TSTP Solution File: GRP315-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP315-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:46:49 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
% 0.06/0.12 % Problem : GRP315-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n016.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 : Mon Jun 13 11:47:59 EDT 2022
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 801 clauses, backtracked 237 clauses, performed 9 splits and kept 568 clauses.
% 0.19/0.46 SPASS allocated 63547 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.12 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 0:00:00.01 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 287 :
% 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_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.46 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.46 6[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.46 7[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 8[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.46 9[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 10[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 11[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 12[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 13[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 15[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 17[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 18[0:Inp] || equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(v,sk_c6),sk_c5)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(w,sk_c6),sk_c7)** equal(inverse(x),sk_c6) equal(multiply(x,sk_c5),sk_c6)** -> .
% 0.19/0.46 19[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 20[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 21[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 22[0:Rew:1.0,18.0] || equal(sk_c5,sk_c5) equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(v,sk_c6),sk_c5)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(w,sk_c6),sk_c7)** equal(inverse(x),sk_c6) equal(multiply(x,sk_c5),sk_c6)** -> .
% 0.19/0.46 23[0:Obv:22.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** -> .
% 0.19/0.46 24[1:Spt:23.3,23.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.19/0.46 25[2:Spt:14.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 28[1:SpL:1.0,24.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.19/0.46 29[3:Spt:8.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 31[4:Spt:9.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 34[1:SpL:19.0,24.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 38[2:SpR:25.0,20.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.46 39[3:SpR:29.0,20.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 40[1:SpL:20.0,24.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c6) -> .
% 0.19/0.46 45[4:SpR:31.0,21.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.19/0.46 47[0:SpR:20.0,21.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 49[2:SpR:38.0,21.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.46 51[2:Rew:19.0,49.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.46 52[0:Rew:19.0,47.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 66[0:SpR:52.0,52.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 68[0:SpR:1.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.46 69[4:SpR:31.0,52.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.19/0.46 70[0:SpR:19.0,52.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.19/0.46 71[0:SpR:20.0,52.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 74[2:SpR:51.0,52.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c3,u))**.
% 0.19/0.46 77[3:SpR:39.0,52.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.46 80[4:Rew:29.0,69.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 84[0:Rew:66.0,71.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 85[3:Rew:84.0,77.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.46 87[3:Rew:85.0,68.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.46 88[4:Rew:31.0,87.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 93[4:Rew:88.0,38.0] || -> equal(multiply(sk_c6,sk_c3),identity)**.
% 0.19/0.46 98[4:Rew:88.0,74.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c3,u))**.
% 0.19/0.46 99[4:Rew:88.0,40.0] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c6) -> .
% 0.19/0.46 111[4:Rew:85.0,98.0] || -> equal(multiply(sk_c4,u),multiply(sk_c3,u))**.
% 0.19/0.46 118[4:Rew:85.0,99.0] || equal(inverse(sk_c4),sk_c6)** equal(identity,sk_c6) -> .
% 0.19/0.46 119[4:Rew:29.0,118.0] || equal(sk_c6,sk_c6) equal(identity,sk_c6)** -> .
% 0.19/0.46 120[4:Obv:119.0] || equal(identity,sk_c6)** -> .
% 0.19/0.46 126[3:SpR:85.0,20.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.19/0.46 127[3:SpR:85.0,52.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.19/0.46 159[4:Rew:111.0,127.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.19/0.46 160[4:Rew:111.0,126.0] || -> equal(multiply(sk_c3,sk_c6),identity)**.
% 0.19/0.46 163[4:Rew:88.0,7.1,88.0,7.0] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.19/0.46 164[4:Rew:160.0,163.1] || -> equal(inverse(sk_c1),sk_c6)** equal(identity,sk_c6).
% 0.19/0.46 165[4:MRR:164.1,120.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.19/0.46 166[4:Rew:111.0,45.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.19/0.46 170[4:Rew:88.0,3.1,88.0,3.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)** equal(multiply(sk_c1,sk_c6),sk_c6).
