TSTP Solution File: GRP388-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP388-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:47:09 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
% 0.11/0.12 % Problem : GRP388-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.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 : Tue Jun 14 04:28:59 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 1447 clauses, backtracked 343 clauses, performed 9 splits and kept 850 clauses.
% 0.19/0.50 SPASS allocated 63930 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.50 0:00:00.04 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 5, length 265 :
% 0.19/0.50 % SZS output start Refutation
% 0.19/0.50 1[0:Inp] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.19/0.50 2[0:Inp] || -> equal(multiply(sk_c10,sk_c4),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c10).
% 0.19/0.50 3[0:Inp] || -> equal(multiply(sk_c3,sk_c10),sk_c4)** equal(multiply(sk_c8,sk_c9),sk_c10).
% 0.19/0.50 4[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.19/0.50 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c10).
% 0.19/0.50 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.19/0.50 8[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.19/0.50 9[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10)** equal(multiply(sk_c8,sk_c9),sk_c10).
% 0.19/0.50 13[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 14[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 16[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 17[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 21[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 22[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 24[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 25[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 29[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 30[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.50 32[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.50 33[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.50 34[0:Inp] || equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c10,u),sk_c9)** equal(multiply(v,sk_c10),u)* equal(inverse(v),sk_c10) equal(multiply(sk_c10,w),sk_c9)** equal(multiply(x,sk_c10),w)* equal(inverse(x),sk_c10) equal(multiply(y,z),sk_c8)** equal(inverse(y),z) equal(multiply(z,sk_c9),sk_c8)** equal(inverse(x1),sk_c10) equal(multiply(x1,sk_c8),sk_c10)** -> .
% 0.19/0.50 35[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.50 36[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.50 37[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.50 38[0:Con:34.5] || equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c10,u),sk_c9)** equal(multiply(v,sk_c10),u)* equal(inverse(v),sk_c10) equal(multiply(w,x),sk_c8)** equal(inverse(w),x) equal(multiply(x,sk_c9),sk_c8)** equal(inverse(y),sk_c10) equal(multiply(y,sk_c8),sk_c10)** -> .
% 0.19/0.50 39[0:Rew:1.0,38.0] || equal(sk_c9,sk_c9) equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c10,u),sk_c9)** equal(multiply(v,sk_c10),u)* equal(inverse(v),sk_c10) equal(multiply(w,x),sk_c8)** equal(inverse(w),x) equal(multiply(x,sk_c9),sk_c8)** equal(inverse(y),sk_c10) equal(multiply(y,sk_c8),sk_c10)** -> .
% 0.19/0.50 40[0:Obv:39.0] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,v),sk_c8)**+ equal(multiply(x,sk_c10),y)* equal(multiply(w,sk_c8),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,y),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c10) -> .
% 0.19/0.50 41[1:Spt:40.2,40.4,40.7] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),v)*+ equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.19/0.50 43[2:Spt:6.1] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.19/0.50 45[3:Spt:30.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.50 47[4:Spt:22.1] || -> equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 49[4:SpL:47.0,41.1] || equal(inverse(sk_c1),sk_c10) equal(sk_c2,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.19/0.50 50[4:Rew:45.0,49.0] || equal(sk_c10,sk_c10) equal(sk_c2,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.19/0.50 51[4:Obv:50.0] || equal(sk_c2,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.19/0.50 53[5:Spt:14.1] || -> equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 58[3:SpR:45.0,36.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.19/0.50 59[0:SpR:1.0,36.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.19/0.50 60[1:SpL:36.0,41.1] || equal(inverse(inverse(sk_c10)),sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.19/0.50 61[1:Rew:1.0,60.0] || equal(inverse(sk_c9),sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.19/0.50 67[3:SpR:58.0,37.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.50 68[2:SpR:43.0,37.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.19/0.50 70[0:SpR:36.0,37.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.50 72[3:Rew:35.0,67.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.19/0.50 73[0:Rew:35.0,70.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.50 76[0:SpR:59.0,37.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(identity,u))**.
% 0.19/0.50 78[0:Rew:35.0,76.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.19/0.50 81[4:SpR:47.0,72.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.19/0.50 82[5:Rew:53.0,81.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 88[5:Rew:82.0,53.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.19/0.50 90[5:Rew:82.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.50 95[5:Rew:82.0,51.1] || equal(sk_c2,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 97[5:Rew:82.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.19/0.50 98[5:Rew:82.0,78.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.19/0.50 133[5:SpR:88.0,98.0] || -> equal(multiply(sk_c9,sk_c9),sk_c2)**.
% 0.19/0.50 137[5:Rew:90.0,133.0] || -> equal(identity,sk_c2)**.
