TSTP Solution File: GRP311-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP311-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 11:46:48 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP311-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 06:28:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 686 clauses, backtracked 317 clauses, performed 13 splits and kept 583 clauses.
% 0.20/0.47 SPASS allocated 63554 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.05 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 279 :
% 0.20/0.47 % SZS output start Refutation
% 0.20/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 6[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c7),sk_c5).
% 0.20/0.47 8[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c7),sk_c5).
% 0.20/0.47 10[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 13[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c6),sk_c7).
% 0.20/0.47 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c2),sk_c6).
% 0.20/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.47 18[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c2),sk_c6).
% 0.20/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.47 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c2),sk_c6).
% 0.20/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 23[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 25[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 26[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 28[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 29[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 30[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(w,sk_c7),x)*+ equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.47 35[1:Spt:31.1,31.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.47 36[2:Spt:6.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 40[3:Spt:7.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.47 46[4:Spt:8.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 48[4:SpL:46.0,35.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 49[4:Obv:48.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.47 50[4:Rew:40.0,49.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 51[4:Obv:50.0] || -> .
% 0.20/0.47 52[4:Spt:51.0,8.1,46.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.20/0.47 53[4:Spt:51.0,8.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.47 54[4:MRR:28.1,52.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 55[4:MRR:23.0,52.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 56[4:MRR:18.0,52.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.47 57[4:MRR:13.0,52.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 58[4:MRR:3.0,52.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 72[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.47 73[4:SpR:53.0,33.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.20/0.47 74[4:SpR:54.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.20/0.47 75[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 86[4:SpR:73.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.20/0.47 88[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.47 95[4:Rew:32.0,86.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.20/0.47 99[0:Rew:32.0,88.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.47 104[4:SpR:56.0,95.0] || -> equal(multiply(sk_c5,sk_c6),sk_c2)**.
% 0.20/0.47 105[4:SpR:72.0,95.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.20/0.47 106[4:SpR:74.0,95.0] || -> equal(multiply(sk_c5,identity),sk_c1)**.
% 0.20/0.47 107[4:Rew:57.0,104.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.47 108[4:Rew:107.0,55.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.47 109[4:Rew:107.0,56.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 112[4:Rew:105.0,106.0] || -> equal(sk_c1,sk_c3)**.
% 0.20/0.47 116[4:Rew:112.0,108.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.47 125[4:SpR:105.0,34.0] || -> equal(multiply(sk_c5,multiply(identity,u)),multiply(sk_c3,u))**.
% 0.20/0.47 127[4:Rew:32.0,125.0] || -> equal(multiply(sk_c3,u),multiply(sk_c5,u))**.
% 0.20/0.47 128[4:Rew:127.0,116.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.20/0.47 132[4:Rew:73.0,128.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 133[4:Rew:132.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 140[4:Rew:132.0,75.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 142[4:Rew:133.0,58.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 143[4:Rew:133.0,109.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 150[4:Rew:142.0,53.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.47 163[4:Rew:143.0,150.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 194[4:Obv:140.1] || equal(inverse(inverse(sk_c6)),sk_c7)** -> .
% 0.20/0.47 195[4:Rew:163.0,194.0,163.0,194.0,143.0,194.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 196[4:Obv:195.0] || -> .
% 0.20/0.47 197[3:Spt:196.0,7.0,40.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.47 198[3:Spt:196.0,7.1] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.47 199[3:MRR:27.0,197.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 200[3:MRR:22.0,197.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 201[3:MRR:17.0,197.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.47 202[3:MRR:12.0,197.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 224[3:SpR:198.0,33.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.20/0.47 235[0:SpR:99.0,99.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.47 240[3:SpR:200.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.20/0.47 247[0:SpR:33.0,99.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.47 251[3:Rew:201.0,240.0,199.0,240.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 254[3:Rew:251.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.47 256[3:Rew:251.0,202.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.20/0.47 261[3:Rew:251.0,75.0] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 269[3:Rew:224.0,256.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 270[3:Rew:269.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 276[3:Rew:270.0,254.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 281[3:Rew:276.0,198.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 312[3:Rew:269.0,261.1,281.0,261.0,281.0,261.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 313[3:Obv:312.1] || -> .
% 0.20/0.47 317[2:Spt:313.0,6.1,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.47 318[2:Spt:313.0,6.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.47 319[0:Rew:235.0,247.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.47 320[2:MRR:26.1,317.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 321[2:MRR:21.0,317.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 322[2:MRR:16.0,317.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.47 324[2:MRR:1.0,317.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 330[2:SpR:321.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.20/0.47 332[2:Rew:320.0,330.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.20/0.47 333[2:Rew:322.0,332.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 334[2:Rew:333.0,317.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.20/0.47 339[2:Rew:333.0,324.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.47 342[2:Rew:339.0,334.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.47 343[2:Obv:342.0] || -> .
