TSTP Solution File: GRP240-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP240-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:46:29 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
% 0.11/0.12 % Problem : GRP240-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 23:59:43 EDT 2022
% 0.12/0.33 % 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 597 clauses, backtracked 548 clauses, performed 15 splits and kept 675 clauses.
% 0.19/0.47 SPASS allocated 63597 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.04 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 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 4, length 269 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c10),sk_c9).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.19/0.47 3[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c10),sk_c9).
% 0.19/0.47 5[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.47 8[0:Inp] || -> equal(inverse(sk_c7),sk_c10)** equal(inverse(sk_c10),sk_c9).
% 0.19/0.47 11[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c9),sk_c10).
% 0.19/0.47 13[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 16[0:Inp] || -> equal(inverse(sk_c7),sk_c10)** equal(inverse(sk_c9),sk_c10).
% 0.19/0.47 19[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 20[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 22[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 23[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 27[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 28[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 29[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 30[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.47 31[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.47 32[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 35[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c9)** equal(multiply(sk_c10,sk_c3),sk_c9).
% 0.19/0.47 36[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.19/0.47 37[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c3),sk_c9).
% 0.19/0.47 43[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.19/0.47 44[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.19/0.47 45[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.19/0.47 51[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 52[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.47 53[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 57[0:Inp] || equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c9),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(inverse(u),sk_c9) equal(multiply(sk_c10,v),sk_c9)** equal(multiply(w,sk_c10),v)* equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(x,sk_c9),sk_c10)** equal(multiply(y,z),sk_c9)** equal(inverse(y),z) equal(multiply(z,sk_c10),sk_c9)** equal(multiply(sk_c10,x1),sk_c9)** equal(multiply(x2,sk_c10),x1)* equal(inverse(x2),sk_c10) -> .
% 0.19/0.47 58[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 59[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 60[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 61[0:Con:57.12] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(inverse(y),sk_c9) equal(inverse(sk_c9),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c9)**+ equal(multiply(x,sk_c10),z)* equal(multiply(v,sk_c10),sk_c9)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(y,sk_c9),sk_c10)** equal(multiply(sk_c10,z),sk_c9)** -> .
% 0.19/0.47 62[1:Spt:61.0,61.6,61.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.19/0.47 63[2:Spt:12.1] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.47 65[3:Spt:4.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.19/0.47 67[4:Spt:52.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.19/0.47 69[5:Spt:32.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 71[6:Spt:44.1] || -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.19/0.47 78[7:Spt:36.1] || -> equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.19/0.47 83[8:Spt:20.1] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 89[2:SpR:63.0,59.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.19/0.47 90[3:SpR:65.0,59.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.19/0.47 91[4:SpR:67.0,59.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.19/0.47 92[5:SpR:69.0,59.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.47 96[2:SpL:89.0,62.1] || equal(inverse(sk_c10),sk_c9) equal(identity,sk_c9) equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.19/0.47 97[3:Rew:65.0,96.0] || equal(sk_c9,sk_c9) equal(identity,sk_c9) equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.19/0.47 98[3:Obv:97.0] || equal(identity,sk_c9) equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.19/0.47 99[3:Rew:90.0,98.1] || equal(identity,sk_c9)** equal(identity,sk_c9)** -> .
% 0.19/0.47 100[3:Obv:99.0] || equal(identity,sk_c9)** -> .
% 0.19/0.47 105[0:SpR:59.0,60.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 108[2:SpR:89.0,60.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(identity,u))**.
% 0.19/0.47 110[2:Rew:58.0,108.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.19/0.47 111[0:Rew:58.0,105.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 127[3:SpR:90.0,110.0] || -> equal(multiply(sk_c10,identity),sk_c10)**.
% 0.19/0.47 128[5:SpR:92.0,110.0] || -> equal(multiply(sk_c10,identity),sk_c1)**.
% 0.19/0.47 130[5:Rew:127.0,128.0] || -> equal(sk_c1,sk_c10)**.
% 0.19/0.47 132[8:Rew:130.0,83.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.19/0.47 136[8:Rew:89.0,132.0] || -> equal(identity,sk_c10)**.
% 0.19/0.47 137[8:Rew:136.0,58.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.47 140[8:Rew:136.0,100.0] || equal(sk_c9,sk_c10)** -> .
% 0.19/0.47 142[8:Rew:136.0,91.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.19/0.47 147[8:Rew:137.0,78.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.47 153[8:Rew:147.0,71.0] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.19/0.47 157[8:Rew:137.0,142.0] || -> equal(sk_c2,sk_c10)**.
