TSTP Solution File: GRP341-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP341-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP341-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 09:23:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 654 clauses, backtracked 287 clauses, performed 10 splits and kept 590 clauses.
% 0.19/0.46 SPASS allocated 63595 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 281 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 1[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 3[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 4[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 5[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 6[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 7[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 9[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 10[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.46 12[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 15[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 17[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 20[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 21[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 22[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 23[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 27[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 28[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 29[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 30[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 31[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 35[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 36[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c6),sk_c5)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.46 37[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 38[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 39[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 40[1:Spt:36.3,36.8] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.46 41[2:Spt:3.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 43[3:Spt:10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 47[4:Spt:17.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 49[4:SpL:47.0,40.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 50[4:Obv:49.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 51[4:Rew:43.0,50.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 52[4:Obv:51.0] || -> .
% 0.19/0.46 53[4:Spt:52.0,17.1,47.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.19/0.46 54[4:Spt:52.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 55[4:MRR:19.1,53.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 56[4:MRR:16.1,53.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 57[4:MRR:21.1,53.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 58[4:MRR:20.1,53.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 60[4:MRR:15.1,53.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 65[4:SpL:57.0,40.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 66[4:Obv:65.1] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.19/0.46 67[4:Rew:54.0,66.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 76[3:SpR:43.0,38.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.46 78[4:SpR:54.0,38.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.19/0.46 79[4:SpR:55.0,38.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 80[4:SpR:56.0,38.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.46 81[1:SpL:38.0,40.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.46 92[4:SpR:60.0,39.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 94[0:SpR:38.0,39.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 97[4:SpR:78.0,39.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.46 102[4:Rew:37.0,97.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.19/0.46 104[0:Rew:37.0,94.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 117[4:SpR:57.0,102.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 118[4:SpR:58.0,102.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.46 119[4:Rew:41.0,117.0] || -> equal(sk_c6,sk_c5)**.
% 0.19/0.46 124[4:Rew:119.0,55.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.19/0.46 126[4:Rew:119.0,67.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.46 132[4:Rew:119.0,78.0] || -> equal(multiply(sk_c5,sk_c5),identity)**.
% 0.19/0.46 133[4:Rew:119.0,79.0] || -> equal(multiply(sk_c5,sk_c4),identity)**.
% 0.19/0.46 140[4:Rew:119.0,92.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.46 144[4:Rew:119.0,118.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 145[4:Rew:144.0,132.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 146[4:Rew:145.0,37.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 148[4:Rew:145.0,76.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.46 149[4:Rew:145.0,80.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.46 151[4:Rew:145.0,133.0] || -> equal(multiply(sk_c5,sk_c4),sk_c7)**.
% 0.19/0.46 154[4:Rew:146.0,148.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.46 155[4:Rew:154.0,43.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 156[4:Rew:146.0,149.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 166[4:Rew:146.0,140.0,156.0,140.0,146.0,140.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 172[4:Rew:166.0,151.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 176[4:Rew:172.0,124.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.46 182[4:Rew:155.0,176.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 183[4:MRR:182.0,126.0] || -> .
% 0.19/0.46 192[3:Spt:183.0,10.1,43.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 193[3:Spt:183.0,10.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 194[3:MRR:12.1,192.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 198[3:MRR:11.0,192.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.46 217[3:SpR:193.0,38.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.19/0.46 218[3:SpR:194.0,38.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 221[3:SpR:218.0,39.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.46 223[3:Rew:37.0,221.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.46 232[3:SpR:198.0,223.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 233[3:Rew:217.0,232.0] || -> equal(sk_c6,identity)**.
% 0.19/0.46 235[3:Rew:233.0,194.0] || -> equal(inverse(sk_c4),identity)**.
% 0.19/0.46 236[3:Rew:233.0,41.0] || -> equal(multiply(identity,sk_c7),sk_c5)**.
