TSTP Solution File: GRP250-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP250-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:31 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP250-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 05:27:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 1130 clauses, backtracked 318 clauses, performed 12 splits and kept 576 clauses.
% 0.21/0.50 SPASS allocated 64025 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.21/0.50 0:00:00.03 for the input.
% 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.08 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 5, length 244 :
% 0.21/0.50 % SZS output start Refutation
% 0.21/0.50 1[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.21/0.50 2[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 5[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 7[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.50 8[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.50 9[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.50 11[0:Inp] || -> equal(inverse(sk_c6),sk_c7)** equal(inverse(sk_c1),sk_c9).
% 0.21/0.50 14[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 17[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 18[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 20[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 21[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 22[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 23[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 24[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.50 26[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 27[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 28[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 29[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 30[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.50 32[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 35[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 37[0:Inp] || equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(v,sk_c8),sk_c7)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c9),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(y,sk_c8),sk_c7)** equal(inverse(y),sk_c8) equal(inverse(z),sk_c7) equal(multiply(z,sk_c8),sk_c7)** -> .
% 0.21/0.50 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.50 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.50 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.50 41[0:Con:37.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** -> .
% 0.21/0.50 42[1:Spt:41.2,41.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.21/0.50 47[2:Spt:10.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.50 56[3:Spt:9.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 58[3:SpL:56.0,42.1] || equal(inverse(sk_c5),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.50 59[3:Obv:58.1] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.50 60[3:Rew:47.0,59.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 61[3:Obv:60.0] || -> .
% 0.21/0.50 62[3:Spt:61.0,9.1,56.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.21/0.50 63[3:Spt:61.0,9.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 65[3:MRR:21.1,62.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 67[3:MRR:15.0,62.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 74[3:SpL:67.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.50 75[3:Obv:74.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.21/0.50 76[3:Rew:65.0,75.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 77[3:Obv:76.0] || -> .
% 0.21/0.50 78[2:Spt:77.0,10.0,47.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.50 79[2:Spt:77.0,10.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 81[2:MRR:22.0,78.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 83[2:MRR:16.0,78.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 90[2:SpL:83.0,42.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.50 91[2:Obv:90.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.21/0.50 92[2:Rew:81.0,91.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 93[2:Obv:92.0] || -> .
% 0.21/0.50 94[1:Spt:93.0,41.0,41.1,41.3,41.4,41.5,41.7] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** -> .
% 0.21/0.50 96[2:Spt:28.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.50 98[3:Spt:20.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.50 100[4:Spt:23.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.50 102[5:Spt:7.1] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.50 105[2:SpR:96.0,39.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.50 106[3:SpR:98.0,39.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.21/0.50 107[4:SpR:100.0,39.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.21/0.50 108[1:SpL:39.0,94.3] || equal(inverse(inverse(sk_c8)),sk_c7) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 109[6:Spt:27.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 114[7:Spt:30.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.50 116[7:SpL:114.0,94.3] || equal(inverse(sk_c6),sk_c7) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 117[7:Obv:116.3] || equal(inverse(sk_c6),sk_c7) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 118[7:Rew:100.0,117.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 119[7:Obv:118.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 125[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.50 128[5:SpR:102.0,40.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.21/0.50 129[2:SpR:105.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.50 131[2:Rew:38.0,129.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.21/0.50 133[0:Rew:38.0,125.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.50 140[6:SpR:109.0,131.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.50 149[0:SpR:133.0,133.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.50 152[0:SpR:39.0,133.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.50 154[7:SpR:114.0,133.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.50 156[2:SpR:105.0,133.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.50 158[6:SpR:140.0,133.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.50 159[3:SpR:106.0,133.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c4)**.
% 0.21/0.50 167[7:Rew:100.0,154.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.21/0.50 169[6:Rew:39.0,158.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 170[6:Rew:169.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 173[6:Rew:169.0,106.0] || -> equal(multiply(sk_c9,sk_c4),sk_c7)**.
% 0.21/0.50 174[6:Rew:169.0,107.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.50 178[7:Rew:170.0,167.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 182[7:Rew:178.0,100.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.21/0.50 186[7:Rew:178.0,119.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 187[7:Rew:178.0,169.0] || -> equal(identity,sk_c8)**.
% 0.21/0.50 188[7:Rew:178.0,170.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.50 191[7:Rew:178.0,174.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.21/0.50 193[7:Rew:188.0,191.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.50 196[7:Rew:193.0,182.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 206[7:Rew:187.0,152.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.21/0.50 213[7:Rew:149.0,206.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.50 215[7:Rew:213.0,186.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)**+ -> .
% 0.21/0.50 467[7:SpL:102.0,215.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c9)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.50 472[7:Obv:467.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c4),sk_c9)** equal(u,sk_c8) -> .
