TSTP Solution File: GRP313-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP313-1 : 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 11:46:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP313-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % 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 : Mon Jun 13 11:38:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 678 clauses, backtracked 411 clauses, performed 15 splits and kept 578 clauses.
% 0.19/0.47 SPASS allocated 63595 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.05 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 264 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 3[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.47 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 8[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 15[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.47 16[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 21[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 27[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.19/0.47 28[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.19/0.47 34[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.47 35[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 36[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 37[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 39[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 40[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 42[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 43[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.47 44[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 47[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.47 49[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 50[0:Inp] || equal(multiply(sk_c8,sk_c9),sk_c7) 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(multiply(w,sk_c8),sk_c9)** equal(inverse(w),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(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(z,sk_c7),sk_c9)** equal(inverse(z),sk_c7) -> .
% 0.19/0.47 51[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 52[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 53[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 54[0:Con:50.7] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c7),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.47 55[1:Spt:54.3,54.7] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.19/0.47 64[2:Spt:2.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.47 70[3:Spt:1.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.47 72[3:SpL:70.0,55.1] || equal(inverse(sk_c4),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.47 73[3:Obv:72.1] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.47 74[3:Rew:64.0,73.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.47 75[3:Obv:74.0] || -> .
% 0.19/0.47 76[3:Spt:75.0,1.0,70.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.19/0.47 77[3:Spt:75.0,1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 80[3:MRR:15.1,76.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 83[3:MRR:8.0,76.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 92[3:SpL:83.0,55.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.47 93[3:Obv:92.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.47 94[3:Rew:80.0,93.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.47 95[3:Obv:94.0] || -> .
% 0.19/0.47 96[2:Spt:95.0,2.0,64.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.47 97[2:Spt:95.0,2.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 100[2:MRR:16.0,96.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 103[2:MRR:9.0,96.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 112[2:SpL:103.0,55.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.47 113[2:Obv:112.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.47 114[2:Rew:100.0,113.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.47 115[2:Obv:114.0] || -> .
% 0.19/0.47 116[1:Spt:115.0,54.0,54.1,54.2,54.4,54.5,54.6,54.8,54.9] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.47 117[2:Spt:5.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.47 118[2:Rew:117.0,116.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c8,sk_c8) equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.47 119[2:Obv:118.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.47 121[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.47 123[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.47 125[5:Spt:7.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.47 127[6:Spt:1.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.47 129[7:Spt:3.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.47 132[8:Spt:6.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.19/0.47 135[3:SpR:121.0,52.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.19/0.47 136[4:SpR:123.0,52.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.47 137[5:SpR:125.0,52.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.19/0.47 147[0:SpR:52.0,53.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 149[3:SpR:135.0,53.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 150[4:SpR:136.0,53.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.47 152[3:Rew:51.0,149.0] || -> equal(multiply(sk_c9,multiply(sk_c4,u)),u)**.
% 0.19/0.47 153[4:Rew:51.0,150.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.47 155[0:Rew:51.0,147.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 159[6:SpR:127.0,152.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.47 165[7:SpR:129.0,153.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.47 170[0:SpR:155.0,155.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 172[2:SpR:117.0,155.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.19/0.47 176[0:SpR:52.0,155.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 177[8:SpR:132.0,155.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.19/0.47 179[3:SpR:152.0,155.0] || -> equal(multiply(inverse(sk_c9),u),multiply(sk_c4,u))**.
% 0.19/0.47 180[6:SpR:159.0,155.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.47 182[4:SpR:153.0,155.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c5,u))**.
% 0.19/0.47 184[5:SpR:137.0,155.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c6)**.
% 0.19/0.47 191[8:Rew:117.0,177.0,125.0,177.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 192[8:Rew:191.0,117.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.47 198[8:Rew:191.0,119.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c8)** -> .
% 0.19/0.47 205[6:Rew:52.0,180.0] || -> equal(identity,sk_c8)**.
% 0.19/0.47 206[6:Rew:205.0,51.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 208[6:Rew:205.0,135.0] || -> equal(multiply(sk_c9,sk_c4),sk_c8)**.
% 0.19/0.47 209[6:Rew:205.0,136.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 214[8:Rew:206.0,192.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.47 217[8:Rew:214.0,121.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 222[8:Rew:206.0,208.0,214.0,208.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.47 223[8:Rew:222.0,217.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 224[6:Rew:206.0,209.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.47 238[6:Rew:205.0,176.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.19/0.47 247[6:Rew:170.0,238.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 252[8:Rew:214.0,198.6,206.0,198.6,247.0,198.5,191.0,198.5,247.0,198.4,214.0,198.4,247.0,198.3,191.0,198.3,214.0,198.3,191.0,198.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.19/0.47 253[8:Obv:252.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.19/0.47 254[8:Con:253.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.47 313[8:SpL:223.0,254.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 315[8:Obv:313.1] || -> .
% 0.19/0.47 316[8:Spt:315.0,6.0,132.0] || equal(multiply(sk_c6,sk_c7),sk_c9)** -> .
