TSTP Solution File: GRP329-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP329-1 : 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 11:46:52 EDT 2022
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP329-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Mon Jun 13 03:58:10 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 632 clauses, backtracked 385 clauses, performed 14 splits and kept 556 clauses.
% 0.22/0.50 SPASS allocated 63577 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.12 on the problem.
% 0.22/0.50 0:00:00.04 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.00 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.05 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 5, length 262 :
% 0.22/0.50 % SZS output start Refutation
% 0.22/0.50 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.22/0.50 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.22/0.50 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.22/0.50 6[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.22/0.50 7[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.22/0.50 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 11[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 13[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 14[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 15[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 18[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 19[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 20[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.50 21[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 22[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.22/0.50 27[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.22/0.50 28[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.22/0.50 29[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.22/0.50 34[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.22/0.50 35[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.22/0.50 36[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.22/0.50 39[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 40[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.22/0.50 41[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.50 42[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.22/0.50 43[0:Inp] || equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(u,sk_c8),sk_c9)** equal(inverse(u),sk_c8) equal(multiply(sk_c9,v),sk_c8)** equal(multiply(w,sk_c9),v)* equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(x,sk_c8),sk_c7)** equal(inverse(x),sk_c8) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(z,sk_c9),sk_c7)** equal(inverse(z),sk_c9) -> .
% 0.22/0.50 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.50 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.50 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.50 47[0:Con:43.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(w,sk_c9),y)*+ equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c8),sk_c9)** equal(multiply(sk_c9,y),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.22/0.50 48[1:Spt:47.3,47.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.22/0.50 53[2:Spt:15.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 61[3:Spt:8.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 63[3:SpL:61.0,48.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c9,sk_c9) -> .
% 0.22/0.50 64[3:Obv:63.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 65[3:Rew:53.0,64.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 66[3:Obv:65.0] || -> .
% 0.22/0.50 67[3:Spt:66.0,8.1,61.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.22/0.50 68[3:Spt:66.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.22/0.50 70[3:MRR:12.1,67.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.50 73[3:MRR:11.1,67.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 81[3:SpL:73.0,48.1] || equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c9) -> .
% 0.22/0.50 82[3:Obv:81.1] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.22/0.50 83[3:Rew:70.0,82.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 84[3:Obv:83.0] || -> .
% 0.22/0.50 85[2:Spt:84.0,15.1,53.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 86[2:Spt:84.0,15.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.22/0.50 88[2:MRR:19.1,85.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.50 91[2:MRR:18.0,85.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 99[2:SpL:91.0,48.1] || equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c9) -> .
% 0.22/0.50 100[2:Obv:99.1] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.22/0.50 101[2:Rew:88.0,100.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 102[2:Obv:101.0] || -> .
% 0.22/0.50 103[1:Spt:102.0,47.0,47.1,47.2,47.4,47.5,47.6,47.7,47.9,47.10] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(w,sk_c9),x)*+ equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,x),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.22/0.50 104[1:EqR:103.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.22/0.50 106[2:Spt:1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.22/0.50 109[2:Rew:106.0,104.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.50 110[2:Obv:109.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.50 114[3:Spt:15.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.22/0.50 117[3:Rew:114.0,110.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.50 118[3:Obv:117.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.50 122[4:Spt:21.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 124[5:Spt:42.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.22/0.50 126[6:Spt:14.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.50 129[3:SpR:114.0,45.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.22/0.50 130[4:SpR:122.0,45.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.22/0.50 131[5:SpR:124.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.22/0.50 132[7:Spt:28.1] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.22/0.50 134[8:Spt:35.1] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.22/0.50 140[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.50 144[3:SpR:129.0,46.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.22/0.50 146[3:Rew:44.0,144.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.22/0.50 147[0:Rew:44.0,140.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.50 157[3:SpR:106.0,146.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.22/0.50 158[4:SpR:130.0,146.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.22/0.50 160[3:SpR:157.0,46.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.22/0.50 163[0:SpR:147.0,147.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.50 166[0:SpR:45.0,147.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.50 167[2:SpR:106.0,147.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.22/0.50 168[8:SpR:134.0,147.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.22/0.50 169[6:SpR:126.0,147.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c8)**.
