TSTP Solution File: GRP302-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP302-1 : 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 11:46:45 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP302-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 11:34:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 1539 clauses, backtracked 253 clauses, performed 10 splits and kept 541 clauses.
% 0.19/0.50 SPASS allocated 64372 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.50 0:00:00.03 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.08 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 6, length 224 :
% 0.19/0.50 % SZS output start Refutation
% 0.19/0.50 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.50 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.50 3[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.50 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 5[0:Inp] || -> equal(inverse(sk_c5),sk_c4)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.50 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.50 7[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c4)**.
% 0.19/0.50 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.50 9[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.50 10[0:Inp] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.50 14[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.50 20[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c2),sk_c8).
% 0.19/0.50 21[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.50 22[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 23[0:Inp] || -> equal(inverse(sk_c5),sk_c4) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.50 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.50 25[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c4)**.
% 0.19/0.50 26[0:Inp] || equal(multiply(sk_c8,sk_c7),sk_c6)** equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(inverse(x),y) equal(inverse(y),sk_c8)** equal(multiply(x,sk_c8),y)* -> .
% 0.19/0.50 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.50 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.50 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.50 30[0:Con:26.6] || equal(multiply(sk_c8,sk_c7),sk_c6)** equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(inverse(w),x) equal(inverse(x),sk_c8)** equal(multiply(w,sk_c8),x)* -> .
% 0.19/0.50 31[0:Rew:1.0,30.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(inverse(w),x) equal(inverse(x),sk_c8)** equal(multiply(w,sk_c8),x)* -> .
% 0.19/0.50 32[0:Obv:31.0] || equal(inverse(u),v) equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),v)*+ equal(multiply(w,sk_c8),sk_c6)** equal(multiply(x,sk_c7),sk_c8)** -> .
% 0.19/0.50 33[1:Spt:32.0,32.1,32.5] || equal(inverse(u),v) equal(inverse(v),sk_c8)** equal(multiply(u,sk_c8),v)*+ -> .
% 0.19/0.50 35[2:Spt:20.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.50 37[3:Spt:2.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.50 39[4:Spt:14.1] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.50 44[5:Spt:8.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.50 49[2:SpR:35.0,28.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.50 50[3:SpR:37.0,28.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.19/0.50 59[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.50 60[2:SpR:49.0,29.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.50 62[2:Rew:27.0,60.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.50 63[0:Rew:27.0,59.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.50 66[3:SpR:50.0,29.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.50 67[3:Rew:27.0,66.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.19/0.50 70[4:SpR:39.0,62.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.50 76[5:SpR:44.0,67.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.50 79[0:SpR:63.0,63.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.50 82[0:SpR:1.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.50 85[0:SpR:28.0,63.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.50 86[2:SpR:49.0,63.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.19/0.50 87[3:SpR:50.0,63.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.19/0.50 88[2:SpR:62.0,63.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c2,u))**.
% 0.19/0.50 90[4:SpR:70.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.50 96[3:Rew:86.0,87.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.50 102[3:Rew:96.0,86.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.19/0.50 103[4:Rew:28.0,90.0] || -> equal(identity,sk_c6)**.
% 0.19/0.50 105[4:Rew:103.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.50 112[4:Rew:82.0,102.0,103.0,102.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 113[4:Rew:112.0,37.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.50 120[4:Rew:103.0,85.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.50 127[4:Rew:79.0,120.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.50 142[5:SpL:76.0,33.2] || equal(inverse(sk_c8),u)* equal(inverse(u),sk_c8)** equal(sk_c7,u) -> .
% 0.19/0.50 163[4:SpR:105.0,63.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.50 170[4:Rew:127.0,163.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.50 183[4:SpR:113.0,170.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 186[5:Rew:183.0,142.0] || equal(sk_c7,u) equal(inverse(u),sk_c8)** equal(sk_c7,u) -> .
% 0.19/0.50 187[5:Obv:186.0] || equal(inverse(u),sk_c8)** equal(sk_c7,u) -> .
