 128[5:MRR:13.1,126.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.37 129[5:MRR:15.1,126.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 130[5:MRR:14.1,126.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 131[5:MRR:12.1,126.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 159[5:SpR:127.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.13/0.37 160[5:SpR:128.0,24.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.13/0.37 173[5:SpR:130.0,58.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.13/0.37 174[5:SpR:159.0,58.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.13/0.37 175[5:SpR:160.0,58.0] || -> equal(multiply(sk_c5,identity),sk_c2)**.
% 0.13/0.37 176[5:Rew:174.0,175.0] || -> equal(sk_c3,sk_c2)**.
% 0.13/0.37 178[5:Rew:176.0,129.0] || -> equal(multiply(sk_c2,sk_c7),sk_c4)**.
% 0.13/0.37 182[5:Rew:176.0,174.0] || -> equal(multiply(sk_c5,identity),sk_c2)**.
% 0.13/0.37 183[5:Rew:131.0,178.0] || -> equal(sk_c4,sk_c6)**.
% 0.13/0.37 184[5:Rew:183.0,130.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.13/0.37 186[5:Rew:183.0,173.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.13/0.37 187[5:Rew:1.0,184.0] || -> equal(sk_c5,sk_c6)**.
% 0.13/0.37 188[5:Rew:187.0,30.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.13/0.37 190[5:Rew:187.0,43.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.13/0.37 192[5:Rew:187.0,32.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.13/0.37 199[5:Rew:187.0,182.0] || -> equal(multiply(sk_c6,identity),sk_c2)**.
% 0.13/0.37 200[5:Rew:187.0,186.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.13/0.37 201[5:Rew:190.0,192.0] || -> equal(identity,sk_c6)**.
% 0.13/0.37 202[5:Rew:201.0,44.0] || -> equal(multiply(sk_c6,sk_c1),sk_c6)**.
% 0.13/0.37 203[5:Rew:201.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.13/0.37 204[5:Rew:201.0,24.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.13/0.37 206[5:Rew:201.0,41.0] || equal(inverse(sk_c6),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c6)** -> .
% 0.13/0.37 208[5:Rew:200.0,199.0,201.0,199.0] || -> equal(sk_c2,sk_c6)**.
% 0.13/0.37 209[5:Rew:208.0,128.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.13/0.37 214[5:Rew:203.0,202.0] || -> equal(sk_c1,sk_c6)**.
% 0.13/0.37 215[5:Rew:203.0,63.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.13/0.37 216[5:Rew:214.0,36.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.13/0.37 218[5:Rew:209.0,216.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.37 224[5:Rew:218.0,188.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.37 231[5:Rew:218.0,214.0] || -> equal(sk_c1,sk_c7)**.
% 0.13/0.37 235[5:Rew:231.0,215.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.37 236[5:Rew:218.0,204.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.13/0.37 255[5:Rew:235.0,206.2,218.0,206.2,224.0,206.0,218.0,206.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.13/0.37 256[5:Obv:255.1] || equal(u,sk_c7)* -> .
% 0.13/0.37 257[5:UnC:256.0,236.0] || -> .
% 0.13/0.37 260[4:Spt:257.0,21.1,36.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.13/0.37 261[4:Spt:257.0,21.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.37 262[4:MRR:18.1,260.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.37 263[4:MRR:20.0,260.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 264[4:MRR:19.0,260.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 265[4:MRR:17.0,260.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 289[4:SpR:261.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.13/0.37 291[4:SpR:262.0,24.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.13/0.37 303[4:SpR:289.0,58.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.13/0.37 304[4:SpR:291.0,58.0] || -> equal(multiply(sk_c5,identity),sk_c2)**.
% 0.13/0.37 305[4:Rew:303.0,304.0] || -> equal(sk_c3,sk_c2)**.
% 0.13/0.37 307[4:Rew:305.0,263.0] || -> equal(multiply(sk_c2,sk_c7),sk_c4)**.
% 0.13/0.37 312[4:Rew:265.0,307.0] || -> equal(sk_c4,sk_c6)**.
% 0.13/0.37 313[4:Rew:312.0,264.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.13/0.37 316[4:Rew:1.0,313.0] || -> equal(sk_c5,sk_c6)**.
% 0.13/0.37 317[4:Rew:316.0,30.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.13/0.37 318[4:Rew:316.0,32.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.13/0.37 320[4:Rew:316.0,43.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.13/0.37 330[4:Rew:318.0,320.0] || -> equal(identity,sk_c6)**.