% 0.22/0.50 172[5:SpR:131.0,147.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.22/0.50 181[8:Rew:132.0,168.0,124.0,168.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.50 182[8:Rew:181.0,106.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.22/0.50 191[8:Rew:181.0,118.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.50 198[6:Rew:122.0,169.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.22/0.50 199[8:Rew:182.0,198.0,181.0,198.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.50 200[8:Rew:199.0,114.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.50 201[8:Rew:199.0,129.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.22/0.50 204[8:Rew:199.0,182.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.22/0.50 206[8:Rew:201.0,204.0] || -> equal(identity,sk_c8)**.
% 0.22/0.50 207[8:Rew:206.0,44.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.50 231[8:Rew:206.0,166.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.22/0.50 238[8:Rew:163.0,231.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.50 245[8:Rew:238.0,191.5,207.0,191.5,181.0,191.5,238.0,191.4,199.0,191.4,238.0,191.3,181.0,191.3,199.0,191.3,181.0,191.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.22/0.50 246[8:Con:245.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.50 310[8:SpL:200.0,246.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 312[8:Obv:310.1] || -> .
% 0.22/0.50 313[8:Spt:312.0,35.1,134.0] || equal(multiply(sk_c2,sk_c9),sk_c3)** -> .
% 0.22/0.50 314[8:Spt:312.0,35.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.50 315[6:Rew:106.0,198.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.50 316[6:Rew:315.0,114.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.50 317[6:Rew:315.0,157.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.22/0.50 319[6:Rew:315.0,129.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.22/0.50 321[6:Rew:319.0,317.0] || -> equal(identity,sk_c9)**.
% 0.22/0.50 322[6:Rew:321.0,131.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.22/0.50 326[6:Rew:321.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.22/0.50 331[6:Rew:326.0,322.0] || -> equal(sk_c2,sk_c9)**.
% 0.22/0.50 332[7:Rew:326.0,132.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.50 342[8:Rew:326.0,313.0,331.0,313.0,332.0,313.0] || equal(sk_c9,sk_c8)** -> .
% 0.22/0.50 346[6:Rew:321.0,166.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.22/0.50 359[6:Rew:163.0,346.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.22/0.50 360[7:Rew:331.0,34.1,359.0,34.1,332.0,34.1,359.0,34.0,315.0,34.0] || -> equal(sk_c6,sk_c8)** equal(sk_c9,sk_c8).
% 0.22/0.50 361[8:MRR:360.1,342.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.50 362[8:Rew:361.0,314.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.22/0.50 363[8:Rew:316.0,362.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.50 364[8:MRR:363.0,342.0] || -> .
% 0.22/0.50 369[6:Rew:359.0,118.5,326.0,118.5,315.0,118.4,359.0,118.3,315.0,118.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c9)** equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.22/0.50 370[6:Con:369.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.50 374[7:Spt:364.0,28.1,132.0] || equal(multiply(sk_c9,sk_c3),sk_c8)** -> .
% 0.22/0.50 375[7:Spt:364.0,28.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.50 376[7:Rew:326.0,374.0] || equal(sk_c3,sk_c8)** -> .
% 0.22/0.50 385[6:Rew:331.0,34.1,359.0,34.1,359.0,34.0,315.0,34.0] || -> equal(sk_c6,sk_c8) equal(sk_c3,sk_c9)**.
% 0.22/0.50 388[6:Rew:385.1,27.1,326.0,27.1,359.0,27.0,315.0,27.0] || -> equal(sk_c6,sk_c8)** equal(sk_c9,sk_c8).
% 0.22/0.50 389[6:Rew:388.1,385.1] || -> equal(sk_c6,sk_c8) equal(sk_c3,sk_c8)**.
% 0.22/0.50 390[7:MRR:389.1,376.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.50 391[7:Rew:390.0,375.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.22/0.50 392[7:Rew:316.0,391.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.50 399[7:Rew:392.0,359.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.50 400[7:Rew:392.0,370.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.50 412[7:Rew:399.0,400.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.22/0.50 413[7:Con:412.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.50 457[7:SpL:316.0,413.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 459[7:Obv:457.1] || -> .