% 0.19/0.46 171[4:Rew:160.0,170.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.19/0.46 172[4:MRR:171.0,120.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.19/0.46 210[4:SpR:172.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.19/0.46 212[4:Rew:80.0,210.0,165.0,210.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 217[4:Rew:212.0,166.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.19/0.46 224[4:Rew:159.0,217.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 225[4:Rew:224.0,93.0] || -> equal(identity,sk_c3)**.
% 0.19/0.46 227[4:Rew:224.0,159.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.46 232[4:Rew:225.0,120.0] || equal(sk_c3,sk_c6)** -> .
% 0.19/0.46 238[4:Rew:225.0,160.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.19/0.46 246[4:Rew:227.0,238.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.46 247[4:MRR:246.0,232.0] || -> .
% 0.19/0.46 249[4:Spt:247.0,9.1,31.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.46 250[4:Spt:247.0,9.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 251[4:Rew:87.0,249.0] || equal(sk_c7,sk_c6)** -> .
% 0.19/0.46 252[3:Rew:87.0,17.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c7,sk_c6).
% 0.19/0.46 253[4:MRR:252.1,251.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 255[3:Rew:87.0,13.0] || -> equal(sk_c7,sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 256[4:MRR:255.0,251.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 257[3:Rew:87.0,5.0] || -> equal(sk_c7,sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 258[4:MRR:257.0,251.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 267[4:SpR:253.0,52.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.46 288[4:SpR:256.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.46 290[4:Rew:253.0,288.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 297[4:SpR:258.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 299[4:Rew:250.0,297.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 301[4:SpR:290.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 303[4:Rew:126.0,301.0,85.0,301.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 305[4:Rew:303.0,126.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.46 307[4:Rew:303.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.46 310[4:Rew:303.0,70.0] || -> equal(multiply(inverse(sk_c5),u),u)**.
% 0.19/0.46 312[4:Rew:307.0,87.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 313[4:Rew:312.0,29.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 319[4:Rew:312.0,305.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 324[4:Rew:299.0,319.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 326[4:Rew:324.0,256.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 349[4:Rew:313.0,310.0,324.0,310.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 350[4:Rew:349.0,267.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 351[4:Rew:350.0,326.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 352[4:MRR:351.0,251.0] || -> .
% 0.19/0.46 366[3:Spt:352.0,8.0,29.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.46 367[3:Spt:352.0,8.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 368[3:MRR:16.0,366.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 369[3:MRR:12.0,366.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 370[3:MRR:4.0,366.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 386[3:SpR:369.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.46 388[3:Rew:368.0,386.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 390[3:SpR:370.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 392[3:Rew:367.0,390.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 394[3:SpR:388.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 396[3:Rew:20.0,394.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 397[3:Rew:396.0,38.0] || -> equal(multiply(sk_c7,sk_c3),sk_c5)**.
% 0.19/0.46 399[3:Rew:396.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.46 401[3:Rew:396.0,34.0] || equal(inverse(sk_c5),sk_c7)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 406[3:Rew:399.0,68.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 411[3:SpR:406.0,52.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.46 416[3:SpR:392.0,21.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 421[3:Rew:411.0,416.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 422[3:Rew:421.0,392.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 424[3:Rew:421.0,397.0] || -> equal(sk_c3,sk_c5)**.
% 0.19/0.46 430[3:Rew:422.0,25.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.46 437[3:Rew:422.0,401.0] || equal(inverse(sk_c5),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.19/0.46 439[3:Rew:424.0,430.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.46 450[3:Rew:422.0,437.1,439.0,437.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 451[3:Obv:450.1] || -> .
