TSTP Solution File: GRP370-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP370-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:04 EDT 2022
% Result : Unsatisfiable 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP370-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 01:38:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 1387 clauses, backtracked 288 clauses, performed 9 splits and kept 683 clauses.
% 0.18/0.51 SPASS allocated 64290 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.17 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.09 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 5, length 237 :
% 0.18/0.51 % SZS output start Refutation
% 0.18/0.51 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c9).
% 0.18/0.51 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.51 5[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c9).
% 0.18/0.51 6[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c9).
% 0.18/0.51 7[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.51 8[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 9[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 10[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 11[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 12[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 13[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 14[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 15[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.51 16[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c1),sk_c2)**.
% 0.18/0.51 19[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.51 20[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.51 21[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c1),sk_c2)**.
% 0.18/0.51 23[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 25[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 26[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 27[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 28[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 29[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(x),sk_c7) equal(inverse(y),sk_c9) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c9),z)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(y,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c9,z),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c9) -> .
% 0.18/0.51 30[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.51 31[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.51 32[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.51 33[1:Spt:29.0,29.4,29.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.18/0.51 34[2:Spt:7.1] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.51 37[3:Spt:21.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.18/0.51 39[4:Spt:28.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 45[5:Spt:14.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 47[5:SpL:45.0,33.1] || equal(inverse(sk_c1),sk_c2) equal(sk_c8,sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.18/0.51 48[5:Obv:47.1] || equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.18/0.51 49[5:Rew:39.0,48.1,37.0,48.0] || equal(sk_c2,sk_c2)* equal(sk_c8,sk_c8) -> .
% 0.18/0.51 50[5:Obv:49.1] || -> .
% 0.18/0.51 51[5:Spt:50.0,14.1,45.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.18/0.51 52[5:Spt:50.0,14.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 53[5:MRR:11.1,51.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.51 54[5:MRR:9.1,51.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.51 57[5:MRR:10.1,51.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.51 58[5:MRR:8.1,51.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.51 79[3:SpR:37.0,31.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.18/0.51 81[5:SpR:53.0,31.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.18/0.51 82[5:SpR:54.0,31.0] || -> equal(multiply(sk_c9,sk_c3),identity)**.
% 0.18/0.51 93[5:SpL:82.0,33.1] || equal(inverse(sk_c9),sk_c3) equal(identity,sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.18/0.51 99[5:SpR:81.0,32.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.51 101[0:SpR:31.0,32.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.51 109[5:Rew:30.0,99.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.18/0.51 113[0:Rew:30.0,101.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.51 117[5:SpR:57.0,109.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.18/0.51 119[5:Rew:34.0,117.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.51 120[5:Rew:119.0,34.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.18/0.51 125[5:Rew:119.0,58.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.18/0.51 127[5:Rew:119.0,82.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.18/0.51 132[5:Rew:119.0,93.0] || equal(inverse(sk_c7),sk_c3) equal(identity,sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)** -> .
% 0.18/0.51 141[5:Rew:125.0,132.2] || equal(inverse(sk_c7),sk_c3)** equal(identity,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.18/0.51 142[5:Obv:141.2] || equal(inverse(sk_c7),sk_c3)** equal(identity,sk_c8) -> .
% 0.18/0.51 189[0:SpR:113.0,113.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.51 191[4:SpR:39.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c7)**.
% 0.18/0.51 199[5:SpR:120.0,113.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.51 204[0:SpR:31.0,113.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.51 205[3:SpR:79.0,113.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.18/0.51 216[5:Rew:31.0,199.0] || -> equal(identity,sk_c8)**.
% 0.18/0.51 221[5:Rew:216.0,127.0] || -> equal(multiply(sk_c7,sk_c3),sk_c8)**.
% 0.18/0.51 224[5:Rew:216.0,142.1] || equal(inverse(sk_c7),sk_c3)** equal(sk_c8,sk_c8) -> .
% 0.18/0.51 249[5:Rew:191.0,205.0,216.0,205.0] || -> equal(sk_c1,sk_c7)**.