% 0.19/0.50 139[5:Rew:137.0,36.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.50 169[0:SpR:73.0,73.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.50 177[5:SpR:139.0,73.0] || -> equal(multiply(inverse(inverse(u)),sk_c2),u)**.
% 0.19/0.50 181[5:Rew:169.0,177.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.50 214[5:SpR:98.0,97.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 218[5:SpR:214.0,181.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.50 225[5:Rew:218.0,181.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 227[5:Rew:218.0,95.0] || equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 268[0:SpR:169.0,73.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.50 320[5:SpL:225.0,227.1] || equal(sk_c8,sk_c8)* equal(sk_c9,sk_c9) -> .
% 0.19/0.50 324[5:Obv:320.1] || -> .
% 0.19/0.50 327[5:Spt:324.0,14.1,53.0] || equal(multiply(sk_c10,sk_c2),sk_c9)** -> .
% 0.19/0.50 328[5:Spt:324.0,14.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.50 329[5:Rew:81.0,327.0] || equal(sk_c10,sk_c9)** -> .
% 0.19/0.50 338[4:Rew:81.0,13.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(sk_c10,sk_c9).
% 0.19/0.50 339[5:MRR:338.1,329.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 348[5:SpR:328.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.50 392[5:SpR:339.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.50 396[5:Rew:348.0,392.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 397[5:Rew:396.0,43.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 401[5:MRR:397.0,329.0] || -> .
% 0.19/0.50 447[4:Spt:401.0,22.1,47.0] || equal(multiply(sk_c1,sk_c10),sk_c2)** -> .
% 0.19/0.50 448[4:Spt:401.0,22.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.50 449[4:MRR:24.1,447.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.50 451[4:MRR:25.1,447.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.50 453[4:MRR:21.1,447.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 457[4:SpR:448.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.50 466[4:SpR:451.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.19/0.50 468[4:Rew:449.0,466.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.50 484[4:SpR:453.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.50 488[4:Rew:457.0,484.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 489[4:Rew:488.0,43.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 493[4:Rew:489.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 499[4:Rew:489.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.50 507[4:Rew:489.0,61.2] || equal(inverse(sk_c9),sk_c10) equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 517[4:Rew:489.0,468.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.50 519[4:Rew:499.0,517.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 521[4:Rew:519.0,36.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.50 540[4:Rew:519.0,507.1,493.0,507.0,489.0,507.0] || equal(sk_c9,sk_c9) equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 541[4:Obv:540.0] || equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 593[4:SpR:521.0,268.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 697[4:SpL:593.0,541.1] || equal(sk_c8,sk_c8)* equal(sk_c9,sk_c9) -> .
% 0.19/0.50 700[4:Obv:697.1] || -> .
% 0.19/0.50 703[3:Spt:700.0,30.1,45.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.19/0.50 704[3:Spt:700.0,30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.50 705[3:MRR:32.1,703.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.50 707[3:MRR:33.0,703.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.50 709[3:MRR:29.0,703.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 713[3:SpR:704.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.50 732[3:SpR:707.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.19/0.50 734[3:Rew:705.0,732.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.50 738[3:SpR:709.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.50 742[3:Rew:713.0,738.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 743[3:Rew:742.0,43.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 747[3:Rew:743.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 751[3:Rew:743.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.50 757[3:Rew:743.0,61.2] || equal(inverse(sk_c9),sk_c10) equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 768[3:Rew:743.0,734.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.50 769[3:Rew:751.0,768.0] || -> equal(identity,sk_c8)**.
% 0.19/0.50 771[3:Rew:769.0,36.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.50 781[3:Rew:769.0,757.1,747.0,757.0,743.0,757.0] || equal(sk_c9,sk_c9) equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 782[3:Obv:781.0] || equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 844[3:SpR:771.0,268.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 953[3:SpL:844.0,782.1] || equal(sk_c8,sk_c8)* equal(sk_c9,sk_c9) -> .
% 0.19/0.50 957[3:Obv:953.1] || -> .
% 0.19/0.50 960[2:Spt:957.0,6.1,43.0] || equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.19/0.50 961[2:Spt:957.0,6.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.50 963[2:MRR:4.1,960.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.50 964[2:MRR:9.1,960.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.50 966[2:MRR:5.1,960.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 967[2:MRR:3.1,960.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.50 968[2:MRR:2.1,960.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.50 970[2:SpR:961.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.50 985[2:SpR:964.0,37.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.19/0.50 992[2:SpR:966.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.50 996[2:Rew:970.0,992.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 997[2:Rew:996.0,960.0] || equal(sk_c10,sk_c9)** -> .
