TSTP Solution File: GRP225-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP225-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:46:24 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP225-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 06:49:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 1248 clauses, backtracked 313 clauses, performed 11 splits and kept 619 clauses.
% 0.19/0.52 SPASS allocated 64217 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 5, length 273 :
% 0.19/0.52 % SZS output start Refutation
% 0.19/0.52 1[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.52 2[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 3[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.52 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.52 5[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.52 6[0:Inp] || -> equal(inverse(sk_c6),sk_c7)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.52 8[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.52 9[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.19/0.52 10[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.19/0.52 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.52 12[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.19/0.52 13[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.52 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.52 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.52 19[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.52 20[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.52 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.52 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.52 26[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.52 27[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.52 29[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.52 30[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 31[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.52 32[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.52 33[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.52 34[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.52 36[0:Inp] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,v),sk_c8)** equal(multiply(w,sk_c9),v)* equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(x,sk_c8),sk_c9)** equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(z,x1),sk_c8)** equal(inverse(z),x1) equal(multiply(x1,sk_c9),sk_c8)** -> .
% 0.19/0.52 37[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.52 38[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.52 39[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.52 40[0:Con:36.5] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c9) equal(multiply(u,v),sk_c8)**+ equal(multiply(x,sk_c9),z)* equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(y,sk_c8),sk_c9)** equal(multiply(sk_c9,z),sk_c8)** -> .
% 0.19/0.52 41[1:Spt:40.3,40.8] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.52 44[2:Spt:6.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.52 52[3:Spt:13.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.52 54[3:SpL:52.0,41.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.19/0.52 55[3:Obv:54.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.52 56[3:Rew:44.0,55.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.52 57[3:Obv:56.0] || -> .
% 0.19/0.52 58[3:Spt:57.0,13.1,52.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.19/0.52 59[3:Spt:57.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.52 61[3:MRR:8.1,58.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.52 65[3:MRR:9.1,58.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 76[3:SpL:65.0,41.1] || equal(inverse(sk_c4),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.19/0.52 77[3:Obv:76.1] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.52 78[3:Rew:61.0,77.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.52 79[3:Obv:78.0] || -> .
% 0.19/0.52 80[2:Spt:79.0,6.1,44.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.52 81[2:Spt:79.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.52 83[2:MRR:1.1,80.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.52 87[2:MRR:2.0,80.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 98[2:SpL:87.0,41.1] || equal(inverse(sk_c4),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.19/0.52 99[2:Obv:98.1] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.52 100[2:Rew:83.0,99.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.52 101[2:Obv:100.0] || -> .
% 0.19/0.52 102[1:Spt:101.0,40.0,40.1,40.2,40.4,40.5,40.6,40.7,40.9] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(x,sk_c9),y)* equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,y),sk_c8)** -> .
% 0.19/0.52 103[1:SpL:37.0,102.3] || equal(inverse(identity),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(u,sk_c8) equal(multiply(w,sk_c9),x)* equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.19/0.52 104[2:Spt:4.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.52 106[3:Spt:32.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.52 108[4:Spt:11.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.52 110[4:SpL:108.0,102.3] || equal(inverse(sk_c1),sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 111[4:Rew:104.0,110.0] || equal(sk_c9,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 112[4:Obv:111.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c8,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 113[5:Spt:18.1] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.52 118[2:SpR:104.0,38.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.52 119[3:SpR:106.0,38.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.19/0.52 121[6:Spt:25.1] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.52 123[6:SpL:121.0,102.3] || equal(inverse(sk_c2),sk_c9) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c3,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c9,sk_c9),sk_c8)** equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 124[6:Rew:106.0,123.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c3,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c9,sk_c9),sk_c8)** equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 125[6:Obv:124.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c3,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c9,sk_c9),sk_c8)** equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 127[2:SpL:118.0,102.3] || equal(inverse(sk_c9),sk_c1) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c1,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 134[0:SpR:38.0,39.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.52 143[0:Rew:37.0,134.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.52 146[0:SpR:143.0,143.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.52 149[0:SpR:38.0,143.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.52 150[6:SpR:121.0,143.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.52 152[5:SpR:113.0,143.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.19/0.52 153[2:SpR:118.0,143.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.19/0.52 154[3:SpR:119.0,143.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.19/0.52 159[6:Rew:113.0,150.0,106.0,150.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.52 161[6:Rew:159.0,104.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.52 163[6:Rew:159.0,108.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.52 165[6:Rew:159.0,121.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.52 167[6:Rew:159.0,119.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.52 173[6:Rew:159.0,125.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c3,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c9,sk_c9),sk_c8)** equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 182[6:Rew:159.0,152.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.19/0.52 183[6:Rew:38.0,182.0] || -> equal(identity,sk_c3)**.