% 0.21/0.50 473[7:Rew:98.0,472.1] || equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(u,sk_c8) -> .
% 0.21/0.50 474[7:Obv:473.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.50 535[7:SpL:196.0,474.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 540[7:Obv:535.1] || -> .
% 0.21/0.50 541[7:Spt:540.0,30.1,114.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.21/0.50 542[7:Spt:540.0,30.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 543[6:Rew:170.0,174.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 549[7:Rew:170.0,541.0,543.0,541.0] || equal(sk_c7,sk_c8)** -> .
% 0.21/0.50 550[6:Rew:169.0,152.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.21/0.50 555[6:Rew:170.0,24.1,543.0,24.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c8).
% 0.21/0.50 556[7:MRR:555.1,549.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 559[6:Rew:149.0,550.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 568[6:Rew:170.0,18.0,543.0,18.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 569[7:MRR:568.0,549.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 593[7:SpR:556.0,133.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.21/0.50 616[6:SpR:173.0,133.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c4)**.
% 0.21/0.50 617[6:Rew:559.0,616.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.50 620[6:SpR:617.0,133.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),u)**.
% 0.21/0.50 622[6:Rew:128.0,620.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.50 623[7:Rew:622.0,593.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.21/0.50 629[7:Rew:623.0,569.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 630[7:MRR:629.0,549.0] || -> .
% 0.21/0.50 631[6:Spt:630.0,27.1,109.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.21/0.50 632[6:Spt:630.0,27.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 633[0:Rew:149.0,152.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.50 635[3:Rew:633.0,159.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.50 636[2:Rew:633.0,156.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.50 640[6:MRR:21.1,631.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 645[6:MRR:15.0,631.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 647[2:Rew:96.0,108.0,636.0,108.0] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(identity,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 654[6:SpR:640.0,133.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.21/0.50 658[3:SpR:635.0,133.0] || -> equal(multiply(sk_c4,multiply(sk_c9,u)),u)**.
% 0.21/0.50 660[5:Rew:128.0,658.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.50 662[6:Rew:660.0,654.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.21/0.50 664[5:Rew:660.0,131.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.50 675[6:Rew:662.0,645.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 678[6:Rew:675.0,631.0] || equal(multiply(sk_c5,sk_c8),sk_c8)** -> .
% 0.21/0.50 687[6:Rew:664.0,678.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 688[6:Obv:687.0] || -> .
% 0.21/0.50 699[5:Spt:688.0,7.1,102.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.21/0.50 700[5:Spt:688.0,7.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 705[5:MRR:1.0,699.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 742[5:SpR:705.0,133.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.50 744[5:Rew:700.0,742.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.50 757[5:SpR:744.0,133.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.50 759[5:Rew:635.0,757.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.50 760[5:MRR:759.0,699.0] || -> .
% 0.21/0.50 761[4:Spt:760.0,23.0,100.0] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.21/0.50 762[4:Spt:760.0,23.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 763[4:MRR:11.0,761.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 764[4:MRR:29.0,761.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 765[4:MRR:35.0,761.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 766[4:MRR:17.0,761.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 767[4:MRR:5.0,761.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 779[4:SpR:766.0,133.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.21/0.50 781[4:Rew:762.0,779.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.50 783[4:SpR:767.0,133.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.21/0.50 785[4:Rew:763.0,783.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.50 792[0:SpR:39.0,133.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.50 795[3:SpR:635.0,39.0] || -> equal(multiply(sk_c4,sk_c9),identity)**.
% 0.21/0.50 796[2:SpR:636.0,39.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.21/0.50 800[0:Rew:633.0,792.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.50 804[4:SpR:781.0,133.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.50 806[4:Rew:636.0,804.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 807[4:Rew:796.0,806.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 812[4:Rew:807.0,633.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 815[4:Rew:807.0,647.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 816[4:Rew:807.0,795.0] || -> equal(multiply(sk_c4,sk_c9),sk_c7)**.
% 0.21/0.50 824[4:Rew:812.0,765.0] || -> equal(sk_c3,sk_c8)**.
% 0.21/0.50 827[4:Rew:824.0,764.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 838[4:Obv:815.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 839[4:Rew:812.0,838.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 847[4:SpR:785.0,133.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.50 849[4:Rew:635.0,847.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.21/0.50 850[4:Rew:816.0,849.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.50 863[4:Rew:850.0,839.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 876[4:Obv:863.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)**+ -> .
% 0.21/0.50 911[0:SpR:800.0,133.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.21/0.50 1209[4:SpL:767.0,876.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.50 1212[4:Obv:1209.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) -> .