% 0.13/0.37 331[4:Rew:330.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.13/0.37 332[4:Rew:330.0,24.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.13/0.37 334[4:Rew:330.0,41.0] || equal(inverse(sk_c6),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c6)** -> .
% 0.13/0.37 341[4:Rew:331.0,318.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.37 348[4:Rew:341.0,317.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.37 354[4:Rew:341.0,331.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.37 357[4:Rew:341.0,332.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.13/0.37 374[4:Rew:354.0,334.2,341.0,334.2,348.0,334.0,341.0,334.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.13/0.37 375[4:Obv:374.1] || equal(u,sk_c7)* -> .
% 0.13/0.37 376[4:UnC:375.0,357.0] || -> .
% 0.13/0.37 379[3:Spt:376.0,6.1,32.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.37 380[3:Spt:376.0,6.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.37 381[3:MRR:3.1,379.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.37 382[3:MRR:5.1,379.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 383[3:MRR:4.1,379.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 384[3:MRR:2.1,379.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 406[3:SpR:380.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.13/0.37 408[3:SpR:381.0,24.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.13/0.37 417[0:SpR:59.0,59.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.13/0.37 422[0:SpR:1.0,59.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.13/0.37 423[3:SpR:383.0,59.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.13/0.37 424[3:SpR:406.0,59.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.13/0.37 425[3:SpR:408.0,59.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.13/0.37 426[3:SpR:382.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.37 428[0:SpR:23.0,59.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.13/0.37 429[0:SpR:24.0,59.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.13/0.37 434[3:Rew:30.0,423.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.13/0.37 435[3:Rew:30.0,424.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.13/0.37 436[3:Rew:30.0,425.0] || -> equal(multiply(sk_c5,identity),sk_c2)**.
% 0.13/0.37 437[3:Rew:435.0,436.0] || -> equal(sk_c3,sk_c2)**.
% 0.13/0.37 439[3:Rew:437.0,382.0] || -> equal(multiply(sk_c2,sk_c7),sk_c4)**.
% 0.13/0.37 444[3:Rew:384.0,439.0] || -> equal(sk_c4,sk_c6)**.
% 0.13/0.37 445[3:Rew:444.0,383.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.13/0.37 447[3:Rew:444.0,434.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.13/0.37 448[3:Rew:1.0,445.0] || -> equal(sk_c5,sk_c6)**.
% 0.13/0.37 449[3:Rew:448.0,30.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.13/0.37 451[3:Rew:448.0,1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.13/0.37 452[3:Rew:448.0,43.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.13/0.37 461[3:Rew:448.0,447.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.13/0.37 462[3:Rew:437.0,426.0,444.0,426.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.13/0.37 463[3:Rew:381.0,462.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.13/0.37 464[3:Rew:451.0,463.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.37 468[3:Rew:464.0,41.2] || equal(inverse(identity),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.13/0.37 473[3:Rew:464.0,449.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.37 474[3:Rew:464.0,461.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.13/0.37 476[3:Rew:464.0,452.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.13/0.37 478[3:Rew:474.0,476.0] || -> equal(identity,sk_c7)**.
% 0.13/0.37 479[3:Rew:478.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.37 510[3:Rew:479.0,468.2,473.0,468.0,478.0,468.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.13/0.37 511[3:Obv:510.1] || equal(u,sk_c7)* -> .
% 0.13/0.37 512[3:UnC:511.0,59.0] || -> .
% 0.13/0.37 515[2:Spt:512.0,11.1,30.0] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.13/0.37 516[2:Spt:512.0,11.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.37 517[0:Rew:417.0,429.0] || -> equal(multiply(u,identity),u)**.
% 0.13/0.37 518[2:MRR:8.1,515.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.37 519[2:MRR:10.0,515.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.37 520[2:MRR:9.0,515.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.37 521[2:MRR:7.0,515.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.37 530[2:SpR:519.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.37 532[2:Rew:516.0,530.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.37 533[2:Rew:520.0,532.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.37 534[2:Rew:533.0,1.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.13/0.37 535[2:Rew:533.0,422.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.13/0.37 537[2:Rew:533.0,520.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.37 538[2:Rew:533.0,521.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.13/0.37 549[2:SpR:537.0,59.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c4)**.