% 0.19/0.46 241[3:Rew:233.0,218.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.19/0.46 242[3:Rew:233.0,217.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.19/0.46 246[3:Rew:233.0,81.0] || equal(inverse(inverse(identity)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.46 254[3:Rew:37.0,236.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 259[3:Rew:37.0,241.0] || -> equal(identity,sk_c4)**.
% 0.19/0.46 260[3:Rew:259.0,37.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 264[3:Rew:259.0,235.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.46 270[3:Rew:254.0,242.0,259.0,242.0] || -> equal(multiply(sk_c4,sk_c7),sk_c4)**.
% 0.19/0.46 271[3:Rew:260.0,270.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 272[3:Rew:271.0,259.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 274[3:Rew:271.0,264.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 297[3:Rew:272.0,246.1,274.0,246.0,274.0,246.0,272.0,246.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 298[3:Obv:297.1] || -> .
% 0.19/0.46 303[2:Spt:298.0,3.1,41.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.46 304[2:Spt:298.0,3.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 305[2:MRR:5.1,303.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 308[2:MRR:6.1,303.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 309[2:MRR:4.1,303.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.46 326[2:SpR:304.0,38.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.19/0.46 327[2:SpR:305.0,38.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 330[2:SpR:326.0,39.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.46 332[2:Rew:37.0,330.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.19/0.46 342[2:SpR:308.0,332.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.46 350[0:SpR:104.0,104.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 355[2:SpR:309.0,104.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c6)**.
% 0.19/0.46 358[0:SpR:38.0,104.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 370[2:Rew:326.0,355.0,305.0,355.0] || -> equal(sk_c6,identity)**.
% 0.19/0.46 372[2:Rew:370.0,305.0] || -> equal(inverse(sk_c4),identity)**.
% 0.19/0.46 378[2:Rew:370.0,327.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.19/0.46 382[2:Rew:370.0,342.0] || -> equal(multiply(identity,identity),sk_c7)**.
% 0.19/0.46 384[2:Rew:370.0,81.0] || equal(inverse(inverse(identity)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.46 396[2:Rew:37.0,378.0] || -> equal(identity,sk_c4)**.
% 0.19/0.46 397[2:Rew:396.0,37.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 402[2:Rew:396.0,372.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.46 409[2:Rew:396.0,382.0] || -> equal(multiply(sk_c4,sk_c4),sk_c7)**.
% 0.19/0.46 410[2:Rew:397.0,409.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 412[2:Rew:410.0,396.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 415[2:Rew:410.0,402.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 455[2:Rew:412.0,384.1,415.0,384.0,415.0,384.0,412.0,384.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 456[2:Obv:455.1] || -> .
% 0.19/0.46 460[1:Spt:456.0,36.0,36.1,36.2,36.4,36.5,36.6,36.7,36.9,36.10,36.11] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c6),sk_c5)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.46 461[0:Rew:350.0,358.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 463[2:Spt:3.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 464[2:Rew:463.0,460.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6) equal(sk_c5,sk_c5) -> .
% 0.19/0.46 466[2:Obv:464.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.19/0.46 469[2:SpR:463.0,104.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.46 471[3:Spt:24.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 472[3:SpR:471.0,104.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.46 474[4:Spt:10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 475[4:SpR:474.0,104.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.46 477[5:Spt:31.1] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 479[5:SpR:477.0,104.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.19/0.46 481[5:Rew:471.0,479.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 482[6:Spt:17.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 484[6:SpR:482.0,104.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 486[6:Rew:474.0,484.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.46 488[5:SpR:481.0,104.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.46 490[5:Rew:469.0,488.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 491[5:Rew:490.0,463.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 492[5:Rew:490.0,471.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 493[5:Rew:490.0,477.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.46 497[5:Rew:490.0,466.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(sk_c5),sk_c7) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.19/0.46 498[5:Rew:490.0,469.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.19/0.46 503[6:Rew:490.0,486.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.46 504[6:Rew:491.0,503.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 506[6:Rew:504.0,493.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.46 507[6:Rew:38.0,498.0,504.0,498.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 511[6:Rew:507.0,461.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 513[6:Rew:511.0,506.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.46 515[6:Rew:513.0,492.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 524[5:Con:497.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c5),sk_c7) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.19/0.46 525[6:Rew:504.0,524.6,511.0,524.6,490.0,524.6,504.0,524.5,511.0,524.5,490.0,524.5,511.0,524.4,504.0,524.4,490.0,524.4,511.0,524.3,490.0,524.3,504.0,524.3,515.0,524.2,504.0,524.2,490.0,524.1,490.0,524.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) equal(v,sk_c7) equal(sk_c7,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.46 526[6:Obv:525.6] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.19/0.46 527[6:Con:526.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 589[6:SpL:515.0,527.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 591[6:Obv:589.1] || -> .