% 0.19/0.50 392[5:SpL:113.0,187.0] || equal(sk_c8,sk_c8)* equal(sk_c7,sk_c7) -> .
% 0.19/0.50 396[5:Obv:392.1] || -> .
% 0.19/0.50 398[5:Spt:396.0,8.1,44.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.19/0.50 399[5:Spt:396.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 400[5:Rew:112.0,398.0] || equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.50 405[4:Rew:112.0,9.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 406[5:MRR:405.1,400.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 409[4:Rew:112.0,10.1] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c7),sk_c8).
% 0.19/0.50 410[5:MRR:409.1,400.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 428[5:SpR:406.0,170.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.19/0.50 432[5:Rew:183.0,428.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 434[5:Rew:432.0,410.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 437[5:MRR:434.0,400.0] || -> .
% 0.19/0.50 440[4:Spt:437.0,14.1,39.0] || equal(multiply(sk_c2,sk_c8),sk_c6)** -> .
% 0.19/0.50 441[4:Spt:437.0,14.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 442[4:Rew:441.0,102.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.19/0.50 444[4:Rew:96.0,440.0] || equal(multiply(sk_c1,sk_c8),sk_c6)** -> .
% 0.19/0.50 446[4:Rew:441.0,88.0,96.0,88.0] || -> equal(multiply(sk_c1,u),multiply(sk_c7,u))**.
% 0.19/0.50 448[4:Rew:446.0,444.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.50 460[0:Rew:79.0,85.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.50 461[4:Rew:460.0,442.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 464[4:Rew:461.0,50.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.50 466[4:Rew:1.0,464.0] || -> equal(identity,sk_c6)**.
% 0.19/0.50 468[4:Rew:466.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.50 560[4:SpR:441.0,468.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.50 567[4:MRR:560.0,448.0] || -> .
% 0.19/0.50 572[3:Spt:567.0,2.1,37.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.50 573[3:Spt:567.0,2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 575[3:Rew:460.0,86.0,573.0,86.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.50 576[3:Rew:575.0,35.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.50 577[3:Rew:575.0,49.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.50 578[3:Rew:1.0,577.0] || -> equal(identity,sk_c6)**.
% 0.19/0.50 579[3:Rew:578.0,460.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.50 582[3:Rew:578.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.50 586[3:MRR:6.1,572.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 587[3:MRR:5.1,572.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.50 588[3:MRR:3.1,572.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 591[3:MRR:7.0,572.0] || -> equal(multiply(sk_c5,sk_c8),sk_c4)**.
% 0.19/0.50 592[3:MRR:4.0,572.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 611[3:SpR:591.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c8)**.
% 0.19/0.50 612[3:SpL:591.0,33.2] || equal(inverse(sk_c5),u)* equal(inverse(u),sk_c8)** equal(sk_c4,u) -> .
% 0.19/0.50 613[3:Rew:587.0,611.0] || -> equal(multiply(sk_c4,sk_c4),sk_c8)**.
% 0.19/0.50 614[3:Rew:587.0,612.0] || equal(sk_c4,u) equal(inverse(u),sk_c8)** equal(sk_c4,u) -> .
% 0.19/0.50 615[3:Obv:614.0] || equal(inverse(u),sk_c8)** equal(sk_c4,u) -> .
% 0.19/0.50 618[3:SpR:592.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.50 619[3:Rew:588.0,618.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.50 621[3:SpR:613.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c4)**.
% 0.19/0.50 623[3:Rew:586.0,621.0] || -> equal(multiply(sk_c8,sk_c8),sk_c4)**.
% 0.19/0.50 624[3:Rew:619.0,623.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.50 626[3:Rew:624.0,587.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.50 632[3:Rew:624.0,615.1] || equal(inverse(u),sk_c8)** equal(sk_c7,u) -> .
% 0.19/0.50 683[3:SpR:626.0,582.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.50 710[3:SpR:683.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.50 712[3:Rew:579.0,710.0,576.0,710.0] || -> equal(sk_c8,sk_c5)**.
