TSTP Solution File: GRP334-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP334-1 : 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 11:46:54 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP334-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 18:07:28 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 572 clauses, backtracked 242 clauses, performed 10 splits and kept 457 clauses.
% 0.19/0.46 SPASS allocated 63450 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 5, length 229 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 2[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 3[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 4[0:Inp] || -> equal(multiply(sk_c6,sk_c4),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 5[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c4)** equal(multiply(sk_c1,sk_c6),sk_c7).
% 0.19/0.46 6[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 7[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 8[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 9[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.19/0.46 10[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 11[0:Inp] || -> equal(inverse(sk_c3),sk_c6)** equal(inverse(sk_c1),sk_c6).
% 0.19/0.46 12[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 13[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.19/0.46 15[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 18[0:Inp] || -> equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 22[0:Inp] || equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c5),sk_c6)** equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c7),sk_c5) equal(multiply(sk_c6,w),sk_c5)** equal(multiply(x,sk_c6),w)* equal(inverse(x),sk_c6) -> .
% 0.19/0.46 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 26[0:Con:22.7] || equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c5),sk_c6)** equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c7),sk_c5) -> .
% 0.19/0.46 27[0:Rew:1.0,26.0] || equal(sk_c5,sk_c5) equal(multiply(u,sk_c6),sk_c7)** equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c5),sk_c6)** equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c7),sk_c5) -> .
% 0.19/0.46 28[0:Obv:27.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c7),sk_c5) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.19/0.46 29[1:Spt:28.1,28.5] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.46 30[2:Spt:13.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 32[3:Spt:8.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 37[4:Spt:3.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 39[4:SpL:37.0,29.1] || equal(inverse(sk_c1),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 40[4:Obv:39.1] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.19/0.46 41[4:Rew:32.0,40.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 42[4:Obv:41.0] || -> .
% 0.19/0.46 43[4:Spt:42.0,3.1,37.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.19/0.46 44[4:Spt:42.0,3.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.46 45[4:MRR:6.1,43.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 46[4:MRR:2.1,43.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.46 47[4:MRR:5.1,43.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 48[4:MRR:4.1,43.0] || -> equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.19/0.46 58[1:SpL:23.0,29.1] || equal(inverse(identity),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 60[2:SpR:30.0,24.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.19/0.46 62[4:SpR:44.0,24.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.19/0.46 65[1:SpL:24.0,29.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c7) -> .
% 0.19/0.46 70[0:SpR:1.0,25.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.46 74[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 76[0:Rew:23.0,74.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 109[0:SpR:76.0,76.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 111[4:SpR:47.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.19/0.46 115[2:SpR:60.0,76.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c2)**.
% 0.19/0.46 123[0:SpR:24.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 132[4:Rew:48.0,111.0,45.0,111.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 133[4:Rew:132.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 136[4:Rew:132.0,46.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 138[4:Rew:132.0,62.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.46 149[4:Rew:133.0,138.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 150[4:Rew:149.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 155[4:Rew:149.0,58.0] || equal(inverse(sk_c6),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 161[4:Rew:150.0,133.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 215[4:Rew:161.0,155.1,136.0,155.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 216[4:Obv:215.1] || -> .
% 0.19/0.46 220[3:Spt:216.0,8.1,32.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.19/0.46 221[3:Spt:216.0,8.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.46 222[0:Rew:109.0,123.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 223[2:Rew:222.0,115.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.19/0.46 226[3:MRR:11.1,220.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 227[2:Rew:223.0,7.0] || -> equal(sk_c2,sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 228[3:MRR:227.1,220.0] || -> equal(sk_c2,sk_c5)**.
% 0.19/0.46 229[3:Rew:228.0,30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 230[3:Rew:228.0,60.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.19/0.46 234[3:MRR:10.0,220.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 235[3:MRR:9.0,220.0] || -> equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.19/0.46 238[3:SpR:221.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.19/0.46 248[0:SpR:1.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.46 261[3:SpR:234.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.19/0.46 263[3:Rew:226.0,261.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.46 264[3:Rew:235.0,263.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 267[3:Rew:264.0,229.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 269[3:Rew:264.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.46 270[3:Rew:264.0,230.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.19/0.46 273[3:Rew:264.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 275[3:Rew:264.0,238.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.46 280[3:Rew:275.0,273.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 284[3:Rew:280.0,270.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 285[3:Rew:280.0,269.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 293[3:Rew:284.0,58.0] || equal(inverse(sk_c6),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 304[3:Rew:285.0,293.1,267.0,293.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 305[3:Obv:304.1] || -> .