% 0.19/0.47 162[8:Rew:137.0,153.0,157.0,153.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.47 163[8:MRR:162.0,140.0] || -> .
% 0.19/0.47 177[8:Spt:163.0,20.1,83.0] || equal(multiply(sk_c1,sk_c9),sk_c10)** -> .
% 0.19/0.47 178[8:Spt:163.0,20.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 179[8:Rew:89.0,177.0,130.0,177.0] || equal(identity,sk_c10)** -> .
% 0.19/0.47 188[5:Rew:89.0,21.1,130.0,21.1] || -> equal(multiply(sk_c6,sk_c10),sk_c9)** equal(identity,sk_c10).
% 0.19/0.47 189[8:MRR:188.1,179.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 190[5:Rew:89.0,19.1,130.0,19.1] || -> equal(multiply(sk_c5,sk_c6),sk_c9)** equal(identity,sk_c10).
% 0.19/0.47 191[8:MRR:190.1,179.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 242[8:SpL:191.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 243[8:Obv:242.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 244[8:Rew:189.0,243.1,178.0,243.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 245[8:Obv:244.1] || -> .
% 0.19/0.47 246[7:Spt:245.0,36.1,78.0] || equal(multiply(sk_c10,sk_c3),sk_c9)** -> .
% 0.19/0.47 247[7:Spt:245.0,36.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 259[7:MRR:37.1,246.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 260[7:MRR:35.1,246.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 281[7:SpL:260.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 282[7:Obv:281.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 283[7:Rew:259.0,282.1,247.0,282.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 284[7:Obv:283.1] || -> .
% 0.19/0.47 285[6:Spt:284.0,44.1,71.0] || equal(multiply(sk_c2,sk_c10),sk_c3)** -> .
% 0.19/0.47 286[6:Spt:284.0,44.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 291[6:MRR:45.1,285.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 292[6:MRR:43.1,285.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 313[6:SpL:292.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 314[6:Obv:313.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 315[6:Rew:291.0,314.1,286.0,314.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 316[6:Obv:315.1] || -> .
% 0.19/0.47 317[5:Spt:316.0,32.1,69.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.47 318[5:Spt:316.0,32.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.47 319[5:MRR:28.1,317.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 323[5:MRR:29.0,317.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 324[5:MRR:27.0,317.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 345[5:SpL:324.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 346[5:Obv:345.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 347[5:Rew:323.0,346.1,319.0,346.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 348[5:Obv:347.1] || -> .
% 0.19/0.47 349[4:Spt:348.0,52.1,67.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.19/0.47 350[4:Spt:348.0,52.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 355[4:MRR:53.0,349.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 356[4:MRR:51.0,349.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 377[4:SpL:356.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 378[4:Obv:377.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 379[4:Rew:355.0,378.1,350.0,378.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 380[4:Obv:379.1] || -> .
% 0.19/0.47 381[3:Spt:380.0,4.1,65.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.19/0.47 382[3:Spt:380.0,4.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 387[3:MRR:5.0,381.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 388[3:MRR:3.0,381.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 409[3:SpL:388.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 410[3:Obv:409.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 411[3:Rew:387.0,410.1,382.0,410.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 412[3:Obv:411.1] || -> .
% 0.19/0.47 413[2:Spt:412.0,12.1,63.0] || equal(inverse(sk_c9),sk_c10)** -> .
% 0.19/0.47 414[2:Spt:412.0,12.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 419[2:MRR:13.0,413.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 420[2:MRR:11.0,413.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 440[2:SpL:420.0,62.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c9,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 441[2:Obv:440.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.19/0.47 442[2:Rew:419.0,441.1,414.0,441.0] || equal(sk_c6,sk_c6)* equal(sk_c9,sk_c9) -> .
% 0.19/0.47 443[2:Obv:442.1] || -> .
% 0.19/0.47 444[1:Spt:443.0,61.1,61.2,61.3,61.4,61.5,61.7,61.9,61.10,61.11] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(v,sk_c10),x)*+ equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,x),sk_c9)** -> .
% 0.19/0.47 445[1:EqR:444.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 447[2:Spt:4.1] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.19/0.47 450[2:Rew:447.0,445.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c10) equal(sk_c9,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 451[2:Obv:450.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 455[3:Spt:16.1] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.47 458[3:Rew:455.0,451.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(sk_c10,sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 459[3:Obv:458.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 463[4:Spt:28.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.47 467[5:Spt:20.1] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.19/0.47 480[2:SpR:447.0,59.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.19/0.47 481[3:SpR:455.0,59.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.19/0.47 482[4:SpR:463.0,59.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.47 488[3:SpR:481.0,60.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(identity,u))**.
