TSTP Solution File: GRP336-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP336-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:46:54 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP336-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 : Mon Jun 13 11:30:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 713 clauses, backtracked 420 clauses, performed 12 splits and kept 667 clauses.
% 0.19/0.48 SPASS allocated 63604 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 4, length 206 :
% 0.19/0.48 % SZS output start Refutation
% 0.19/0.48 3[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c10),sk_c8).
% 0.19/0.48 4[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.19/0.48 5[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c10)** equal(multiply(sk_c9,sk_c10),sk_c8).
% 0.19/0.48 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(multiply(sk_c9,sk_c10),sk_c8).
% 0.19/0.48 7[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.19/0.48 9[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 10[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.48 11[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 12[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.48 13[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 19[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.48 25[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 26[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 27[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 28[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 29[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 30[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 31[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 33[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 35[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 36[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 37[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 38[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.48 39[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 41[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.48 42[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.48 43[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.48 44[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.48 45[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.19/0.48 49[0:Inp] || equal(multiply(sk_c9,sk_c10),sk_c8) equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,w),sk_c9)** equal(inverse(v),w) equal(multiply(w,sk_c10),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)** equal(inverse(y),sk_c10) equal(multiply(y,sk_c9),sk_c10)** equal(multiply(z,x1),sk_c9)** equal(inverse(z),x1) equal(multiply(x1,sk_c8),sk_c9)** -> .
% 0.19/0.48 50[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.48 51[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.48 52[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.48 53[0:Con:49.9] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,v),sk_c9)**+ equal(multiply(w,sk_c10),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c10),sk_c8) -> .
% 0.19/0.48 54[1:Spt:53.0,53.3,53.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.19/0.48 58[2:Spt:35.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 60[3:Spt:11.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.48 62[4:Spt:27.1] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 64[4:SpL:62.0,54.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c9,sk_c9) equal(multiply(sk_c3,sk_c10),sk_c9)** -> .
% 0.19/0.48 65[4:Obv:64.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c10),sk_c9)** -> .
% 0.19/0.48 66[4:Rew:58.0,65.0] || equal(sk_c3,sk_c3) equal(multiply(sk_c3,sk_c10),sk_c9)** -> .
% 0.19/0.48 67[4:Obv:66.0] || equal(multiply(sk_c3,sk_c10),sk_c9)** -> .
% 0.19/0.48 69[4:MRR:44.1,67.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 70[4:MRR:42.1,67.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.48 73[4:MRR:45.1,67.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 74[4:MRR:43.1,67.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 75[4:MRR:41.1,67.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 95[4:SpL:75.0,54.1] || equal(inverse(sk_c4),sk_c10) equal(sk_c9,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 96[4:Obv:95.1] || equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 97[4:Rew:70.0,96.0] || equal(sk_c10,sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 98[4:Obv:97.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 103[3:SpR:60.0,51.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.19/0.48 105[4:SpR:69.0,51.0] || -> equal(multiply(sk_c10,sk_c5),identity)**.
% 0.19/0.48 106[4:SpR:70.0,51.0] || -> equal(multiply(sk_c10,sk_c4),identity)**.
% 0.19/0.48 126[0:SpR:51.0,52.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.48 136[0:Rew:50.0,126.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.48 145[0:SpR:136.0,136.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.48 151[4:SpR:74.0,136.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.19/0.48 155[0:SpR:51.0,136.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.48 157[3:SpR:103.0,136.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.19/0.48 158[4:SpR:105.0,136.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c5)**.
% 0.19/0.48 159[4:SpR:106.0,136.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c4)**.
% 0.19/0.48 173[4:Rew:157.0,158.0] || -> equal(sk_c1,sk_c5)**.
% 0.19/0.48 178[4:Rew:173.0,157.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c5)**.
% 0.19/0.48 179[4:Rew:159.0,178.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 181[4:Rew:179.0,73.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.19/0.48 190[0:Rew:145.0,155.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.48 192[4:Rew:190.0,159.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.19/0.48 199[4:Rew:192.0,151.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.48 201[4:Rew:181.0,199.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 204[4:Rew:201.0,74.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.48 212[4:MRR:204.0,98.0] || -> .
% 0.19/0.48 221[4:Spt:212.0,27.1,62.0] || equal(multiply(sk_c2,sk_c3),sk_c9)** -> .