% 0.13/0.37 551[2:Rew:24.0,549.0] || -> equal(identity,sk_c4)**.
% 0.13/0.37 553[2:Rew:551.0,24.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.13/0.37 556[2:Rew:551.0,517.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.13/0.37 562[2:SpR:538.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.13/0.37 564[2:Rew:534.0,562.0,518.0,562.0] || -> equal(sk_c5,sk_c7)**.
% 0.13/0.37 565[2:Rew:564.0,515.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.13/0.37 567[2:Rew:564.0,535.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.13/0.37 569[2:Rew:553.0,567.0] || -> equal(sk_c4,sk_c7)**.
% 0.13/0.37 570[2:Rew:569.0,519.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.13/0.37 573[2:Rew:569.0,556.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.13/0.37 585[2:Rew:573.0,570.0] || -> equal(sk_c3,sk_c7)**.
% 0.13/0.37 587[2:Rew:585.0,516.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.37 589[2:MRR:587.0,565.0] || -> .
% 0.13/0.37 600[1:Spt:589.0,27.1,27.2,27.3,27.5,27.6,27.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c7),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.37 602[2:Spt:8.1] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.13/0.37 603[2:Rew:602.0,600.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(sk_c5,sk_c5) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.37 606[2:Obv:603.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.37 608[2:SpR:602.0,59.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.13/0.37 610[3:Spt:3.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.13/0.37 612[3:Rew:610.0,606.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(sk_c5,sk_c5) -> .
% 0.13/0.37 613[3:Obv:612.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.13/0.37 615[3:SpR:610.0,25.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.13/0.37 616[3:SpR:610.0,59.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.13/0.37 618[4:Spt:21.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.13/0.37 619[4:SpR:618.0,59.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.13/0.37 625[5:Spt:16.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.13/0.37 627[5:SpR:625.0,59.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.13/0.37 629[5:Rew:610.0,627.0,618.0,627.0] || -> equal(sk_c5,sk_c6)**.
% 0.13/0.37 630[5:Rew:629.0,602.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.13/0.37 637[5:Rew:629.0,616.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.13/0.37 638[5:Rew:24.0,637.0] || -> equal(identity,sk_c7)**.
% 0.13/0.38 639[5:Rew:638.0,517.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.13/0.38 641[5:Rew:638.0,428.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.13/0.38 644[5:Rew:639.0,613.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.13/0.38 645[5:Rew:630.0,641.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.13/0.38 646[5:Rew:645.0,619.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.13/0.38 647[5:Rew:646.0,625.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.38 650[5:Rew:647.0,630.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.38 655[5:Rew:639.0,644.3,647.0,644.3,647.0,644.2,647.0,644.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.13/0.38 656[5:Con:655.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.13/0.38 727[5:SpL:650.0,656.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.13/0.38 729[5:Obv:727.1] || -> .
% 0.13/0.38 730[5:Spt:729.0,16.1,625.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.13/0.38 731[5:Spt:729.0,16.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.38 732[5:MRR:13.1,730.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.38 733[5:MRR:15.1,730.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.38 734[5:MRR:14.1,730.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.38 735[5:MRR:12.1,730.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.38 752[5:SpR:733.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.38 754[5:Rew:731.0,752.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.38 755[5:Rew:734.0,754.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.38 757[5:Rew:755.0,1.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.13/0.38 761[5:Rew:755.0,730.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.13/0.38 762[5:Rew:755.0,619.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.13/0.38 763[5:Rew:755.0,615.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.13/0.38 766[5:Rew:755.0,735.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.13/0.38 788[5:SpR:766.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.13/0.38 790[5:Rew:757.0,788.0,732.0,788.0] || -> equal(sk_c5,sk_c7)**.
% 0.13/0.38 794[5:Rew:790.0,608.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.13/0.38 795[5:Rew:790.0,763.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.13/0.38 805[5:Rew:794.0,795.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.38 806[5:Rew:805.0,762.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.13/0.38 811[5:UnC:806.0,761.0] || -> .