% 0.19/0.47 490[3:Rew:58.0,488.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.19/0.47 492[0:SpR:111.0,111.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 495[5:SpR:467.0,111.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c9)**.
% 0.19/0.47 499[0:SpR:59.0,111.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 506[5:Rew:480.0,495.0,463.0,495.0] || -> equal(identity,sk_c9)**.
% 0.19/0.47 507[5:Rew:506.0,58.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.47 509[5:Rew:506.0,480.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.19/0.47 515[5:Rew:507.0,490.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.47 517[5:Rew:507.0,509.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.47 518[5:Rew:517.0,447.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.47 524[5:Rew:517.0,459.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 526[5:Rew:517.0,506.0] || -> equal(identity,sk_c10)**.
% 0.19/0.47 546[5:Rew:526.0,499.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.19/0.47 554[5:Rew:492.0,546.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.47 556[5:Con:524.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.47 557[5:Rew:554.0,556.3,515.0,556.3,517.0,556.3,554.0,556.2,517.0,556.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) -> .
% 0.19/0.47 558[5:Con:557.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.47 620[5:SpL:518.0,558.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.47 622[5:Obv:620.1] || -> .
% 0.19/0.47 623[5:Spt:622.0,20.1,467.0] || equal(multiply(sk_c1,sk_c9),sk_c10)** -> .
% 0.19/0.47 624[5:Spt:622.0,20.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.47 627[5:MRR:24.1,623.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.47 629[0:Rew:492.0,499.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 630[5:MRR:23.1,623.0] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.47 631[5:MRR:22.1,623.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.47 632[5:MRR:21.1,623.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.47 633[5:MRR:19.1,623.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.47 650[5:SpR:630.0,111.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c10)**.
% 0.19/0.47 652[5:Rew:627.0,650.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.47 653[5:Rew:631.0,652.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.47 655[5:Rew:653.0,455.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.47 657[5:Rew:653.0,481.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.19/0.47 659[5:Rew:653.0,482.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.19/0.47 660[5:Rew:653.0,623.0] || equal(multiply(sk_c1,sk_c10),sk_c10)** -> .
% 0.19/0.47 664[5:Rew:653.0,631.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.47 665[5:Rew:653.0,632.0] || -> equal(multiply(sk_c6,sk_c10),sk_c10)**.
% 0.19/0.47 666[5:Rew:653.0,633.0] || -> equal(multiply(sk_c5,sk_c6),sk_c10)**.
% 0.19/0.47 692[5:SpR:664.0,111.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c8)**.
% 0.19/0.47 694[5:Rew:655.0,692.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.47 695[5:Rew:657.0,694.0] || -> equal(identity,sk_c8)**.
% 0.19/0.47 696[5:Rew:695.0,58.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 699[5:Rew:695.0,629.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.47 700[5:Rew:695.0,657.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.47 701[5:Rew:695.0,659.0] || -> equal(multiply(sk_c10,sk_c1),sk_c8)**.
% 0.19/0.48 710[5:SpR:666.0,111.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c6)**.
% 0.19/0.48 712[5:Rew:665.0,710.0,624.0,710.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.48 714[5:Rew:712.0,665.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.19/0.48 719[5:Rew:700.0,714.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 722[5:Rew:719.0,696.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.48 723[5:Rew:719.0,699.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.48 725[5:Rew:719.0,701.0] || -> equal(multiply(sk_c10,sk_c1),sk_c10)**.
% 0.19/0.48 738[5:Rew:723.0,660.0] || equal(sk_c1,sk_c10)** -> .
% 0.19/0.48 743[5:Rew:722.0,725.0] || -> equal(sk_c1,sk_c10)**.
% 0.19/0.48 744[5:MRR:743.0,738.0] || -> .
% 0.19/0.48 756[4:Spt:744.0,28.1,463.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.48 757[4:Spt:744.0,28.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.48 758[4:MRR:32.1,756.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.48 760[4:MRR:31.0,756.0] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.48 761[4:MRR:30.0,756.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 762[4:MRR:29.0,756.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.48 763[4:MRR:27.0,756.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.48 776[2:SpR:480.0,111.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.19/0.48 786[4:SpR:760.0,111.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c10)**.
% 0.19/0.48 788[4:Rew:758.0,786.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.48 789[4:Rew:761.0,788.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.48 790[4:Rew:789.0,447.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.48 792[4:Rew:789.0,480.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.19/0.48 797[4:Rew:789.0,761.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.48 798[4:Rew:789.0,762.0] || -> equal(multiply(sk_c6,sk_c10),sk_c10)**.