% 0.19/0.46 592[6:Spt:591.0,17.1,482.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.19/0.46 593[6:Spt:591.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 594[6:Rew:490.0,593.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.46 595[6:Rew:490.0,592.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.19/0.46 601[5:Rew:490.0,21.1,490.0,21.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.46 602[6:MRR:601.1,595.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.19/0.46 628[6:SpR:594.0,104.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.19/0.46 632[6:SpR:602.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.46 633[6:SpR:602.0,104.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c7)**.
% 0.19/0.46 635[6:Rew:594.0,633.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.46 636[6:Rew:491.0,635.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 644[6:Rew:636.0,628.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.46 649[6:Rew:644.0,632.0,636.0,632.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 654[6:Rew:649.0,475.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.46 655[6:UnC:654.0,595.0] || -> .
% 0.19/0.46 659[5:Spt:655.0,31.1,477.0] || equal(multiply(sk_c2,sk_c5),sk_c6)** -> .
% 0.19/0.46 660[5:Spt:655.0,31.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 662[5:MRR:30.1,659.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 663[5:MRR:35.1,659.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 666[5:MRR:29.1,659.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 671[5:SpR:660.0,104.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.19/0.46 677[5:SpR:662.0,104.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.46 682[5:SpR:663.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 683[5:SpR:663.0,104.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.19/0.46 685[5:Rew:463.0,683.0,660.0,683.0] || -> equal(sk_c6,sk_c5)**.
% 0.19/0.46 692[5:Rew:685.0,659.0] || equal(multiply(sk_c2,sk_c5),sk_c5)** -> .
% 0.19/0.46 693[5:Rew:685.0,472.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),u)**.
% 0.19/0.46 697[5:Rew:685.0,666.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.46 700[5:Rew:685.0,671.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.19/0.46 703[5:Rew:700.0,682.0,685.0,682.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 704[5:Rew:703.0,677.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.46 706[5:Rew:704.0,697.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 714[5:Rew:706.0,692.0] || equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.19/0.46 715[5:Rew:706.0,693.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.46 718[5:Rew:703.0,715.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 719[5:UnC:718.0,714.0] || -> .
% 0.19/0.46 727[4:Spt:719.0,10.1,474.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.19/0.46 728[4:Spt:719.0,10.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 730[4:MRR:9.1,727.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 731[4:MRR:14.0,727.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 732[4:MRR:13.0,727.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 734[4:MRR:8.0,727.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 735[4:Rew:732.0,466.8,731.0,466.7,728.0,466.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(sk_c7,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.19/0.46 736[4:Obv:735.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.19/0.46 739[4:SpR:728.0,104.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.19/0.46 745[4:SpR:730.0,104.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.46 750[4:SpR:731.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 751[4:SpR:731.0,104.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.19/0.46 753[4:Rew:463.0,751.0,728.0,751.0] || -> equal(sk_c6,sk_c5)**.