% 0.19/0.48 222[4:Spt:212.0,27.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 225[4:MRR:28.1,221.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 226[4:MRR:26.1,221.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.48 229[4:MRR:29.1,221.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 230[4:MRR:25.1,221.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 283[4:SpR:229.0,136.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c9)**.
% 0.19/0.48 286[4:Rew:225.0,283.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.48 294[4:SpL:230.0,54.1] || equal(inverse(sk_c4),sk_c10) equal(sk_c9,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 296[4:Obv:294.1] || equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 297[4:Rew:226.0,296.0] || equal(sk_c10,sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 298[4:Obv:297.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 299[4:Rew:286.0,298.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.48 300[4:Obv:299.0] || -> .
% 0.19/0.48 301[3:Spt:300.0,11.0,60.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.19/0.48 302[3:Spt:300.0,11.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 304[3:MRR:12.1,301.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 305[3:MRR:10.1,301.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.48 308[3:MRR:13.0,301.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 309[3:MRR:9.0,301.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 346[3:SpR:308.0,136.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c9)**.
% 0.19/0.48 349[3:Rew:304.0,346.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.48 357[3:SpL:309.0,54.1] || equal(inverse(sk_c4),sk_c10) equal(sk_c9,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 359[3:Obv:357.1] || equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 360[3:Rew:305.0,359.0] || equal(sk_c10,sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 361[3:Obv:360.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 362[3:Rew:349.0,361.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.48 363[3:Obv:362.0] || -> .
% 0.19/0.48 364[2:Spt:363.0,35.0,58.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.19/0.48 365[2:Spt:363.0,35.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 367[2:MRR:36.1,364.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 368[2:MRR:34.1,364.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.48 371[2:MRR:37.0,364.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 372[2:MRR:33.0,364.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.48 401[2:SpR:371.0,136.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c9)**.
% 0.19/0.48 404[2:Rew:367.0,401.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.48 412[2:SpL:372.0,54.1] || equal(inverse(sk_c4),sk_c10) equal(sk_c9,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 414[2:Obv:412.1] || equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 415[2:Rew:368.0,414.0] || equal(sk_c10,sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 416[2:Obv:415.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 417[2:Rew:404.0,416.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.48 418[2:Obv:417.0] || -> .
% 0.19/0.48 419[1:Spt:418.0,53.1,53.2,53.4,53.6,53.7,53.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c10),sk_c8) -> .
% 0.19/0.48 421[1:SpL:51.0,419.2] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c10),sk_c8) -> .
% 0.19/0.48 423[2:Spt:3.1] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.19/0.48 426[2:Rew:423.0,421.5] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.48 429[2:Obv:426.5] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.19/0.48 435[3:Spt:11.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 438[3:Rew:435.0,429.4] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(sk_c9,sk_c9) -> .
% 0.19/0.48 441[3:Obv:438.4] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.48 445[3:SpR:435.0,136.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.19/0.48 447[4:Spt:39.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 448[4:SpR:447.0,51.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.19/0.48 455[5:Spt:31.1] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 461[4:SpR:448.0,136.0] || -> equal(multiply(inverse(sk_c3),identity),sk_c2)**.
% 0.19/0.48 463[4:Rew:190.0,461.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.19/0.48 475[4:SpR:463.0,51.0] || -> equal(multiply(sk_c2,sk_c3),identity)**.
% 0.19/0.48 478[5:Rew:455.0,475.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 479[5:Rew:478.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.48 484[5:Rew:478.0,190.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.48 485[5:Rew:478.0,441.2] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.48 487[5:Rew:479.0,423.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 495[5:Rew:487.0,445.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c10)**.
% 0.19/0.48 522[5:Obv:485.2] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.48 573[5:Rew:484.0,495.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.48 600[5:Rew:484.0,522.2] || equal(inverse(inverse(sk_c10)),sk_c10)** equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 648[5:Rew:573.0,600.0,573.0,600.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 649[5:Obv:648.0] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 763[5:SpL:573.0,649.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.48 765[5:Obv:763.1] || -> .
% 0.19/0.48 766[5:Spt:765.0,31.1,455.0] || equal(multiply(sk_c2,sk_c3),sk_c9)** -> .