% 0.19/0.52 184[6:Rew:183.0,37.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.52 188[6:Rew:183.0,167.0] || -> equal(multiply(sk_c8,sk_c2),sk_c3)**.
% 0.19/0.52 189[6:Rew:159.0,153.0,183.0,153.0] || -> equal(multiply(inverse(sk_c8),sk_c3),sk_c1)**.
% 0.19/0.52 190[6:Rew:189.0,154.0,159.0,154.0,183.0,154.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.52 192[6:Rew:190.0,165.0] || -> equal(multiply(sk_c1,sk_c8),sk_c3)**.
% 0.19/0.52 193[6:Rew:190.0,188.0] || -> equal(multiply(sk_c8,sk_c1),sk_c3)**.
% 0.19/0.52 194[6:Rew:163.0,192.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.52 196[6:Rew:194.0,183.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 197[6:Rew:194.0,184.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.52 200[6:Rew:194.0,193.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.19/0.52 201[6:Rew:197.0,200.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.52 202[6:Rew:201.0,159.0] || -> equal(sk_c9,sk_c1)**.
% 0.19/0.52 203[6:Rew:201.0,161.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.52 205[6:Rew:201.0,194.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.52 206[6:Rew:201.0,196.0] || -> equal(identity,sk_c1)**.
% 0.19/0.52 207[6:Rew:201.0,197.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.52 211[6:Rew:206.0,149.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.19/0.52 216[6:Rew:146.0,211.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.52 220[6:Rew:207.0,173.6,202.0,173.6,201.0,173.6,216.0,173.5,201.0,173.5,202.0,173.5,216.0,173.4,202.0,173.4,201.0,173.4,216.0,173.3,202.0,173.3,205.0,173.2,201.0,173.2,201.0,173.1,201.0,173.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(v,w)* equal(sk_c1,sk_c1) equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.19/0.52 221[6:Obv:220.4] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.19/0.52 551[6:SpL:203.0,221.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.19/0.52 555[6:Obv:551.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.19/0.52 556[6:SpL:203.0,555.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.19/0.52 560[6:Obv:556.1] || equal(u,sk_c1)* -> .
% 0.19/0.52 561[6:AED:560.0] || -> .
% 0.19/0.52 562[6:Spt:561.0,25.1,121.0] || equal(multiply(sk_c2,sk_c9),sk_c3)** -> .
% 0.19/0.52 563[6:Spt:561.0,25.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.52 565[3:Rew:153.0,154.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.52 568[6:Rew:565.0,562.0] || equal(multiply(sk_c1,sk_c9),sk_c3)** -> .
% 0.19/0.52 573[3:Rew:565.0,27.1] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c3)**.
% 0.19/0.52 574[6:MRR:573.1,568.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.52 575[0:Rew:146.0,149.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.52 576[2:Rew:575.0,153.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.19/0.52 577[5:Rew:576.0,152.0] || -> equal(multiply(sk_c1,sk_c8),sk_c3)**.
% 0.19/0.52 578[5:Rew:108.0,577.0] || -> equal(sk_c9,sk_c3)**.
% 0.19/0.52 582[5:Rew:578.0,108.0] || -> equal(multiply(sk_c1,sk_c8),sk_c3)**.
% 0.19/0.52 584[6:Rew:578.0,568.0] || equal(multiply(sk_c1,sk_c3),sk_c3)** -> .
% 0.19/0.52 593[5:Rew:565.0,26.1,578.0,26.1] || -> equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c3),sk_c3).
% 0.19/0.52 594[6:MRR:593.1,584.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.52 595[5:Rew:565.0,24.1,578.0,24.1,578.0,24.0] || -> equal(multiply(sk_c5,sk_c8),sk_c3)** equal(multiply(sk_c1,sk_c3),sk_c3).
% 0.19/0.52 596[6:MRR:595.1,584.0] || -> equal(multiply(sk_c5,sk_c8),sk_c3)**.