% 0.20/0.47 346[1:Spt:343.0,31.0,31.2,31.3,31.4,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(v,sk_c7),w)*+ equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 347[1:EqR:346.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 349[2:Spt:6.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 352[2:Rew:349.0,347.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 353[2:Obv:352.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 357[2:SpR:349.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.47 359[3:Spt:7.1] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.47 362[3:Rew:359.0,353.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(sk_c5,sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 363[3:Obv:362.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 366[3:SpR:359.0,99.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.20/0.47 368[4:Spt:12.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 371[4:Rew:368.0,363.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 372[4:Obv:371.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 376[4:SpR:368.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.47 378[5:Spt:2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 381[5:Rew:378.0,372.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.47 382[5:Obv:381.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.20/0.47 392[6:Spt:27.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 395[7:Spt:22.1] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.47 397[7:SpR:395.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.20/0.47 399[7:Rew:392.0,397.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.20/0.47 400[7:Rew:399.0,20.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(sk_c6,sk_c7).
% 0.20/0.47 402[7:Rew:399.0,19.1] || -> equal(inverse(sk_c4),sk_c6)** equal(sk_c6,sk_c7).
% 0.20/0.47 405[7:SpR:399.0,99.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c2)**.
% 0.20/0.47 407[7:Rew:359.0,405.0] || -> equal(multiply(sk_c5,sk_c7),sk_c2)**.
% 0.20/0.47 411[7:SpR:407.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c2,u))**.
% 0.20/0.47 412[7:SpR:407.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c2),sk_c7)**.
% 0.20/0.47 414[7:Rew:366.0,411.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.47 426[7:SpR:414.0,319.0] || -> equal(identity,sk_c2)**.
% 0.20/0.47 429[7:Rew:426.0,319.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.20/0.47 430[7:Rew:426.0,33.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.20/0.47 432[7:Rew:429.0,412.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.47 433[7:Rew:432.0,376.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 437[7:SpR:430.0,99.0] || -> equal(multiply(inverse(inverse(u)),sk_c2),u)**.
% 0.20/0.47 441[7:Rew:429.0,437.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.47 464[8:Spt:402.1] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 465[8:Rew:464.0,349.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.47 466[8:Rew:464.0,368.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.20/0.47 469[8:Rew:464.0,433.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.47 478[8:Rew:464.0,382.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.20/0.47 479[8:Rew:407.0,466.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.47 481[8:Rew:479.0,414.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 484[8:Rew:479.0,429.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.47 487[8:Rew:465.0,469.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 488[8:Rew:487.0,359.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 505[8:Rew:484.0,478.3,481.0,478.3,464.0,478.3,484.0,478.2,487.0,478.2,464.0,478.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.20/0.47 506[8:Con:505.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.47 540[8:SpL:488.0,506.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 542[8:Obv:540.1] || -> .
% 0.20/0.47 543[8:Spt:542.0,402.1,464.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.47 544[8:Spt:542.0,402.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.47 546[8:MRR:400.1,543.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 549[8:SpR:544.0,441.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.47 551[8:Rew:549.0,357.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.47 552[8:Rew:546.0,551.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 553[8:MRR:552.0,543.0] || -> .
% 0.20/0.47 554[7:Spt:553.0,22.1,395.0] || equal(multiply(sk_c1,sk_c7),sk_c2)** -> .
% 0.20/0.47 555[7:Spt:553.0,22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.47 556[7:MRR:24.1,554.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.47 557[7:MRR:23.1,554.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 558[7:MRR:25.1,554.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 571[7:SpR:557.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 573[7:Rew:555.0,571.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 585[7:SpR:558.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.47 587[7:Rew:556.0,585.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 595[7:SpR:587.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.47 596[7:SpR:587.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.47 598[7:Rew:357.0,596.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.47 602[7:Rew:598.0,378.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.47 606[7:Rew:598.0,573.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.47 617[7:Rew:598.0,382.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.20/0.47 622[7:Rew:602.0,606.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 623[7:Rew:622.0,359.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 624[7:Rew:622.0,366.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.20/0.47 633[7:Rew:624.0,595.0,598.0,595.0,622.0,595.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 644[7:Rew:633.0,617.3,598.0,617.3,622.0,617.2,598.0,617.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.20/0.47 645[7:Con:644.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.47 665[7:SpR:633.0,319.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 668[7:Rew:665.0,319.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.47 671[7:Rew:668.0,645.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.47 704[7:SpL:623.0,671.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 705[7:Obv:704.1] || -> .