% 0.19/0.46 308[2:Spt:305.0,13.1,30.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.19/0.46 309[2:Spt:305.0,13.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.46 310[2:MRR:16.1,308.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 311[2:MRR:12.1,308.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.46 312[2:Rew:311.0,248.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.46 313[2:MRR:15.0,308.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 314[2:MRR:14.0,308.0] || -> equal(multiply(sk_c6,sk_c4),sk_c5)**.
% 0.19/0.46 315[2:Rew:311.0,65.0] || equal(inverse(sk_c5),sk_c6)** equal(identity,sk_c7) -> .
% 0.19/0.46 316[2:SpR:309.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.19/0.46 327[2:SpR:313.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.19/0.46 329[2:Rew:310.0,327.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.46 330[2:Rew:314.0,329.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 332[2:Rew:330.0,311.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 334[2:Rew:330.0,312.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.46 335[2:Rew:330.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 337[2:Rew:330.0,315.0] || equal(inverse(sk_c6),sk_c6)** equal(identity,sk_c7) -> .
% 0.19/0.46 338[2:Rew:330.0,316.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.46 340[2:Rew:338.0,335.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 344[2:Rew:340.0,334.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 355[2:Rew:344.0,337.1,332.0,337.0] || equal(sk_c6,sk_c6) equal(identity,sk_c6)** -> .
% 0.19/0.46 356[2:Obv:355.0] || equal(identity,sk_c6)** -> .
% 0.19/0.46 376[2:SpR:340.0,222.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 378[2:MRR:376.0,356.0] || -> .
% 0.19/0.46 380[1:Spt:378.0,28.0,28.2,28.3,28.4] || equal(inverse(u),sk_c6) equal(inverse(sk_c7),sk_c5) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c5),sk_c6)** -> .
% 0.19/0.46 382[1:SpL:23.0,380.3] || equal(inverse(identity),sk_c6)** equal(inverse(sk_c7),sk_c5) equal(inverse(sk_c6),sk_c5) equal(sk_c5,sk_c6) -> .
% 0.19/0.46 383[2:Spt:8.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.19/0.46 386[2:Rew:383.0,382.1] || equal(inverse(identity),sk_c6)** equal(sk_c5,sk_c5) equal(inverse(sk_c6),sk_c5) equal(sk_c5,sk_c6) -> .
% 0.19/0.46 387[2:Obv:386.1] || equal(inverse(identity),sk_c6)** equal(inverse(sk_c6),sk_c5) equal(sk_c5,sk_c6) -> .
% 0.19/0.46 390[2:SpR:383.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.19/0.46 392[3:Spt:12.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.46 396[3:Rew:392.0,387.1] || equal(inverse(identity),sk_c6)** equal(sk_c5,sk_c5) equal(sk_c5,sk_c6) -> .
% 0.19/0.46 397[3:Obv:396.1] || equal(inverse(identity),sk_c6)** equal(sk_c5,sk_c6) -> .
% 0.19/0.46 400[3:SpR:392.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.19/0.46 402[4:Spt:16.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 409[5:Spt:15.1] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.46 411[5:SpR:409.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c6)**.
% 0.19/0.46 413[5:Rew:402.0,411.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.46 415[5:Rew:413.0,4.0] || -> equal(sk_c5,sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 416[5:Rew:413.0,9.1] || -> equal(inverse(sk_c1),sk_c6)** equal(sk_c5,sk_c6).
% 0.19/0.46 422[5:SpR:413.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.19/0.46 424[5:Rew:392.0,422.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.19/0.46 425[5:SpR:424.0,25.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c4,u))**.
% 0.19/0.46 426[5:SpR:424.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.19/0.46 428[5:Rew:400.0,425.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 433[5:SpR:428.0,222.0] || -> equal(identity,sk_c4)**.
% 0.19/0.46 436[5:Rew:433.0,222.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.46 438[5:Rew:433.0,397.0] || equal(inverse(sk_c4),sk_c6)** equal(sk_c5,sk_c6) -> .
% 0.19/0.46 439[5:Rew:433.0,24.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.19/0.46 440[5:Rew:436.0,426.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 445[5:SpR:383.0,439.0] || -> equal(multiply(sk_c5,sk_c7),sk_c4)**.
% 0.19/0.46 456[5:SpR:445.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c7)**.
% 0.19/0.46 458[5:Rew:440.0,456.0] || -> equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.19/0.46 459[5:Rew:436.0,458.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 461[5:Rew:459.0,1.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 467[5:Rew:459.0,415.1] || -> equal(sk_c5,sk_c6) equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.19/0.46 497[6:Spt:416.1] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 498[6:Rew:497.0,392.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 499[6:Rew:497.0,424.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.19/0.46 501[6:Rew:497.0,461.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.46 507[6:Rew:497.0,438.1] || equal(inverse(sk_c4),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 512[6:Rew:499.0,501.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.46 523[6:Obv:507.1] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.46 524[6:Rew:498.0,523.0,512.0,523.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 525[6:Obv:524.0] || -> .