% 0.19/0.50 716[3:Rew:712.0,576.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.50 726[3:Rew:712.0,632.0] || equal(inverse(u),sk_c5)** equal(sk_c7,u) -> .
% 0.19/0.50 866[3:SpL:716.0,726.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.19/0.50 869[3:Obv:866.1] || -> .
% 0.19/0.50 870[2:Spt:869.0,20.1,35.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.50 871[2:Spt:869.0,20.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 872[2:Rew:871.0,82.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.50 873[2:MRR:24.1,870.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 874[2:MRR:23.1,870.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.50 875[2:MRR:21.1,870.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 877[2:MRR:25.0,870.0] || -> equal(multiply(sk_c5,sk_c8),sk_c4)**.
% 0.19/0.50 878[2:MRR:22.0,870.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 894[2:SpR:872.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.50 896[2:Rew:28.0,894.0] || -> equal(identity,sk_c6)**.
% 0.19/0.50 898[2:Rew:896.0,460.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.50 899[2:Rew:896.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.50 908[2:SpR:877.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c8)**.
% 0.19/0.50 910[2:Rew:874.0,908.0] || -> equal(multiply(sk_c4,sk_c4),sk_c8)**.
% 0.19/0.50 912[2:SpR:878.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.50 914[2:Rew:875.0,912.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.50 916[2:SpR:910.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c4)**.
% 0.19/0.50 918[2:Rew:873.0,916.0] || -> equal(multiply(sk_c8,sk_c8),sk_c4)**.
% 0.19/0.50 919[2:Rew:914.0,918.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.50 920[2:Rew:919.0,873.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.50 921[2:Rew:919.0,874.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.50 955[2:SpR:921.0,899.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.50 977[2:SpR:955.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.50 979[2:Rew:920.0,977.0] || -> equal(multiply(sk_c8,sk_c6),sk_c5)**.
% 0.19/0.50 980[2:Rew:898.0,979.0] || -> equal(sk_c8,sk_c5)**.
% 0.19/0.50 984[2:Rew:980.0,920.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.50 985[2:Rew:980.0,914.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.50 991[2:Rew:980.0,33.2] || equal(inverse(u),v) equal(inverse(v),sk_c8)** equal(multiply(u,sk_c5),v)* -> .
% 0.19/0.50 1004[2:Rew:980.0,991.1] || equal(inverse(u),v) equal(inverse(v),sk_c5)** equal(multiply(u,sk_c5),v)*+ -> .
% 0.19/0.50 1135[2:SpL:985.0,1004.2] || equal(inverse(sk_c5),u)* equal(inverse(u),sk_c5)** equal(sk_c7,u) -> .
% 0.19/0.50 1138[2:Rew:921.0,1135.0] || equal(sk_c7,u) equal(inverse(u),sk_c5)** equal(sk_c7,u) -> .
% 0.19/0.50 1139[2:Obv:1138.0] || equal(inverse(u),sk_c5)** equal(sk_c7,u) -> .
% 0.19/0.50 1189[2:SpL:984.0,1139.0] || equal(sk_c5,sk_c5)* equal(sk_c7,sk_c7) -> .
% 0.19/0.50 1193[2:Obv:1189.1] || -> .
% 0.19/0.50 1194[1:Spt:1193.0,32.2,32.3,32.4,32.6,32.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.50 1198[2:Spt:2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 1199[2:Rew:1198.0,1194.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.50 1200[2:Rew:1198.0,82.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.50 1202[2:Obv:1199.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.50 1213[3:Spt:6.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.50 1227[2:SpR:1200.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.50 1229[2:Rew:28.0,1227.0] || -> equal(identity,sk_c6)**.
% 0.19/0.50 1231[2:Rew:1229.0,460.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.50 1233[2:Rew:1229.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.50 1250[2:SpR:1233.0,63.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.50 1254[2:SpR:1198.0,1233.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.50 1256[3:SpR:1213.0,1233.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.19/0.50 1258[2:Rew:1231.0,1250.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.50 1268[2:SpR:1254.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.19/0.50 1270[2:Rew:1231.0,1268.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.50 1298[3:SpR:1256.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c1)**.