% 0.19/0.52 650[6:SpR:594.0,143.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.19/0.52 652[6:Rew:574.0,650.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.52 654[6:SpR:596.0,143.0] || -> equal(multiply(inverse(sk_c5),sk_c3),sk_c8)**.
% 0.19/0.52 656[6:Rew:563.0,654.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.52 667[6:SpR:652.0,143.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.52 669[6:Rew:38.0,667.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 671[6:Rew:669.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.52 675[6:Rew:669.0,575.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.52 679[6:Rew:671.0,656.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.52 692[6:Rew:679.0,582.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.52 695[6:Rew:679.0,584.0] || equal(multiply(sk_c1,sk_c8),sk_c8)** -> .
% 0.19/0.52 710[6:Rew:675.0,692.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.52 719[6:Rew:710.0,675.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.52 731[6:Rew:719.0,695.0,710.0,695.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.52 732[6:Obv:731.0] || -> .
% 0.19/0.52 760[5:Spt:732.0,18.1,113.0] || equal(multiply(sk_c9,sk_c3),sk_c8)** -> .
% 0.19/0.52 761[5:Spt:732.0,18.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.52 765[5:MRR:20.1,760.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.52 771[5:MRR:19.1,760.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.52 772[5:MRR:17.1,760.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.52 805[5:SpR:771.0,143.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.19/0.52 807[5:Rew:765.0,805.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.52 809[5:SpR:772.0,143.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.19/0.52 811[5:Rew:761.0,809.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.52 812[5:Rew:811.0,112.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 813[5:Obv:812.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 819[5:SpR:807.0,143.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.52 821[5:Rew:38.0,819.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 823[5:Rew:821.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.52 824[5:Rew:821.0,575.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.52 831[5:Rew:823.0,811.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.52 838[5:Rew:831.0,576.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.52 842[5:Rew:831.0,108.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.52 849[5:Rew:831.0,813.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c9,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.52 856[5:Rew:824.0,842.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.52 860[5:Rew:856.0,823.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.52 861[5:Rew:856.0,831.0] || -> equal(sk_c9,sk_c1)**.
% 0.19/0.52 862[5:Rew:856.0,838.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.52 865[5:Rew:856.0,824.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.52 892[5:Rew:860.0,849.5,861.0,849.5,856.0,849.5,865.0,849.4,856.0,849.4,861.0,849.4,865.0,849.3,861.0,849.3,861.0,849.2,856.0,849.2,856.0,849.1,856.0,849.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.19/0.52 893[5:Obv:892.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.19/0.52 1112[5:SpL:862.0,893.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.19/0.52 1115[5:Obv:1112.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.19/0.52 1186[5:SpL:862.0,1115.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.19/0.52 1190[5:Obv:1186.1] || equal(u,sk_c1)* -> .
% 0.19/0.52 1191[5:AED:1190.0] || -> .
% 0.19/0.52 1192[4:Spt:1191.0,11.1,108.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.19/0.52 1193[4:Spt:1191.0,11.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.52 1195[4:MRR:8.1,1192.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.52 1196[4:MRR:13.1,1192.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.52 1198[4:MRR:12.1,1192.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.19/0.52 1199[4:MRR:10.1,1192.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.52 1200[4:MRR:9.1,1192.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 1221[4:SpR:1198.0,143.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.19/0.52 1223[4:Rew:1196.0,1221.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.52 1233[4:SpR:1223.0,143.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.52 1235[4:Rew:38.0,1233.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 1236[4:Rew:1235.0,118.0] || -> equal(multiply(sk_c9,sk_c1),sk_c8)**.
% 0.35/0.54 1237[4:Rew:1235.0,575.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.35/0.54 1238[4:Rew:1235.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.35/0.54 1244[4:Rew:1237.0,1200.0] || -> equal(sk_c9,sk_c4)**.
% 0.35/0.54 1245[4:Rew:1237.0,1199.0] || -> equal(sk_c9,sk_c5)**.
% 0.35/0.54 1250[4:Rew:1237.0,1192.0] || equal(sk_c9,sk_c1)** -> .
% 0.35/0.54 1252[4:Rew:1244.0,1195.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.35/0.54 1263[4:Rew:1244.0,1236.0] || -> equal(multiply(sk_c4,sk_c1),sk_c8)**.