% 0.22/0.50 460[6:Spt:459.0,14.1,126.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.22/0.50 461[6:Spt:459.0,14.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.50 465[0:Rew:163.0,166.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.50 466[4:Rew:465.0,158.0] || -> equal(sk_c1,sk_c7)**.
% 0.22/0.50 467[5:Rew:465.0,172.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.22/0.50 468[4:Rew:466.0,122.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.22/0.50 469[4:Rew:466.0,130.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.22/0.50 470[6:Rew:466.0,460.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.22/0.50 473[6:Rew:129.0,470.0] || equal(identity,sk_c9)** -> .
% 0.22/0.50 474[4:Rew:129.0,12.1,466.0,12.1] || -> equal(inverse(sk_c5),sk_c8)** equal(identity,sk_c9).
% 0.22/0.50 475[6:MRR:474.1,473.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.50 478[4:Rew:129.0,13.1,466.0,13.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(identity,sk_c9).
% 0.22/0.50 479[6:MRR:478.1,473.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.50 480[4:Rew:129.0,11.1,466.0,11.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(identity,sk_c9).
% 0.22/0.50 481[6:MRR:480.1,473.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 504[6:SpR:479.0,147.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.22/0.50 506[6:Rew:461.0,504.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.22/0.50 527[6:SpR:481.0,147.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.22/0.50 529[6:Rew:106.0,527.0,475.0,527.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.50 531[6:Rew:529.0,114.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.50 538[6:Rew:529.0,146.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.22/0.50 542[6:Rew:529.0,160.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.22/0.50 547[6:Rew:529.0,506.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.22/0.50 552[6:Rew:538.0,542.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.22/0.50 553[6:Rew:552.0,131.0] || -> equal(identity,sk_c2)**.
% 0.22/0.50 554[6:Rew:552.0,547.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.50 561[6:Rew:553.0,473.0] || equal(sk_c2,sk_c9)** -> .
% 0.22/0.50 568[6:Rew:554.0,467.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.50 574[6:Rew:554.0,561.0] || equal(sk_c2,sk_c8)** -> .
% 0.22/0.50 575[6:Rew:531.0,568.0] || -> equal(sk_c2,sk_c8)**.
% 0.22/0.50 576[6:MRR:575.0,574.0] || -> .
% 0.22/0.50 590[5:Spt:576.0,42.1,124.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.22/0.50 591[5:Spt:576.0,42.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.50 592[5:MRR:40.1,590.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.50 594[5:MRR:41.0,590.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.50 595[5:MRR:39.0,590.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 631[5:SpR:595.0,147.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.22/0.50 633[5:Rew:106.0,631.0,592.0,631.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.50 635[5:Rew:633.0,468.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.50 637[5:Rew:633.0,469.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.22/0.50 639[5:Rew:633.0,157.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.22/0.50 641[5:Rew:633.0,594.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.22/0.50 650[5:Rew:633.0,118.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.50 652[5:Rew:637.0,639.0] || -> equal(identity,sk_c9)**.
% 0.22/0.50 653[5:Rew:652.0,465.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.22/0.50 654[5:Rew:652.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.22/0.50 658[5:Rew:653.0,641.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.50 659[5:Rew:658.0,591.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.22/0.50 661[5:Rew:635.0,659.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.50 666[5:Rew:661.0,653.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.50 667[5:Rew:661.0,654.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.50 686[5:Rew:666.0,650.5,667.0,650.5,661.0,650.5,666.0,650.4,633.0,650.4,666.0,650.3,661.0,650.3,661.0,650.2,661.0,650.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.22/0.50 687[5:Con:686.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.50 752[5:SpL:635.0,687.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 754[5:Obv:752.1] || -> .
% 0.22/0.50 755[4:Spt:754.0,21.1,122.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 756[4:Spt:754.0,21.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.50 761[4:MRR:19.1,755.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.50 764[4:MRR:20.0,755.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.50 765[4:MRR:18.0,755.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.50 791[4:SpR:764.0,147.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.22/0.50 793[4:Rew:756.0,791.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.22/0.51 795[4:SpR:765.0,147.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.22/0.51 797[4:Rew:106.0,795.0,761.0,795.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 798[4:Rew:797.0,114.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 801[4:Rew:797.0,157.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.22/0.51 802[4:Rew:797.0,129.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.22/0.51 812[4:Rew:797.0,118.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c8)** -> .