% 0.19/0.47 317[8:Spt:315.0,6.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 318[7:Rew:206.0,165.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 320[6:Rew:205.0,137.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 321[7:Rew:318.0,320.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.47 322[7:Rew:206.0,321.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 325[7:Rew:318.0,117.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.47 326[7:Rew:206.0,325.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.47 334[6:Rew:247.0,172.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.47 338[6:Rew:247.0,184.0,205.0,184.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 345[8:Rew:322.0,316.0,318.0,316.0,326.0,316.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.19/0.47 346[8:Rew:206.0,345.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 347[8:Obv:346.0] || -> .
% 0.19/0.47 373[6:Rew:247.0,27.1] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(sk_c2,sk_c7).
% 0.19/0.47 382[7:Spt:347.0,3.0,129.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.19/0.47 383[7:Spt:347.0,3.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 384[6:Rew:334.0,338.0] || -> equal(sk_c6,sk_c9)**.
% 0.19/0.47 389[6:Rew:384.0,320.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.47 394[7:Rew:206.0,383.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.47 395[7:Rew:394.0,334.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.47 398[7:Rew:394.0,389.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.47 406[7:Rew:206.0,382.0,224.0,382.0] || equal(sk_c7,sk_c8)** -> .
% 0.19/0.47 407[7:Rew:394.0,406.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.47 417[7:Rew:394.0,373.1,398.0,373.0,384.0,373.0,394.0,373.0] || -> equal(sk_c9,sk_c8) equal(sk_c2,sk_c9)**.
% 0.19/0.47 418[7:MRR:417.0,407.0] || -> equal(sk_c2,sk_c9)**.
% 0.19/0.47 433[7:Rew:398.0,34.1,384.0,34.1,394.0,34.1,395.0,34.0,418.0,34.0] || -> equal(sk_c9,sk_c8)** equal(sk_c9,sk_c8)**.
% 0.19/0.47 434[7:Obv:433.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.47 435[7:MRR:434.0,407.0] || -> .
% 0.19/0.47 455[6:Spt:435.0,1.0,127.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.19/0.47 456[6:Spt:435.0,1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 459[6:MRR:43.1,455.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 461[6:MRR:15.1,455.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 462[0:Rew:170.0,176.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 463[5:Rew:462.0,184.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 465[6:MRR:36.0,455.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 467[6:MRR:8.0,455.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 471[6:SpR:456.0,155.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.47 473[6:Rew:182.0,471.0] || -> equal(multiply(sk_c5,sk_c7),sk_c9)**.
% 0.19/0.47 486[5:SpR:463.0,155.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.47 504[6:SpR:465.0,155.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c8)**.
% 0.19/0.47 506[6:Rew:456.0,504.0,459.0,504.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 509[6:Rew:506.0,463.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 516[6:Rew:506.0,473.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.47 518[6:Rew:506.0,486.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.19/0.47 519[6:Rew:509.0,182.0] || -> equal(multiply(sk_c6,u),multiply(sk_c5,u))**.
% 0.19/0.47 522[6:Rew:519.0,518.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.47 533[6:SpR:467.0,155.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.19/0.47 535[6:Rew:461.0,533.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.47 550[6:SpR:516.0,53.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.47 554[6:Rew:522.0,550.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.47 556[6:Rew:554.0,535.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.47 561[6:Rew:554.0,152.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.47 574[6:Rew:556.0,455.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.19/0.47 593[6:Rew:561.0,574.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 594[6:Obv:593.0] || -> .
% 0.19/0.47 600[5:Spt:594.0,7.0,125.0] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.19/0.47 601[5:Spt:594.0,7.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.47 602[5:MRR:49.0,600.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 603[5:MRR:35.0,600.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 604[5:MRR:21.0,600.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 605[5:MRR:42.0,600.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.47 606[5:MRR:28.0,600.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.19/0.47 607[5:MRR:14.0,600.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.47 608[5:Rew:601.0,119.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.47 609[5:Obv:608.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.47 611[5:SpR:601.0,155.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.47 613[5:Rew:182.0,611.0] || -> equal(multiply(sk_c5,sk_c7),sk_c9)**.
% 0.19/0.47 638[5:SpR:605.0,155.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c8)**.
% 0.19/0.47 640[5:Rew:601.0,638.0,602.0,638.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.47 646[5:Rew:640.0,606.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.19/0.47 647[5:Rew:640.0,609.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.47 648[5:Rew:640.0,613.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.47 651[5:Rew:640.0,647.5,640.0,647.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.19/0.47 652[5:Con:651.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.47 655[5:SpR:607.0,155.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.19/0.47 657[5:Rew:604.0,655.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.19/0.47 663[5:SpR:646.0,155.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c8)**.