% 0.18/0.51 250[5:Rew:249.0,37.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.18/0.51 263[5:Rew:216.0,204.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.51 276[5:Rew:189.0,263.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.51 277[5:Obv:224.1] || equal(inverse(sk_c7),sk_c3)** -> .
% 0.18/0.51 278[5:Rew:250.0,277.0] || equal(sk_c2,sk_c3)** -> .
% 0.18/0.51 311[5:SpR:221.0,113.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c3)**.
% 0.18/0.51 314[5:Rew:250.0,311.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.51 315[5:Rew:276.0,314.0] || -> equal(sk_c2,sk_c3)**.
% 0.18/0.51 316[5:MRR:315.0,278.0] || -> .
% 0.18/0.51 321[4:Spt:316.0,28.1,39.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.18/0.51 322[4:Spt:316.0,28.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 323[0:Rew:189.0,204.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.51 328[4:MRR:27.1,321.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.51 329[4:MRR:26.1,321.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.51 346[2:SpR:34.0,113.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c8)**.
% 0.18/0.51 350[4:SpR:328.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.51 353[4:Rew:322.0,350.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.51 354[4:Rew:329.0,353.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.51 365[4:Rew:354.0,346.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.51 366[4:Rew:31.0,365.0] || -> equal(identity,sk_c8)**.
% 0.18/0.51 369[4:Rew:366.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.51 372[4:Rew:366.0,323.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.51 451[4:SpR:369.0,113.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.51 459[4:SpL:369.0,33.1] || equal(inverse(inverse(u)),u) equal(sk_c8,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 462[4:Rew:372.0,451.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.51 470[4:Obv:459.1] || equal(inverse(inverse(u)),u) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 471[4:Rew:462.0,470.0] || equal(u,u) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 472[4:Obv:471.0] || equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 473[4:UnC:472.0,369.0] || -> .
% 0.18/0.51 474[3:Spt:473.0,21.1,37.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.18/0.51 475[3:Spt:473.0,21.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 478[3:MRR:20.0,474.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.51 479[3:MRR:19.0,474.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.51 493[3:SpR:478.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.51 496[3:Rew:475.0,493.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.51 497[3:Rew:479.0,496.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.51 502[3:Rew:497.0,346.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.51 509[3:Rew:31.0,502.0] || -> equal(identity,sk_c8)**.
% 0.18/0.51 510[3:Rew:509.0,323.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.51 514[3:Rew:509.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.51 595[3:SpR:514.0,113.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.51 601[3:SpL:514.0,33.1] || equal(inverse(inverse(u)),u) equal(sk_c8,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 602[3:Rew:510.0,595.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.51 609[3:Obv:601.1] || equal(inverse(inverse(u)),u) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 610[3:Rew:602.0,609.0] || equal(u,u) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 611[3:Obv:610.0] || equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 612[3:UnC:611.0,514.0] || -> .
% 0.18/0.51 613[2:Spt:612.0,7.1,34.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.18/0.51 614[2:Spt:612.0,7.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 615[2:MRR:4.1,613.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.51 617[2:MRR:6.1,613.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.51 618[2:MRR:5.1,613.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.51 619[2:MRR:3.1,613.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.51 628[2:SpR:617.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.51 631[2:Rew:614.0,628.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.51 632[2:Rew:618.0,631.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.51 636[2:Rew:632.0,613.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.18/0.51 650[2:SpR:619.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.18/0.51 653[2:Rew:615.0,650.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.18/0.51 654[2:MRR:653.0,636.0] || -> .
% 0.18/0.51 658[1:Spt:654.0,29.1,29.2,29.3,29.5,29.6,29.7,29.9,29.10] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),x)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c9) -> .
% 0.18/0.51 659[1:EqR:658.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c9) -> .
% 0.18/0.51 661[2:Spt:4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.51 662[2:Rew:661.0,658.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c7)** equal(sk_c9,sk_c9) -> .
% 0.18/0.51 664[2:Rew:661.0,659.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c7)** equal(sk_c9,sk_c9) -> .
% 0.18/0.51 665[2:Obv:664.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c7)** -> .