% 0.22/0.51 813[4:Rew:797.0,793.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.22/0.51 814[4:Rew:801.0,802.0] || -> equal(identity,sk_c9)**.
% 0.22/0.51 815[4:Rew:814.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.22/0.51 816[4:Rew:814.0,465.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.22/0.51 819[4:Rew:815.0,813.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.51 827[4:Rew:819.0,815.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 828[4:Rew:819.0,816.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 845[4:Rew:828.0,812.5,827.0,812.5,819.0,812.5,828.0,812.4,797.0,812.4,828.0,812.3,819.0,812.3,819.0,812.2,819.0,812.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.22/0.51 846[4:Con:845.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.51 922[4:SpL:798.0,846.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 924[4:Obv:922.1] || -> .
% 0.22/0.51 925[3:Spt:924.0,15.0,114.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.22/0.51 926[3:Spt:924.0,15.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 927[3:MRR:36.0,925.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.22/0.51 928[3:MRR:8.0,925.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.22/0.51 929[3:MRR:22.0,925.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.22/0.51 930[3:MRR:29.0,925.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.22/0.51 931[3:SpR:926.0,147.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.22/0.51 933[3:SpR:927.0,147.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.22/0.51 939[3:SpR:928.0,147.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c8)**.
% 0.22/0.51 941[3:Rew:106.0,939.0,926.0,939.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 943[3:Rew:941.0,925.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.22/0.51 944[3:Rew:941.0,167.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.22/0.51 946[3:Rew:45.0,944.0] || -> equal(identity,sk_c9)**.
% 0.22/0.51 947[3:Rew:946.0,465.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.22/0.51 948[3:Rew:946.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.22/0.51 951[3:Rew:947.0,930.0] || -> equal(sk_c2,sk_c3)**.
% 0.22/0.51 952[3:Rew:951.0,927.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.22/0.51 953[3:Rew:951.0,933.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.22/0.51 954[3:Rew:948.0,929.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 956[3:Rew:954.0,952.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.22/0.51 957[3:Rew:956.0,943.0] || equal(sk_c9,sk_c8)** -> .
% 0.22/0.51 958[3:Rew:948.0,953.0,954.0,953.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 959[3:Rew:958.0,931.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.22/0.51 960[3:Rew:959.0,928.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.51 961[3:MRR:960.0,957.0] || -> .
% 0.22/0.51 964[2:Spt:961.0,1.1,106.0] || equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.22/0.51 965[2:Spt:961.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.22/0.51 966[2:MRR:7.1,964.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.22/0.51 967[2:MRR:5.1,964.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.51 969[2:MRR:6.1,964.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.22/0.51 970[2:MRR:4.1,964.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.22/0.51 972[2:SpR:965.0,147.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.22/0.51 980[2:SpR:969.0,46.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c7,u))**.
% 0.22/0.51 981[2:SpR:969.0,147.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.22/0.51 983[2:Rew:966.0,981.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.22/0.51 985[2:SpR:970.0,147.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.22/0.51 987[2:Rew:967.0,985.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.22/0.51 988[2:Rew:987.0,964.0] || equal(sk_c7,sk_c8)** -> .
% 0.22/0.51 994[2:SpR:983.0,147.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.22/0.51 996[2:Rew:45.0,994.0] || -> equal(identity,sk_c7)**.
% 0.22/0.51 997[2:Rew:996.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.51 1001[2:Rew:997.0,972.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 1002[2:Rew:997.0,980.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.22/0.51 1004[2:Rew:1001.0,987.0] || -> equal(sk_c9,sk_c8)**.
% 0.22/0.51 1009[2:Rew:1004.0,969.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.51 1014[2:Rew:1001.0,1002.0,1004.0,1002.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.51 1015[2:Rew:1014.0,1009.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 1016[2:MRR:1015.0,988.0] || -> .
% 0.22/0.51 % SZS output end Refutation
% 0.22/0.51 Formulae used in the proof : prove_this_1 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_27 prove_this_28 prove_this_29 prove_this_34 prove_this_35 prove_this_36 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 left_identity left_inverse associativity
% 0.22/0.51
%------------------------------------------------------------------------------