% 0.19/0.47 665[5:Rew:603.0,663.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.47 674[5:SpR:657.0,155.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.47 676[5:Rew:179.0,674.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.47 678[5:SpR:665.0,155.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.47 680[5:Rew:182.0,678.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.19/0.47 681[5:Rew:648.0,680.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.47 682[5:Rew:681.0,121.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 697[5:Rew:681.0,652.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.47 698[5:Rew:681.0,676.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.47 705[5:Con:697.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.47 779[0:SpR:462.0,52.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 795[5:SpL:698.0,705.1] || equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.47 799[5:Obv:795.1] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.47 800[5:Rew:682.0,799.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 801[5:Obv:800.0] || -> .
% 0.19/0.47 804[4:Spt:801.0,4.0,123.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.47 805[4:Spt:801.0,4.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 806[4:MRR:46.0,804.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 808[4:MRR:18.0,804.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.48 809[4:MRR:39.0,804.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.48 811[4:MRR:11.0,804.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.48 812[4:Rew:805.0,119.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.48 813[4:Obv:812.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.48 827[4:SpR:808.0,52.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.48 833[3:SpR:135.0,155.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c4)**.
% 0.19/0.48 835[3:Rew:462.0,833.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.19/0.48 842[4:SpR:809.0,155.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c8)**.
% 0.19/0.48 844[4:Rew:805.0,842.0,806.0,842.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 847[4:Rew:844.0,172.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.19/0.48 850[4:Rew:844.0,813.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.48 853[4:Rew:52.0,847.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 854[4:Rew:853.0,51.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.48 856[4:Rew:853.0,462.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.48 857[4:Rew:853.0,779.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.48 861[4:Rew:853.0,827.0] || -> equal(multiply(sk_c9,sk_c1),sk_c9)**.
% 0.19/0.48 863[4:Rew:835.0,857.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.48 864[4:Rew:863.0,121.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.48 869[4:Rew:856.0,811.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.48 872[4:Rew:854.0,861.0,869.0,861.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 876[4:Rew:872.0,864.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.48 878[4:Rew:872.0,856.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 901[4:Rew:878.0,850.5,844.0,850.5,878.0,850.4,872.0,850.4,878.0,850.3,844.0,850.3,872.0,850.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.19/0.48 902[4:Con:901.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.48 962[4:SpL:876.0,902.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 964[4:Obv:962.1] || -> .
% 0.19/0.48 965[3:Spt:964.0,2.0,121.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.48 966[3:Spt:964.0,2.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 967[3:MRR:44.0,965.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 969[3:MRR:16.0,965.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.48 970[3:MRR:37.0,965.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.48 972[3:MRR:9.0,965.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.48 973[3:Rew:966.0,119.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.48 974[3:Obv:973.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.48 976[3:SpR:966.0,155.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.48 991[3:SpR:970.0,155.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c8)**.
% 0.19/0.48 993[3:Rew:966.0,991.0,967.0,991.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 996[3:Rew:993.0,172.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.19/0.48 999[3:Rew:993.0,974.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.19/0.48 1000[3:Rew:993.0,976.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.19/0.48 1002[3:Rew:52.0,996.0] || -> equal(identity,sk_c9)**.
% 0.19/0.48 1003[3:Rew:1002.0,779.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.48 1004[3:Rew:1002.0,462.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.48 1005[3:Rew:1002.0,51.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.48 1007[3:Rew:1004.0,972.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.48 1008[3:Rew:1007.0,969.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.19/0.48 1010[3:Rew:1005.0,1000.0,1008.0,1000.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 1014[3:Rew:1010.0,1003.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.48 1015[3:Rew:1010.0,1004.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 1031[3:Rew:1015.0,999.5,993.0,999.5,1015.0,999.4,1010.0,999.4,1015.0,999.3,993.0,999.3,1010.0,999.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.19/0.48 1032[3:Con:1031.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.48 1074[3:SpL:1014.0,1032.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 1076[3:Obv:1074.1] || -> .
% 0.19/0.48 1077[2:Spt:1076.0,5.0,117.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.48 1078[2:Spt:1076.0,5.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 1079[2:MRR:47.1,1077.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 1082[2:MRR:40.0,1077.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.19/0.48 1098[2:SpR:1082.0,155.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c8)**.
% 0.19/0.48 1100[2:Rew:1078.0,1098.0,1079.0,1098.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 1101[2:Rew:1100.0,1078.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.48 1102[2:Rew:1100.0,1077.0] || equal(multiply(sk_c8,sk_c9),sk_c8)** -> .
% 0.19/0.48 1106[2:Rew:1101.0,1102.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 1107[2:Obv:1106.0] || -> .
% 0.19/0.48 % SZS output end Refutation
% 0.19/0.48 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_11 prove_this_14 prove_this_15 prove_this_16 prove_this_18 prove_this_21 prove_this_27 prove_this_28 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_39 prove_this_40 prove_this_42 prove_this_43 prove_this_44 prove_this_46 prove_this_47 prove_this_49 prove_this_50 left_identity left_inverse associativity
% 0.19/0.48
%------------------------------------------------------------------------------