% 0.18/0.51 666[2:Obv:662.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c7)** -> .
% 0.18/0.51 669[2:SpR:661.0,113.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c8)**.
% 0.18/0.51 671[3:Spt:21.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.18/0.51 672[3:SpR:671.0,113.0] || -> equal(multiply(sk_c2,multiply(sk_c1,u)),u)**.
% 0.18/0.51 674[4:Spt:14.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.51 676[4:SpR:674.0,113.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.18/0.51 678[4:Rew:671.0,676.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.18/0.51 679[5:Spt:28.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 681[5:SpR:679.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c7)**.
% 0.18/0.51 684[4:SpR:678.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.18/0.51 686[4:Rew:31.0,684.0] || -> equal(identity,sk_c8)**.
% 0.18/0.51 688[4:Rew:686.0,323.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.51 689[4:Rew:686.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.51 694[4:Rew:688.0,661.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.51 695[5:Rew:688.0,681.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.51 696[4:Rew:694.0,666.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c7)** -> .
% 0.18/0.51 697[4:Rew:694.0,665.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c7)** -> .
% 0.18/0.51 702[4:Rew:694.0,697.5,694.0,697.4,694.0,697.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.18/0.51 703[4:Con:702.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)**+ -> .
% 0.18/0.51 704[4:Rew:694.0,696.6,694.0,696.5,694.0,696.3,694.0,696.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,x),sk_c7)** -> .
% 0.18/0.51 705[4:Con:704.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,w),sk_c7)** -> .
% 0.18/0.51 723[4:SpR:689.0,113.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.18/0.51 729[4:Rew:688.0,723.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.51 734[5:SpL:679.0,705.2] || equal(inverse(sk_c2),sk_c7) equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.51 738[5:Rew:695.0,734.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.51 739[5:Obv:738.0] || equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.51 759[4:SpR:729.0,113.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.18/0.51 966[5:SpL:679.0,739.2] || equal(inverse(sk_c2),sk_c7) equal(sk_c8,u) equal(sk_c8,sk_c8) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.51 970[5:Obv:966.2] || equal(inverse(sk_c2),sk_c7) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.51 971[5:Rew:695.0,970.0] || equal(sk_c7,sk_c7) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.51 972[5:Obv:971.0] || equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.51 1090[4:SpL:759.0,703.3] || equal(inverse(inverse(sk_c7)),sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.51 1094[4:Obv:1090.3] || equal(inverse(inverse(sk_c7)),sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 1188[5:SpL:688.0,972.1] || equal(sk_c8,sk_c8)* equal(sk_c7,sk_c7) -> .
% 0.18/0.51 1195[5:Obv:1188.1] || -> .
% 0.18/0.51 1198[5:Spt:1195.0,28.1,679.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.18/0.51 1199[5:Spt:1195.0,28.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 1202[5:MRR:25.1,1198.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.51 1203[4:Rew:694.0,23.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.18/0.51 1204[5:MRR:1203.1,1198.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.51 1213[4:Rew:729.0,1094.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 1214[4:Obv:1213.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.18/0.51 1217[5:SpR:1202.0,729.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.51 1246[5:SpR:1204.0,729.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.18/0.51 1250[5:Rew:1217.0,1246.0] || -> equal(sk_c4,sk_c3)**.
% 0.18/0.51 1254[5:Rew:1250.0,1217.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.18/0.51 1397[4:SpL:689.0,1214.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.18/0.51 1405[4:Obv:1397.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.18/0.51 1406[5:Rew:1204.0,1405.0,1254.0,1405.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.51 1407[5:Obv:1406.0] || -> .
% 0.18/0.51 1409[4:Spt:1407.0,14.1,674.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.18/0.51 1410[4:Spt:1407.0,14.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.51 1414[4:MRR:13.1,1409.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.51 1415[4:MRR:12.1,1409.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.51 1429[4:SpR:1414.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.52 1431[4:Rew:1410.0,1429.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.52 1432[4:Rew:1415.0,1431.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.52 1437[4:Rew:1432.0,669.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.52 1446[4:Rew:31.0,1437.0] || -> equal(identity,sk_c8)**.