% 0.19/0.46 754[4:Rew:753.0,728.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.19/0.46 764[4:Rew:753.0,734.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.46 765[4:Rew:753.0,736.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.19/0.46 767[4:Rew:753.0,739.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.19/0.46 770[4:Rew:767.0,750.0,753.0,750.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 771[4:Rew:770.0,745.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.46 772[4:Rew:771.0,764.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 773[4:Rew:772.0,753.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 774[4:Rew:772.0,754.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 787[4:Rew:772.0,765.5,773.0,765.5,773.0,765.4,773.0,765.3,772.0,765.3,773.0,765.2,772.0,765.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.46 788[4:Con:787.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 814[4:SpR:770.0,461.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 816[4:Rew:814.0,461.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 820[4:Rew:816.0,788.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 846[4:SpL:774.0,820.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 847[4:Obv:846.1] || -> .
% 0.19/0.46 848[3:Spt:847.0,24.1,471.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.19/0.46 849[3:Spt:847.0,24.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 851[3:MRR:23.1,848.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 852[3:MRR:28.0,848.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 853[3:MRR:27.0,848.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.46 855[3:MRR:22.0,848.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.47 856[3:Rew:853.0,466.8,852.0,466.7,849.0,466.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(sk_c7,sk_c7) equal(sk_c6,sk_c6) -> .
% 0.19/0.47 857[3:Obv:856.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.19/0.47 860[3:SpR:849.0,104.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.19/0.47 864[3:SpR:851.0,104.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.47 869[3:SpR:852.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 870[3:SpR:852.0,104.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.19/0.47 872[3:Rew:463.0,870.0,849.0,870.0] || -> equal(sk_c6,sk_c5)**.
% 0.19/0.47 873[3:Rew:872.0,849.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.19/0.47 882[3:Rew:872.0,855.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.47 883[3:Rew:872.0,857.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c5)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.19/0.47 885[3:Rew:872.0,860.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),u)**.
% 0.19/0.47 888[3:Rew:885.0,869.0,872.0,869.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 889[3:Rew:888.0,864.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 890[3:Rew:889.0,882.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 891[3:Rew:890.0,872.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 892[3:Rew:890.0,873.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 903[3:Rew:890.0,883.5,891.0,883.5,891.0,883.4,891.0,883.3,890.0,883.3,891.0,883.2,890.0,883.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.47 904[3:Con:903.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 927[3:SpR:888.0,461.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 930[3:Rew:927.0,461.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 933[3:Rew:930.0,904.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 961[3:SpL:892.0,933.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 962[3:Obv:961.1] || -> .
% 0.19/0.47 963[2:Spt:962.0,3.1,463.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 964[2:Spt:962.0,3.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 967[2:MRR:7.1,963.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.47 968[2:MRR:6.1,963.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 970[2:MRR:1.1,963.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.47 978[2:SpR:967.0,104.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.19/0.47 980[2:Rew:964.0,978.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.47 981[2:Rew:980.0,963.0] || equal(sk_c6,sk_c5)** -> .
% 0.19/0.47 995[2:SpR:980.0,104.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.47 997[2:Rew:38.0,995.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 998[2:Rew:997.0,461.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1002[2:Rew:998.0,970.0] || -> equal(sk_c6,sk_c3)**.
% 0.19/0.47 1003[2:Rew:998.0,968.0] || -> equal(sk_c6,sk_c5)**.
% 0.19/0.47 1007[2:Rew:1002.0,981.0] || equal(sk_c3,sk_c5)** -> .
% 0.19/0.47 1018[2:Rew:1002.0,1003.0] || -> equal(sk_c3,sk_c5)**.
% 0.19/0.47 1024[2:Rew:1018.0,1007.0] || equal(sk_c5,sk_c5)* -> .
% 0.19/0.47 1025[2:Obv:1024.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 Formulae used in the proof : prove_this_1 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_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_35 prove_this_36 left_identity left_inverse associativity
% 0.19/0.47
%------------------------------------------------------------------------------