% 0.19/0.50 998[2:Rew:996.0,985.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.19/0.50 1005[2:Rew:998.0,968.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.19/0.50 1014[2:SpR:967.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.50 1016[2:Rew:963.0,1014.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.50 1017[2:Rew:1005.0,1016.0,998.0,1016.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 1018[2:MRR:1017.0,997.0] || -> .
% 0.19/0.50 1020[1:Spt:1018.0,40.0,40.1,40.3,40.5,40.6,40.8] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.19/0.50 1024[1:SpL:59.0,1020.2] || equal(inverse(sk_c9),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c10) -> .
% 0.19/0.50 1027[2:Spt:8.1] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.19/0.50 1032[2:Rew:1027.0,1024.5] || equal(inverse(sk_c9),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** equal(sk_c10,sk_c10) -> .
% 0.19/0.50 1033[2:Obv:1032.5] || equal(inverse(sk_c9),sk_c10) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** -> .
% 0.19/0.50 1038[2:SpR:1027.0,37.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.19/0.50 1041[3:Spt:30.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.19/0.50 1045[4:Spt:14.1] || -> equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.19/0.50 1047[4:SpR:1045.0,73.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c2)**.
% 0.19/0.50 1049[4:Rew:1.0,1047.0] || -> equal(multiply(sk_c9,sk_c9),sk_c2)**.
% 0.19/0.50 1050[5:Spt:22.1] || -> equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.19/0.50 1052[5:SpR:1050.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c10)**.
% 0.19/0.50 1054[5:Rew:1045.0,1052.0,1041.0,1052.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 1055[5:Rew:1054.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.50 1056[5:Rew:1054.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.50 1064[5:Rew:1054.0,1038.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.19/0.50 1066[5:Rew:1054.0,1033.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** -> .
% 0.19/0.50 1074[5:Rew:1049.0,1056.0] || -> equal(identity,sk_c2)**.
% 0.19/0.50 1076[5:Rew:1074.0,36.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.50 1080[5:Rew:1049.0,1066.4,1054.0,1066.4,1054.0,1066.3,1074.0,1066.2,1054.0,1066.1,1055.0,1066.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) equal(sk_c2,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c2,sk_c8) -> .
% 0.19/0.50 1081[5:Obv:1080.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c2,sk_c8) -> .
% 0.19/0.50 1122[5:SpR:1076.0,268.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.50 1177[5:SpR:268.0,1064.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1185[5:SpR:1177.0,1122.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.50 1192[5:Rew:1185.0,1122.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.50 1194[5:Rew:1185.0,1081.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.50 1207[5:Obv:1194.2] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.50 1208[5:Rew:1192.0,1207.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.50 1264[5:SpL:1055.0,1208.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.50 1267[5:Obv:1264.1] || -> .
% 0.19/0.50 1269[5:Spt:1267.0,22.1,1050.0] || equal(multiply(sk_c1,sk_c10),sk_c2)** -> .
% 0.19/0.50 1270[5:Spt:1267.0,22.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.50 1271[5:MRR:24.1,1269.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.50 1273[5:MRR:25.1,1269.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.50 1275[5:MRR:21.1,1269.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.50 1279[5:SpR:1270.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1294[5:SpR:1273.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.19/0.50 1296[5:Rew:1271.0,1294.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.50 1314[5:SpR:1275.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.50 1318[5:Rew:1279.0,1314.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1319[5:Rew:1318.0,1027.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.50 1323[5:Rew:1319.0,1041.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.51 1324[5:Rew:1319.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.51 1329[5:Rew:1319.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.51 1332[5:Rew:1319.0,1269.0] || equal(multiply(sk_c1,sk_c9),sk_c2)** -> .
% 0.19/0.51 1349[5:Rew:1319.0,1296.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1351[5:Rew:1049.0,1329.0] || -> equal(identity,sk_c2)**.
% 0.19/0.51 1353[5:Rew:1351.0,36.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.51 1354[5:Rew:1049.0,1349.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.51 1355[5:Rew:1354.0,1049.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1362[5:Rew:1354.0,1332.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.19/0.51 1363[5:Rew:1354.0,1353.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.51 1440[5:SpR:1363.0,268.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1444[5:SpR:1323.0,1363.0] || -> equal(multiply(sk_c9,sk_c1),sk_c8)**.
% 0.19/0.51 1497[5:SpR:1444.0,73.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c1)**.
% 0.19/0.51 1499[5:Rew:1324.0,1497.0] || -> equal(multiply(sk_c9,sk_c8),sk_c1)**.
% 0.19/0.51 1500[5:Rew:1440.0,1499.0] || -> equal(sk_c1,sk_c9)**.
% 0.19/0.51 1502[5:Rew:1500.0,1362.0] || equal(multiply(sk_c9,sk_c9),sk_c8)** -> .
% 0.19/0.51 1506[5:Rew:1355.0,1502.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.51 1507[5:Obv:1506.0] || -> .