% 0.18/0.52 1447[4:Rew:1446.0,323.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.52 1450[4:Rew:1446.0,31.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.52 1501[4:SpR:1447.0,672.0] || -> equal(multiply(sk_c2,sk_c1),sk_c8)**.
% 0.18/0.52 1506[4:SpR:1501.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c1)**.
% 0.18/0.52 1508[4:Rew:1447.0,1506.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.18/0.52 1521[4:SpR:1508.0,1450.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.18/0.52 1523[4:MRR:1521.0,1409.0] || -> .
% 0.18/0.52 1527[3:Spt:1523.0,21.1,671.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.18/0.52 1528[3:Spt:1523.0,21.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.52 1530[3:MRR:16.1,1527.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.18/0.52 1531[3:MRR:20.0,1527.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.52 1532[3:MRR:19.0,1527.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.52 1534[3:MRR:15.0,1527.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.18/0.52 1545[3:SpR:1531.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.52 1547[3:Rew:1528.0,1545.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.52 1548[3:Rew:1532.0,1547.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.52 1550[3:Rew:1548.0,1530.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.52 1553[3:Rew:1548.0,669.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.52 1556[3:Rew:1548.0,1534.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.18/0.52 1557[3:Rew:1548.0,666.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c9) equal(multiply(u,sk_c9),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c7)** -> .
% 0.18/0.52 1562[3:Rew:31.0,1553.0] || -> equal(identity,sk_c8)**.
% 0.18/0.52 1564[3:Rew:1562.0,323.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.52 1571[3:Rew:1548.0,1557.6,1548.0,1557.5,1548.0,1557.3,1548.0,1557.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,x),sk_c7)** -> .
% 0.18/0.52 1572[3:Con:1571.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,w),sk_c7)** -> .
% 0.18/0.52 1688[3:SpL:1556.0,1572.2] || equal(inverse(sk_c3),sk_c7) equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.52 1692[3:Rew:1550.0,1688.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.52 1693[3:Obv:1692.0] || equal(inverse(u),sk_c7) equal(sk_c8,v) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(sk_c7,v),sk_c7)** -> .
% 0.18/0.52 1964[3:SpL:1556.0,1693.2] || equal(inverse(sk_c3),sk_c7) equal(sk_c8,u) equal(sk_c8,sk_c8) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.52 1967[3:Obv:1964.2] || equal(inverse(sk_c3),sk_c7) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.52 1968[3:Rew:1550.0,1967.0] || equal(sk_c7,sk_c7) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.52 1969[3:Obv:1968.0] || equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.18/0.52 2165[3:SpL:1564.0,1969.1] || equal(sk_c8,sk_c8)* equal(sk_c7,sk_c7) -> .
% 0.18/0.52 2171[3:Obv:2165.1] || -> .
% 0.18/0.52 2174[2:Spt:2171.0,4.1,661.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.18/0.52 2175[2:Spt:2171.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.52 2178[2:MRR:7.1,2174.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.52 2179[2:MRR:6.1,2174.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.18/0.52 2180[2:MRR:5.1,2174.0] || -> equal(multiply(sk_c9,sk_c6),sk_c7)**.
% 0.18/0.52 2181[2:MRR:3.1,2174.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.52 2198[2:SpR:2179.0,113.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.18/0.52 2200[2:Rew:2178.0,2198.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.18/0.52 2201[2:Rew:2180.0,2200.0] || -> equal(sk_c9,sk_c7)**.
% 0.18/0.52 2205[2:Rew:2201.0,2174.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.18/0.52 2217[2:SpR:2181.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.18/0.52 2219[2:Rew:2175.0,2217.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.18/0.52 2220[2:MRR:2219.0,2205.0] || -> .
% 0.18/0.52 % SZS output end Refutation
% 0.18/0.52 Formulae used in the proof : 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_19 prove_this_20 prove_this_21 prove_this_23 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 left_identity left_inverse associativity
% 0.18/0.52
%------------------------------------------------------------------------------