% 0.20/0.47 706[6:Spt:705.0,27.1,392.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.47 707[6:Spt:705.0,27.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.47 708[6:MRR:29.1,706.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.47 709[6:MRR:28.0,706.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 710[6:MRR:30.0,706.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 731[6:SpR:709.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 733[6:Rew:707.0,731.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 735[6:SpR:710.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.48 737[6:Rew:708.0,735.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 742[6:SpR:737.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.48 743[6:SpR:737.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.48 745[6:Rew:357.0,743.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 747[6:Rew:745.0,349.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 753[6:Rew:745.0,733.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 767[6:Rew:745.0,382.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c6)** -> .
% 0.20/0.48 769[6:Rew:747.0,753.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 770[6:Rew:769.0,359.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 771[6:Rew:769.0,366.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.20/0.48 780[6:Rew:771.0,742.0,745.0,742.0,769.0,742.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 789[6:Rew:780.0,767.3,745.0,767.3,769.0,767.2,745.0,767.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.20/0.48 790[6:Con:789.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.48 813[6:SpR:780.0,319.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 815[6:Rew:813.0,319.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 819[6:Rew:815.0,790.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.48 847[6:SpL:770.0,819.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 848[6:Obv:847.1] || -> .
% 0.20/0.48 849[5:Spt:848.0,2.1,378.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.48 850[5:Spt:848.0,2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 851[5:MRR:4.1,849.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 852[5:MRR:3.1,849.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 853[5:MRR:5.1,849.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 867[5:SpR:852.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.48 869[5:Rew:850.0,867.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 871[5:SpR:853.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.48 873[5:Rew:851.0,871.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 879[5:SpR:873.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.48 881[5:Rew:357.0,879.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 884[5:Rew:881.0,349.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 887[5:Rew:881.0,869.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 888[5:Rew:881.0,873.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 891[5:Rew:881.0,849.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.20/0.48 898[5:Rew:884.0,887.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 904[5:Rew:898.0,888.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 907[5:Rew:904.0,891.0,898.0,891.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 908[5:Obv:907.0] || -> .
% 0.20/0.48 916[4:Spt:908.0,12.1,368.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.48 917[4:Spt:908.0,12.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 919[4:MRR:13.1,916.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 931[4:SpR:919.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.48 933[4:Rew:917.0,931.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 939[4:SpR:933.0,99.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.48 941[4:Rew:359.0,939.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 942[4:MRR:941.0,916.0] || -> .
% 0.20/0.48 943[3:Spt:942.0,7.1,359.0] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.20/0.48 944[3:Spt:942.0,7.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.48 945[3:MRR:9.1,943.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 946[3:MRR:8.0,943.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.48 947[3:MRR:10.0,943.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.48 953[3:SpR:946.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.48 955[3:Rew:944.0,953.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 957[3:SpR:947.0,99.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.48 959[3:Rew:945.0,957.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.48 961[3:SpR:955.0,99.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.48 967[3:SpR:959.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.48 969[3:Rew:357.0,967.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 970[3:Rew:969.0,349.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 974[3:Rew:969.0,955.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.48 976[3:Rew:969.0,357.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.20/0.48 982[3:Rew:969.0,961.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.48 983[3:Rew:970.0,974.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 984[3:Rew:983.0,943.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.20/0.48 988[3:Rew:33.0,976.0,983.0,976.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 990[3:Rew:988.0,319.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 1001[3:Rew:990.0,982.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 1002[3:MRR:1001.0,984.0] || -> .
% 0.20/0.48 1008[2:Spt:1002.0,6.1,349.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.48 1009[2:Spt:1002.0,6.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.48 1010[2:MRR:26.1,1008.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 1011[2:MRR:21.0,1008.0] || -> equal(multiply(sk_c1,sk_c7),sk_c2)**.
% 0.20/0.48 1012[2:MRR:16.0,1008.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.20/0.48 1014[2:MRR:1.0,1008.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 1020[2:SpR:1011.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c7)**.
% 0.20/0.48 1022[2:Rew:1010.0,1020.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.20/0.48 1023[2:Rew:1012.0,1022.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 1024[2:Rew:1023.0,1008.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.20/0.48 1027[2:Rew:1023.0,1014.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.48 1028[2:Rew:1027.0,1024.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.48 1029[2:Obv:1028.0] || -> .
% 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_12 prove_this_13 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 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.20/0.48
%------------------------------------------------------------------------------