% 0.21/0.50 1213[4:Rew:763.0,1212.1] || equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(u,sk_c8) -> .
% 0.21/0.50 1214[4:Obv:1213.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.50 1271[4:SpL:827.0,1214.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.50 1276[4:Obv:1271.1] || -> .
% 0.21/0.50 1277[3:Spt:1276.0,20.0,98.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.21/0.50 1278[3:Spt:1276.0,20.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.50 1279[3:MRR:8.0,1277.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.50 1280[3:MRR:26.0,1277.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.50 1282[3:MRR:32.0,1277.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 1283[3:MRR:14.0,1277.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.50 1284[3:MRR:2.0,1277.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.50 1286[3:SpR:1278.0,800.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.21/0.50 1289[3:Rew:636.0,1286.0] || -> equal(sk_c2,sk_c5)**.
% 0.21/0.50 1291[3:Rew:1289.0,1283.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.21/0.50 1292[3:Rew:796.0,1291.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1294[3:Rew:1292.0,105.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.21/0.50 1296[3:Rew:1292.0,633.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1300[3:Rew:1292.0,647.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(sk_c7,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 1302[3:Rew:1296.0,1282.0] || -> equal(sk_c3,sk_c8)**.
% 0.21/0.50 1303[3:Rew:1302.0,1280.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 1304[3:Rew:636.0,1303.0] || -> equal(sk_c5,sk_c8)**.
% 0.21/0.50 1305[3:Rew:1304.0,636.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.50 1310[3:Rew:1304.0,1294.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.21/0.50 1314[3:Obv:1300.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.50 1315[3:Rew:1296.0,1314.3] || equal(sk_c7,sk_c8) equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.51 1323[3:SpR:1279.0,911.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),u)**.
% 0.21/0.51 1333[3:SpR:1284.0,40.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.21/0.51 1337[3:Rew:1323.0,1333.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 1339[3:Rew:1337.0,1310.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.51 1345[3:Rew:1339.0,1315.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.51 1348[3:Obv:1345.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)**+ -> .
% 0.21/0.51 1529[3:SpL:1284.0,1348.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.51 1531[3:Obv:1529.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) -> .
% 0.21/0.51 1532[3:Rew:1279.0,1531.1] || equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(u,sk_c8) -> .
% 0.21/0.51 1533[3:Obv:1532.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.51 1619[3:SpL:1305.0,1533.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.51 1623[3:Obv:1619.1] || -> .
% 0.21/0.51 1624[2:Spt:1623.0,28.0,96.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.51 1625[2:Spt:1623.0,28.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.51 1626[2:MRR:22.0,1624.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 1627[2:MRR:10.0,1624.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 1629[2:MRR:16.0,1624.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.21/0.51 1630[2:MRR:4.0,1624.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.21/0.51 1649[2:SpR:1627.0,911.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),u)**.
% 0.21/0.51 1660[2:SpR:1629.0,133.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c8)**.
% 0.21/0.51 1662[2:Rew:1626.0,1660.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.51 1664[2:SpR:1630.0,40.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.21/0.51 1668[2:Rew:1649.0,1664.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 1669[2:Rew:1668.0,1662.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.51 1675[2:Rew:1669.0,94.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** -> .
% 0.21/0.51 1682[2:Rew:1669.0,1675.4,1669.0,1675.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** -> .
% 0.21/0.51 1683[2:Con:1682.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.51 1705[2:SpR:1668.0,633.0] || -> equal(identity,sk_c8)**.
% 0.21/0.51 1709[2:Rew:1705.0,633.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.51 1711[2:Rew:1705.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.51 1713[2:Rew:1709.0,1683.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c9) equal(u,sk_c8) equal(multiply(v,sk_c9),sk_c8)**+ -> .
% 0.21/0.51 1723[2:SpR:1626.0,1711.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.21/0.51 1727[2:Rew:1668.0,1723.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.51 1728[2:Rew:1727.0,1626.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.51 1750[2:SpL:1630.0,1713.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.21/0.51 1753[2:Obv:1750.3] || equal(inverse(u),sk_c8)** equal(inverse(sk_c1),sk_c9)** equal(u,sk_c8) -> .
% 0.21/0.51 1754[2:Rew:1627.0,1753.1] || equal(inverse(u),sk_c8)** equal(sk_c9,sk_c9) equal(u,sk_c8) -> .
% 0.21/0.51 1755[2:Obv:1754.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.51 1805[2:SpL:1728.0,1755.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.51 1806[2:Obv:1805.1] || -> .
% 0.21/0.51 % SZS output end Refutation
% 0.21/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_32 prove_this_35 prove_this_37 left_identity left_inverse associativity
% 0.21/0.51
%------------------------------------------------------------------------------