% 0.35/0.54 1264[4:Rew:1244.0,1245.0] || -> equal(sk_c5,sk_c4)**.
% 0.35/0.54 1265[4:Rew:1264.0,1193.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.35/0.54 1268[4:Rew:1244.0,1250.0] || equal(sk_c4,sk_c1)** -> .
% 0.35/0.54 1271[4:Rew:1252.0,1265.0] || -> equal(sk_c8,sk_c4)**.
% 0.35/0.54 1276[4:Rew:1271.0,1238.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.35/0.54 1280[4:Rew:1276.0,1263.0,1271.0,1263.0] || -> equal(sk_c4,sk_c1)**.
% 0.35/0.54 1281[4:MRR:1280.0,1268.0] || -> .
% 0.35/0.54 1312[3:Spt:1281.0,32.1,106.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.35/0.54 1313[3:Spt:1281.0,32.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.54 1314[3:MRR:29.1,1312.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.35/0.54 1315[3:MRR:34.1,1312.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.35/0.54 1317[3:MRR:33.0,1312.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.35/0.54 1318[3:MRR:31.0,1312.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.54 1319[3:MRR:30.0,1312.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.35/0.54 1322[2:Rew:576.0,127.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c1,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.35/0.54 1323[2:Obv:1322.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c1,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.35/0.54 1343[3:SpR:1317.0,143.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.35/0.54 1345[3:Rew:1315.0,1343.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.35/0.54 1347[3:SpR:1318.0,143.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.35/0.54 1349[3:Rew:1313.0,1347.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.35/0.54 1355[3:SpR:1345.0,143.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.35/0.54 1357[3:Rew:38.0,1355.0] || -> equal(identity,sk_c8)**.
% 0.35/0.54 1359[3:Rew:1357.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.35/0.54 1360[3:Rew:1357.0,575.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.35/0.54 1365[3:Rew:1357.0,1323.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c8,sk_c8) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c1,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.35/0.54 1366[3:Rew:1359.0,1349.0] || -> equal(sk_c9,sk_c8)**.
% 0.35/0.54 1372[3:Rew:1366.0,576.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.35/0.54 1373[3:Rew:1366.0,1314.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.35/0.54 1374[3:Rew:1366.0,104.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.35/0.54 1378[3:Rew:1366.0,1319.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.35/0.54 1392[3:Rew:1360.0,1378.0] || -> equal(sk_c8,sk_c4)**.
% 0.35/0.54 1395[3:Rew:1392.0,1359.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.35/0.54 1396[3:Rew:1392.0,1366.0] || -> equal(sk_c9,sk_c4)**.
% 0.35/0.54 1397[3:Rew:1392.0,1372.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.35/0.54 1398[3:Rew:1392.0,1373.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.35/0.54 1399[3:Rew:1392.0,1374.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.35/0.54 1400[3:Rew:1392.0,1360.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.35/0.54 1404[3:Rew:1397.0,1398.0] || -> equal(sk_c4,sk_c1)**.
% 0.35/0.54 1405[3:Rew:1404.0,1392.0] || -> equal(sk_c8,sk_c1)**.
% 0.35/0.54 1407[3:Rew:1404.0,1396.0] || -> equal(sk_c9,sk_c1)**.
% 0.35/0.54 1411[3:Rew:1404.0,1399.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.35/0.54 1416[3:Rew:1404.0,1395.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.35/0.54 1417[3:Rew:1404.0,1400.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.35/0.54 1433[3:Obv:1365.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(v,sk_c9),w)* equal(multiply(sk_c1,sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.35/0.54 1434[3:Rew:1416.0,1433.5,1407.0,1433.5,1405.0,1433.5,1417.0,1433.4,1405.0,1433.4,1407.0,1433.4,1407.0,1433.3,1416.0,1433.3,1405.0,1433.3,1417.0,1433.2,1407.0,1433.2,1407.0,1433.1,1405.0,1433.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,w)* equal(sk_c1,sk_c1) equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.35/0.54 1435[3:Obv:1434.3] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(v,w)* equal(u,sk_c1) equal(w,sk_c1)* -> .
% 0.35/0.54 1616[3:SpL:1411.0,1435.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(u,v)* equal(sk_c1,sk_c1) equal(v,sk_c1)* -> .
% 0.35/0.54 1618[3:Obv:1616.3] || equal(inverse(u),sk_c1)**+ equal(u,v)* equal(v,sk_c1)* -> .