% 0.19/0.46 454[2:Spt:451.0,14.0,25.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.46 455[2:Spt:451.0,14.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 456[2:MRR:6.0,454.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 457[2:MRR:10.0,454.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 458[2:MRR:2.0,454.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 459[2:SpR:455.0,52.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.46 467[2:SpR:457.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.46 469[2:Rew:455.0,467.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 471[2:SpR:458.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 473[2:Rew:456.0,471.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 475[2:SpR:469.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 477[2:Rew:20.0,475.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 478[2:Rew:477.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.46 484[2:Rew:478.0,68.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 485[2:Rew:484.0,28.0] || equal(sk_c7,sk_c7) equal(sk_c5,sk_c6)** -> .
% 0.19/0.46 488[2:Obv:485.0] || equal(sk_c5,sk_c6)** -> .
% 0.19/0.46 491[2:SpR:484.0,52.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.46 496[2:SpR:473.0,21.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 501[2:Rew:491.0,496.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 503[2:Rew:501.0,491.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 516[2:Rew:503.0,459.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 520[2:Rew:516.0,457.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 521[2:MRR:520.0,488.0] || -> .
% 0.19/0.46 527[1:Spt:521.0,23.0,23.1,23.2,23.4,23.5,23.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.46 529[2:Spt:16.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 530[2:SpR:529.0,52.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.46 532[3:Spt:6.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 538[4:Spt:15.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 540[4:SpR:538.0,52.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.19/0.46 542[4:Rew:532.0,540.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.46 543[5:Spt:9.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 545[5:SpR:543.0,52.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.19/0.46 547[5:SpL:543.0,527.3] || equal(inverse(sk_c4),sk_c6) equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.19/0.46 548[5:Rew:529.0,545.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 549[5:Obv:547.3] || equal(inverse(sk_c4),sk_c6) equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.19/0.46 550[5:Rew:529.0,549.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.19/0.46 551[5:Obv:550.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.19/0.46 559[5:SpR:548.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.46 561[5:Rew:68.0,559.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.46 565[5:Rew:561.0,542.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.46 566[5:Rew:561.0,68.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.46 570[5:Rew:561.0,551.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.19/0.46 573[5:Rew:548.0,565.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 574[5:Rew:573.0,543.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.19/0.46 577[5:Rew:20.0,566.0,573.0,566.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 579[5:Rew:577.0,84.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.46 583[5:Rew:579.0,574.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.46 585[5:Rew:583.0,529.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.46 595[5:Rew:579.0,570.3,573.0,570.3,579.0,570.2,561.0,570.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.19/0.46 596[5:Con:595.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.19/0.46 654[5:SpL:585.0,596.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.46 656[5:Obv:654.1] || -> .
% 0.19/0.46 657[5:Spt:656.0,9.1,543.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.46 658[5:Spt:656.0,9.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 659[5:MRR:17.1,657.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 660[5:MRR:13.0,657.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 661[5:MRR:5.0,657.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 681[5:SpR:660.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.46 683[5:Rew:659.0,681.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 685[5:SpR:661.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 687[5:Rew:658.0,685.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 689[5:SpR:683.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.46 691[5:Rew:20.0,689.0] || -> equal(identity,sk_c5)**.
% 0.19/0.46 692[5:Rew:691.0,19.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 693[5:Rew:691.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.46 694[5:Rew:691.0,20.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.46 699[5:Rew:693.0,657.0] || equal(sk_c4,sk_c6)** -> .
% 0.19/0.46 707[5:SpR:687.0,52.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.46 709[5:Rew:694.0,707.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 713[5:Rew:709.0,692.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 714[5:Rew:709.0,693.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.46 721[5:Rew:713.0,530.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.46 778[5:SpR:721.0,714.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.46 780[5:MRR:778.0,699.0] || -> .