% 0.19/0.51 1510[4:Spt:1507.0,14.1,1045.0] || equal(multiply(sk_c10,sk_c2),sk_c9)** -> .
% 0.19/0.51 1511[4:Spt:1507.0,14.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 1512[4:MRR:16.1,1510.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.51 1514[4:MRR:17.1,1510.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.51 1516[4:MRR:13.1,1510.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.51 1520[4:SpR:1511.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.51 1542[4:SpR:1514.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.19/0.51 1544[4:Rew:1512.0,1542.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.51 1548[4:SpR:1516.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.51 1552[4:Rew:1520.0,1548.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1553[4:Rew:1552.0,1027.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.51 1557[4:Rew:1553.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.51 1561[4:Rew:1553.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.51 1574[4:Rew:1553.0,1033.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** -> .
% 0.19/0.51 1581[4:Rew:1553.0,1544.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1582[4:Rew:1561.0,1581.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1584[4:Rew:1582.0,36.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.51 1585[4:Rew:1582.0,1561.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1592[4:Rew:1585.0,1574.4,1553.0,1574.4,1553.0,1574.3,1582.0,1574.2,1553.0,1574.1,1557.0,1574.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.51 1593[4:Obv:1592.4] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.51 1660[4:SpR:1584.0,268.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1667[4:Rew:1660.0,1593.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.51 1744[4:SpL:1557.0,1667.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.51 1746[4:Obv:1744.1] || -> .
% 0.19/0.51 1748[3:Spt:1746.0,30.1,1041.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.19/0.51 1749[3:Spt:1746.0,30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 1750[3:MRR:32.1,1748.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.51 1752[3:MRR:33.0,1748.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.51 1754[3:MRR:29.0,1748.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.51 1758[3:SpR:1749.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.51 1777[3:SpR:1752.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.19/0.51 1779[3:Rew:1750.0,1777.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.51 1783[3:SpR:1754.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.51 1787[3:Rew:1758.0,1783.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1788[3:Rew:1787.0,1027.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.51 1792[3:Rew:1788.0,1.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.51 1796[3:Rew:1788.0,59.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.19/0.51 1806[3:Rew:1788.0,1033.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(identity,sk_c8) equal(multiply(u,sk_c8),sk_c10)** equal(multiply(sk_c10,sk_c9),sk_c8)** -> .
% 0.19/0.51 1813[3:Rew:1788.0,1779.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1814[3:Rew:1796.0,1813.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1816[3:Rew:1814.0,36.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.51 1817[3:Rew:1814.0,1796.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1824[3:Rew:1817.0,1806.4,1788.0,1806.4,1788.0,1806.3,1814.0,1806.2,1788.0,1806.1,1792.0,1806.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.51 1825[3:Obv:1824.4] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.19/0.51 1889[3:SpR:1816.0,268.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1895[3:Rew:1889.0,1825.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.51 1991[3:SpL:1792.0,1895.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.51 1994[3:Obv:1991.1] || -> .
% 0.19/0.51 1996[2:Spt:1994.0,8.1,1027.0] || equal(multiply(sk_c8,sk_c9),sk_c10)** -> .
% 0.19/0.51 1997[2:Spt:1994.0,8.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.51 1998[2:MRR:4.1,1996.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.19/0.51 1999[2:MRR:6.1,1996.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 2000[2:MRR:9.1,1996.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.19/0.51 2002[2:MRR:5.1,1996.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.19/0.51 2003[2:MRR:3.1,1996.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.19/0.51 2004[2:MRR:2.1,1996.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.19/0.51 2015[2:SpR:1999.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.51 2021[2:SpR:2000.0,37.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.19/0.51 2028[2:SpR:2002.0,37.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.51 2032[2:Rew:2015.0,2028.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 2033[2:Rew:2032.0,1996.0] || equal(sk_c10,sk_c9)** -> .
% 0.19/0.51 2034[2:Rew:2032.0,2021.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.19/0.51 2037[2:Rew:2034.0,2004.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.19/0.51 2045[2:SpR:2003.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.19/0.51 2047[2:Rew:1998.0,2045.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.19/0.51 2048[2:Rew:2037.0,2047.0,2034.0,2047.0] || -> equal(sk_c10,sk_c9)**.
% 0.19/0.51 2049[2:MRR:2048.0,2033.0] || -> .
% 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_8 prove_this_9 prove_this_13 prove_this_14 prove_this_16 prove_this_17 prove_this_21 prove_this_22 prove_this_24 prove_this_25 prove_this_29 prove_this_30 prove_this_32 prove_this_33 prove_this_34 left_identity left_inverse associativity
% 0.19/0.51
%------------------------------------------------------------------------------