% 0.19/0.50 1300[3:Rew:1231.0,1298.0,1198.0,1298.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 1303[3:Rew:1300.0,10.1] || -> equal(multiply(sk_c3,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c7),sk_c8).
% 0.19/0.50 1305[3:Rew:1300.0,9.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 1324[4:Spt:1305.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 1327[4:SpR:1324.0,1233.0] || -> equal(multiply(sk_c8,sk_c3),sk_c6)**.
% 0.19/0.50 1331[4:SpR:1327.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c3)**.
% 0.19/0.50 1333[4:Rew:1231.0,1331.0,1198.0,1331.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 1336[4:Rew:1333.0,1303.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 1341[4:Obv:1336.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 1592[2:SpL:1254.0,1202.2] || equal(inverse(sk_c7),sk_c8) equal(inverse(u),sk_c8) equal(sk_c6,sk_c6) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 1593[2:Obv:1592.2] || equal(inverse(sk_c7),sk_c8) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 1594[2:Rew:1270.0,1593.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 1595[2:Obv:1594.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 1954[4:SpL:1341.0,1595.1] || equal(inverse(sk_c7),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.50 1957[4:Obv:1954.1] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.19/0.50 1958[4:Rew:1270.0,1957.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.50 1959[4:Obv:1958.0] || -> .
% 0.19/0.50 1963[4:Spt:1959.0,1305.0,1324.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.19/0.50 1964[4:Spt:1959.0,1305.1] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 1982[4:SpL:1964.0,1595.1] || equal(inverse(sk_c7),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.50 1986[4:Obv:1982.1] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.19/0.50 1987[4:Rew:1270.0,1986.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.50 1988[4:Obv:1987.0] || -> .
% 0.19/0.50 1989[3:Spt:1988.0,6.1,1213.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.50 1990[3:Spt:1988.0,6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 1991[3:MRR:5.1,1989.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.50 1992[3:MRR:3.1,1989.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.50 1994[3:MRR:4.0,1989.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.50 1998[3:SpR:1990.0,1258.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.50 2007[3:Rew:1198.0,1998.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.50 2009[3:Rew:2007.0,1991.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.50 2031[3:SpR:1992.0,1258.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.19/0.50 2040[3:Rew:1198.0,2031.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 2042[3:Rew:2040.0,1994.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 2067[3:SpR:2009.0,1258.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.50 2076[3:Rew:1270.0,2067.0] || -> equal(sk_c8,sk_c5)**.
% 0.19/0.50 2080[3:Rew:2076.0,1270.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.50 2087[3:Rew:2076.0,1595.0] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.50 2098[3:Rew:2076.0,2042.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.50 2105[3:Rew:2076.0,2087.1] || equal(inverse(u),sk_c5) equal(multiply(u,sk_c7),sk_c5)** -> .
% 0.19/0.50 2439[3:SpL:2098.0,2105.1] || equal(inverse(sk_c7),sk_c5)** equal(sk_c5,sk_c5) -> .
% 0.19/0.50 2442[3:Obv:2439.1] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.19/0.50 2443[3:Rew:2080.0,2442.0] || equal(sk_c5,sk_c5)* -> .
% 0.19/0.50 2444[3:Obv:2443.0] || -> .
% 0.19/0.51 2449[2:Spt:2444.0,2.0,1198.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.51 2450[2:Spt:2444.0,2.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.51 2451[2:MRR:20.0,2449.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 2453[2:MRR:14.0,2449.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.19/0.51 2476[2:SpR:2453.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.19/0.51 2478[2:Rew:2451.0,2476.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.51 2489[2:SpR:2478.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.51 2491[2:Rew:28.0,2489.0] || -> equal(identity,sk_c6)**.
% 0.19/0.51 2493[2:Rew:2491.0,460.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.51 2496[2:Rew:2493.0,82.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.51 2497[2:MRR:2496.0,2449.0] || -> .
% 0.19/0.51 % SZS output end Refutation
% 0.19/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_14 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.19/0.51
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