% 0.13/0.38 812[4:Spt:811.0,21.1,618.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.13/0.38 813[4:Spt:811.0,21.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.38 814[4:MRR:18.1,812.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.38 815[4:MRR:20.0,812.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.38 816[4:MRR:19.0,812.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.38 817[4:MRR:17.0,812.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.38 835[4:SpR:815.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.38 837[4:Rew:813.0,835.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.38 838[4:Rew:816.0,837.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.38 839[4:Rew:838.0,610.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.13/0.38 844[4:Rew:838.0,53.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.13/0.38 848[4:Rew:838.0,817.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.13/0.38 849[4:Rew:838.0,613.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.13/0.38 853[4:Rew:838.0,849.3,838.0,849.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.13/0.38 854[4:Con:853.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.13/0.38 869[4:SpR:848.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.13/0.38 871[4:Rew:839.0,869.0,814.0,869.0] || -> equal(sk_c5,sk_c7)**.
% 0.13/0.38 872[4:Rew:871.0,602.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.38 875[4:Rew:871.0,608.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.13/0.38 877[4:Rew:871.0,844.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.13/0.38 886[4:Rew:875.0,877.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.13/0.38 908[0:SpR:24.0,517.0] || -> equal(inverse(identity),identity)**.
% 0.13/0.38 910[4:SpR:813.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.13/0.38 914[4:Rew:886.0,910.0] || -> equal(identity,sk_c3)**.
% 0.13/0.38 916[4:Rew:914.0,517.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.13/0.38 918[4:Rew:914.0,908.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.13/0.38 919[4:Rew:813.0,918.0] || -> equal(sk_c3,sk_c7)**.
% 0.13/0.38 929[4:Rew:919.0,916.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.13/0.38 930[4:Rew:929.0,854.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.13/0.38 987[4:SpL:872.0,930.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.13/0.38 989[4:Obv:987.1] || -> .
% 0.13/0.38 990[3:Spt:989.0,3.1,610.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.13/0.38 991[3:Spt:989.0,3.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.38 994[3:MRR:6.1,990.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.38 996[3:MRR:5.1,990.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.38 997[3:MRR:4.1,990.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.38 1016[3:SpR:996.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.38 1018[3:Rew:994.0,1016.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.38 1019[3:Rew:997.0,1018.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.38 1021[3:Rew:1019.0,1.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.13/0.38 1023[3:Rew:1019.0,990.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.13/0.38 1028[3:Rew:1021.0,1023.0] || equal(sk_c5,sk_c5)* -> .
% 0.13/0.38 1029[3:Obv:1028.0] || -> .
% 0.13/0.38 1030[2:Spt:1029.0,8.1,602.0] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.13/0.38 1031[2:Spt:1029.0,8.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.13/0.38 1032[2:MRR:11.1,1030.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.13/0.38 1033[2:MRR:10.0,1030.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.13/0.38 1034[2:MRR:9.0,1030.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.13/0.38 1035[2:MRR:7.0,1030.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.13/0.38 1044[2:SpR:1033.0,59.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.13/0.38 1046[2:Rew:1032.0,1044.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.38 1047[2:Rew:1034.0,1046.0] || -> equal(sk_c6,sk_c7)**.
% 0.13/0.38 1048[2:Rew:1047.0,1.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.13/0.38 1049[2:Rew:1047.0,422.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.13/0.38 1051[2:Rew:1047.0,1034.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.13/0.38 1052[2:Rew:1047.0,1035.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.13/0.38 1058[2:SpR:1051.0,59.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c4)**.
% 0.13/0.38 1060[2:Rew:24.0,1058.0] || -> equal(identity,sk_c4)**.
% 0.13/0.38 1062[2:Rew:1060.0,517.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.13/0.38 1064[2:Rew:1060.0,24.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.13/0.38 1069[2:SpR:1052.0,59.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.13/0.38 1071[2:Rew:1048.0,1069.0,1031.0,1069.0] || -> equal(sk_c5,sk_c7)**.
% 0.13/0.38 1072[2:Rew:1071.0,1030.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.13/0.38 1074[2:Rew:1071.0,1049.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.13/0.38 1076[2:Rew:1064.0,1074.0] || -> equal(sk_c4,sk_c7)**.
% 0.13/0.38 1077[2:Rew:1076.0,1033.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.13/0.38 1080[2:Rew:1076.0,1062.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.13/0.38 1085[2:Rew:1080.0,1077.0] || -> equal(sk_c3,sk_c7)**.
% 0.13/0.38 1088[2:Rew:1085.0,1032.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.13/0.38 1092[2:MRR:1088.0,1072.0] || -> .
% 0.13/0.38 % SZS output end Refutation
% 0.13/0.38 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 prove_this_22 left_identity left_inverse associativity
% 0.13/0.38
%------------------------------------------------------------------------------