% 0.19/0.48 767[5:Spt:765.0,31.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.48 768[5:Rew:475.0,766.0] || equal(identity,sk_c9)** -> .
% 0.19/0.48 775[4:Rew:475.0,30.1] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(identity,sk_c9).
% 0.19/0.48 776[5:MRR:775.1,768.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.48 813[5:SpR:776.0,136.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.19/0.48 815[5:Rew:767.0,813.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.19/0.48 839[5:SpR:815.0,136.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.19/0.48 841[5:Rew:51.0,839.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 842[5:MRR:841.0,768.0] || -> .
% 0.19/0.48 843[4:Spt:842.0,39.1,447.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.19/0.48 844[4:Spt:842.0,39.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.48 845[4:MRR:36.1,843.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 848[4:MRR:38.0,843.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.48 849[4:MRR:37.0,843.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 861[4:SpR:848.0,136.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.19/0.48 863[4:Rew:844.0,861.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.19/0.48 881[4:SpR:863.0,136.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.19/0.48 883[4:Rew:51.0,881.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 886[4:Rew:883.0,190.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.48 889[4:Rew:883.0,441.2] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.48 905[4:Rew:886.0,849.0] || -> equal(sk_c5,sk_c10)**.
% 0.19/0.48 908[4:Rew:905.0,845.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.48 919[4:Obv:889.2] || equal(inverse(inverse(sk_c10)),sk_c10) equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.19/0.48 920[4:Rew:886.0,919.2,908.0,919.0,908.0,919.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 921[4:Obv:920.0] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 1017[4:SpL:908.0,921.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.48 1020[4:Obv:1017.1] || -> .
% 0.19/0.48 1022[3:Spt:1020.0,11.1,435.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.19/0.48 1023[3:Spt:1020.0,11.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.48 1024[3:MRR:35.1,1022.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.19/0.48 1026[3:MRR:19.0,1022.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.48 1027[3:MRR:27.0,1022.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.19/0.48 1039[3:SpR:1026.0,136.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c9)**.
% 0.19/0.48 1041[3:Rew:1023.0,1039.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.19/0.48 1043[3:SpR:1027.0,136.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c3)**.
% 0.19/0.48 1045[3:Rew:1024.0,1043.0] || -> equal(multiply(sk_c3,sk_c9),sk_c3)**.
% 0.19/0.48 1050[3:SpR:1045.0,136.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c9)**.
% 0.19/0.48 1052[3:Rew:51.0,1050.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 1053[3:Rew:1052.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.48 1057[3:Rew:1053.0,423.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 1064[3:Rew:1057.0,1022.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.19/0.48 1070[3:Rew:1041.0,1064.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.48 1071[3:Obv:1070.0] || -> .
% 0.19/0.48 1075[2:Spt:1071.0,3.1,423.0] || equal(multiply(sk_c9,sk_c10),sk_c8)** -> .
% 0.19/0.48 1076[2:Spt:1071.0,3.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 1077[2:MRR:7.1,1075.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.48 1078[2:MRR:4.1,1075.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.19/0.48 1081[2:MRR:6.1,1075.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.48 1082[2:MRR:5.1,1075.0] || -> equal(multiply(sk_c5,sk_c9),sk_c10)**.
% 0.19/0.48 1085[2:SpR:1076.0,136.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.19/0.48 1097[2:SpR:1081.0,136.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.19/0.48 1099[2:Rew:1077.0,1097.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.19/0.48 1112[2:SpR:1099.0,136.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.19/0.48 1114[2:Rew:51.0,1112.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 1115[2:Rew:1114.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 1116[2:Rew:1114.0,190.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.49 1119[2:Rew:1115.0,1075.0] || equal(sk_c8,sk_c10)** -> .
% 0.19/0.49 1125[2:Rew:1116.0,1082.0] || -> equal(sk_c5,sk_c10)**.
% 0.19/0.49 1127[2:Rew:1116.0,1085.0] || -> equal(inverse(sk_c10),sk_c8)**.
% 0.19/0.49 1128[2:Rew:1125.0,1078.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.49 1130[2:Rew:1127.0,1128.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.49 1131[2:MRR:1130.0,1119.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 Formulae used in the proof : prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_19 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_49 left_identity left_inverse associativity
% 0.19/0.49
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