% 0.19/0.46 528[6:Spt:525.0,416.1,497.0] || equal(sk_c5,sk_c6)** -> .
% 0.19/0.46 529[6:Spt:525.0,416.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 532[6:MRR:467.0,528.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.19/0.46 566[6:SpR:532.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.19/0.46 568[6:Rew:461.0,566.0,529.0,566.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 569[6:MRR:568.0,528.0] || -> .
% 0.19/0.46 570[5:Spt:569.0,15.1,409.0] || equal(multiply(sk_c3,sk_c6),sk_c4)** -> .
% 0.19/0.46 571[5:Spt:569.0,15.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 572[5:MRR:10.1,570.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 573[5:MRR:5.0,570.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 591[5:SpR:573.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 593[5:Rew:1.0,591.0,572.0,591.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 594[5:Rew:593.0,392.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 602[5:Rew:593.0,390.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.46 603[5:Rew:593.0,397.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 604[5:Rew:593.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 608[5:Obv:603.1] || equal(inverse(identity),sk_c6)** -> .
% 0.19/0.46 609[5:Rew:602.0,604.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 641[5:SpR:609.0,222.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 643[5:Rew:641.0,608.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.19/0.46 648[5:Rew:594.0,643.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 649[5:Obv:648.0] || -> .
% 0.19/0.46 654[4:Spt:649.0,16.0,402.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.19/0.46 655[4:Spt:649.0,16.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 656[4:MRR:11.0,654.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 657[4:MRR:6.0,654.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 675[4:SpR:657.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 677[4:Rew:1.0,675.0,656.0,675.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 683[4:Rew:677.0,390.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.46 685[4:Rew:677.0,70.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.46 687[4:Rew:677.0,397.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.19/0.46 692[4:Rew:683.0,685.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 705[4:Obv:687.1] || equal(inverse(identity),sk_c6)** -> .
% 0.19/0.46 723[0:SpR:24.0,222.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.46 725[4:SpR:655.0,24.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.19/0.46 728[4:Rew:723.0,705.0] || equal(identity,sk_c6)** -> .
% 0.19/0.46 730[4:Rew:692.0,725.0] || -> equal(identity,sk_c2)**.
% 0.19/0.46 734[4:Rew:730.0,723.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.46 735[4:Rew:730.0,728.0] || equal(sk_c2,sk_c6)** -> .
% 0.19/0.46 736[4:Rew:655.0,734.0] || -> equal(sk_c2,sk_c6)**.
% 0.19/0.46 740[4:Rew:736.0,735.0] || equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 741[4:Obv:740.0] || -> .
% 0.19/0.46 756[3:Spt:741.0,12.0,392.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.19/0.46 757[3:Spt:741.0,12.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 759[3:MRR:7.0,756.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 761[3:MRR:2.0,756.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 777[3:SpR:761.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 779[3:Rew:1.0,777.0,759.0,777.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 780[3:Rew:779.0,383.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 782[3:Rew:779.0,756.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.19/0.46 783[3:Rew:779.0,248.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.46 787[3:Rew:24.0,783.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 788[3:Rew:787.0,723.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 789[3:Rew:787.0,222.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 792[3:Rew:780.0,788.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 793[3:Rew:792.0,761.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.19/0.46 798[3:Rew:792.0,789.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.46 805[3:Rew:798.0,793.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.46 806[3:Rew:805.0,759.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 807[3:MRR:806.0,782.0] || -> .
% 0.19/0.46 814[2:Spt:807.0,8.0,383.0] || equal(inverse(sk_c7),sk_c5)** -> .
% 0.19/0.46 815[2:Spt:807.0,8.1] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 816[2:MRR:13.0,814.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 817[2:MRR:3.0,814.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.19/0.46 818[2:MRR:18.0,814.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.19/0.46 830[2:SpR:817.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.19/0.46 832[2:Rew:1.0,830.0,815.0,830.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 834[2:Rew:832.0,814.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.46 835[2:Rew:832.0,248.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.46 837[2:Rew:832.0,818.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.19/0.46 838[2:Rew:24.0,835.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 839[2:Rew:838.0,723.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 842[2:Rew:838.0,24.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.46 843[2:Rew:839.0,834.0] || equal(sk_c7,sk_c6)** -> .
% 0.19/0.46 852[2:SpR:837.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.19/0.46 854[2:Rew:816.0,852.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.46 856[2:SpR:854.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.19/0.46 858[2:Rew:842.0,856.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 859[2:MRR:858.0,843.0] || -> .
% 0.19/0.46 % SZS output end Refutation
% 0.19/0.46 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_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_18 prove_this_22 left_identity left_inverse associativity
% 0.19/0.46
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