% 0.35/0.54 1721[3:SpL:1411.0,1618.0] || equal(sk_c1,sk_c1)* equal(sk_c1,u)* equal(u,sk_c1)* -> .
% 0.35/0.54 1725[3:Obv:1721.1] || equal(u,sk_c1)* -> .
% 0.35/0.54 1726[3:AED:1725.0] || -> .
% 0.35/0.54 1727[2:Spt:1726.0,4.1,104.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.35/0.54 1728[2:Spt:1726.0,4.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.54 1729[2:MRR:1.1,1727.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.35/0.54 1730[2:MRR:6.1,1727.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.35/0.54 1733[2:MRR:5.0,1727.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.35/0.54 1734[2:MRR:3.0,1727.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.54 1735[2:MRR:2.0,1727.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.35/0.54 1747[2:SpR:1733.0,143.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.35/0.54 1749[2:Rew:1730.0,1747.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.35/0.54 1759[2:SpR:1749.0,143.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.35/0.54 1761[2:Rew:38.0,1759.0] || -> equal(identity,sk_c8)**.
% 0.35/0.54 1762[2:Rew:1761.0,575.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.35/0.54 1763[2:Rew:1761.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.35/0.54 1766[2:Rew:1761.0,103.0] || equal(inverse(sk_c8),u) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(u,sk_c8) equal(multiply(w,sk_c9),x)* equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.35/0.54 1768[2:Rew:1762.0,1735.0] || -> equal(sk_c9,sk_c4)**.
% 0.35/0.54 1769[2:Rew:1762.0,1734.0] || -> equal(sk_c9,sk_c5)**.
% 0.35/0.54 1774[2:Rew:1768.0,1729.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.35/0.54 1783[2:Rew:1768.0,1769.0] || -> equal(sk_c5,sk_c4)**.
% 0.35/0.54 1784[2:Rew:1783.0,1728.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.35/0.54 1787[2:Rew:1774.0,1784.0] || -> equal(sk_c8,sk_c4)**.
% 0.35/0.54 1791[2:Rew:1787.0,1762.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.35/0.54 1792[2:Rew:1787.0,1763.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.35/0.54 1813[2:Rew:1792.0,1766.7,1768.0,1766.7,1787.0,1766.7,1791.0,1766.6,1787.0,1766.6,1768.0,1766.6,1791.0,1766.5,1768.0,1766.5,1787.0,1766.5,1791.0,1766.4,1768.0,1766.4,1787.0,1766.3,1768.0,1766.2,1787.0,1766.1,1774.0,1766.0,1787.0,1766.0] || equal(sk_c4,u)* equal(inverse(v),sk_c4)** equal(inverse(w),sk_c4)** equal(u,sk_c4)* equal(w,x)* equal(u,sk_c4)* equal(v,sk_c4) equal(x,sk_c4)* -> .
% 0.35/0.54 1814[2:Obv:1813.3] || equal(inverse(u),sk_c4)** equal(inverse(v),sk_c4)** equal(v,w)* equal(x,sk_c4)* equal(u,sk_c4) equal(w,sk_c4)* -> .
% 0.35/0.54 1815[2:Con:1814.3] || equal(inverse(u),sk_c4)**+ equal(inverse(v),sk_c4)** equal(v,w)* equal(u,sk_c4) equal(w,sk_c4)* -> .
% 0.35/0.54 1982[2:SpL:1774.0,1815.0] || equal(sk_c4,sk_c4) equal(inverse(u),sk_c4)** equal(u,v)* equal(sk_c4,sk_c4) equal(v,sk_c4)* -> .
% 0.35/0.54 1984[2:Obv:1982.3] || equal(inverse(u),sk_c4)**+ equal(u,v)* equal(v,sk_c4)* -> .
% 0.35/0.54 2087[2:SpL:1774.0,1984.0] || equal(sk_c4,sk_c4)* equal(sk_c4,u)* equal(u,sk_c4)* -> .
% 0.35/0.54 2091[2:Obv:2087.1] || equal(u,sk_c4)* -> .
% 0.35/0.54 2092[2:AED:2091.0] || -> .
% 0.35/0.54 % SZS output end Refutation
% 0.35/0.54 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_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_36 left_identity left_inverse associativity
% 0.35/0.54
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