% 0.19/0.48 799[4:Rew:789.0,763.0] || -> equal(multiply(sk_c5,sk_c6),sk_c10)**.
% 0.19/0.48 802[4:Rew:789.0,459.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.48 804[4:Con:802.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c9)** -> .
% 0.19/0.48 805[4:Rew:789.0,804.3,789.0,804.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(v,sk_c10)),sk_c10)** -> .
% 0.19/0.48 819[4:SpR:797.0,111.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c8)**.
% 0.19/0.48 821[4:Rew:792.0,819.0,790.0,819.0] || -> equal(identity,sk_c8)**.
% 0.19/0.48 822[4:Rew:821.0,792.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.19/0.48 823[4:Rew:821.0,629.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 824[4:Rew:821.0,58.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 834[4:SpR:799.0,111.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c6)**.
% 0.19/0.48 836[4:Rew:798.0,834.0,757.0,834.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.48 838[4:Rew:836.0,798.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.19/0.48 843[4:Rew:822.0,838.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 847[4:Rew:843.0,823.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.48 848[4:Rew:843.0,824.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.48 854[4:Rew:847.0,805.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(sk_c10,v),sk_c10)** -> .
% 0.19/0.48 871[4:Rew:848.0,854.3,847.0,854.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) -> .
% 0.19/0.48 872[4:Con:871.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.19/0.48 930[4:SpL:790.0,872.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.19/0.48 932[4:Obv:930.1] || -> .
% 0.19/0.48 933[3:Spt:932.0,16.1,455.0] || equal(inverse(sk_c9),sk_c10)** -> .
% 0.19/0.48 934[3:Spt:932.0,16.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.48 937[2:Rew:629.0,776.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.19/0.48 938[3:MRR:937.0,933.0] || -> .
% 0.19/0.48 946[2:Spt:938.0,4.1,447.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.19/0.48 947[2:Spt:938.0,4.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.48 948[2:MRR:8.1,946.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.19/0.48 949[2:MRR:1.1,946.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.48 950[2:MRR:7.0,946.0] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.19/0.48 951[2:MRR:6.0,946.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.19/0.48 952[2:MRR:5.0,946.0] || -> equal(multiply(sk_c6,sk_c10),sk_c9)**.
% 0.19/0.48 953[2:MRR:3.0,946.0] || -> equal(multiply(sk_c5,sk_c6),sk_c9)**.
% 0.19/0.48 954[2:MRR:2.0,946.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.19/0.48 962[2:SpR:950.0,111.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c10)**.
% 0.19/0.48 964[2:Rew:948.0,962.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.48 965[2:Rew:951.0,964.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.48 966[2:Rew:965.0,946.0] || equal(inverse(sk_c10),sk_c10)** -> .
% 0.19/0.48 967[2:Rew:965.0,951.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.19/0.48 968[2:Rew:965.0,952.0] || -> equal(multiply(sk_c6,sk_c10),sk_c10)**.
% 0.19/0.48 969[2:Rew:965.0,953.0] || -> equal(multiply(sk_c5,sk_c6),sk_c10)**.
% 0.19/0.48 970[2:Rew:965.0,954.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.19/0.48 973[2:SpR:967.0,111.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c8)**.
% 0.19/0.48 975[2:Rew:59.0,973.0] || -> equal(identity,sk_c8)**.
% 0.19/0.48 977[2:Rew:975.0,629.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 978[2:Rew:975.0,59.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.19/0.48 984[2:SpR:968.0,111.0] || -> equal(multiply(inverse(sk_c6),sk_c10),sk_c10)**.
% 0.19/0.48 987[2:SpR:969.0,111.0] || -> equal(multiply(inverse(sk_c5),sk_c10),sk_c6)**.
% 0.19/0.48 989[2:Rew:968.0,987.0,947.0,987.0] || -> equal(sk_c6,sk_c10)**.
% 0.19/0.48 994[2:Rew:989.0,984.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.19/0.48 996[2:Rew:978.0,994.0] || -> equal(sk_c8,sk_c10)**.
% 0.19/0.48 1000[2:Rew:996.0,977.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.48 1008[2:Rew:1000.0,970.0] || -> equal(sk_c4,sk_c10)**.
% 0.19/0.48 1011[2:Rew:1008.0,949.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.19/0.48 1014[2:MRR:1011.0,966.0] || -> .
% 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_11 prove_this_12 prove_this_13 prove_this_16 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_35 prove_this_36 prove_this_37 prove_this_43 prove_this_44 prove_this_45 prove_this_51 prove_this_52 prove_this_53 prove_this_57 left_identity left_inverse associativity
% 0.19/0.48
%------------------------------------------------------------------------------