% 0.19/0.46 782[4:Spt:780.0,15.1,538.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.46 783[4:Spt:780.0,15.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 784[4:MRR:7.1,782.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 785[4:MRR:11.0,782.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.46 786[4:MRR:3.0,782.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 797[4:SpR:785.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.46 799[4:Rew:783.0,797.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.46 801[4:SpR:786.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 803[4:Rew:784.0,801.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 805[4:SpR:799.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 807[4:Rew:20.0,805.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 808[4:Rew:807.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 809[4:Rew:807.0,19.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 811[4:Rew:807.0,20.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 825[4:SpR:803.0,52.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 827[4:Rew:811.0,825.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 828[4:Rew:827.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.47 831[4:Rew:827.0,809.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 832[4:Rew:827.0,808.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 834[4:Rew:827.0,811.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.47 837[4:Rew:831.0,828.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.47 843[4:Rew:837.0,532.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.47 848[4:Rew:837.0,782.0] || equal(multiply(sk_c3,sk_c6),sk_c6)** -> .
% 0.19/0.47 860[4:Rew:832.0,848.0] || equal(sk_c3,sk_c6)** -> .
% 0.19/0.47 903[4:SpR:843.0,834.0] || -> equal(multiply(sk_c6,sk_c3),sk_c6)**.
% 0.19/0.47 905[4:Rew:831.0,903.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.47 906[4:MRR:905.0,860.0] || -> .
% 0.19/0.47 910[3:Spt:906.0,6.0,532.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 911[3:Spt:906.0,6.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 912[3:MRR:14.0,910.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 913[3:MRR:10.0,910.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 914[3:MRR:2.0,910.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 925[3:SpR:913.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 927[3:Rew:912.0,925.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 929[3:SpR:914.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 931[3:Rew:911.0,929.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 933[3:SpR:927.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 935[3:Rew:20.0,933.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 936[3:Rew:935.0,19.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 937[3:Rew:935.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 938[3:Rew:935.0,20.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 943[3:Rew:937.0,68.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.47 944[3:Rew:937.0,527.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.47 953[3:SpR:931.0,52.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 955[3:Rew:938.0,953.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 956[3:Rew:955.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.47 959[3:Rew:955.0,936.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 960[3:Rew:955.0,937.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 963[3:Rew:955.0,944.5] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.19/0.47 965[3:Rew:959.0,956.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.47 974[3:Rew:965.0,943.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.47 989[3:Rew:960.0,963.5,960.0,963.4,965.0,963.4,965.0,963.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.19/0.47 990[3:Con:989.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.19/0.47 1022[3:SpL:974.0,990.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 1023[3:Obv:1022.1] || -> .
% 0.19/0.47 1024[2:Spt:1023.0,16.0,529.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 1025[2:Spt:1023.0,16.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 1026[2:MRR:8.0,1024.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1027[2:MRR:12.0,1024.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 1028[2:MRR:4.0,1024.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 1037[2:SpR:1027.0,52.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 1039[2:Rew:1025.0,1037.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 1041[2:SpR:1028.0,52.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 1043[2:Rew:1026.0,1041.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 1045[2:SpR:1039.0,52.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 1047[2:Rew:20.0,1045.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 1048[2:Rew:1047.0,84.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 1049[2:Rew:1047.0,19.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 1051[2:Rew:1047.0,20.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 1053[2:Rew:1048.0,68.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.47 1054[2:Rew:1048.0,527.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.47 1065[2:SpR:1043.0,52.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 1067[2:Rew:1051.0,1065.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 1068[2:Rew:1067.0,1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.47 1070[2:Rew:1067.0,1049.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 1072[2:Rew:1067.0,1048.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 1075[2:Rew:1067.0,1054.5] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.19/0.47 1076[2:Rew:1070.0,1068.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.47 1084[2:Rew:1076.0,1053.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.47 1099[2:Rew:1072.0,1075.5,1072.0,1075.4,1076.0,1075.4,1076.0,1075.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.19/0.47 1100[2:Con:1099.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.19/0.47 1141[2:SpL:1084.0,1100.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.47 1143[2:Obv:1141.1] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 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_17 prove_this_18 left_identity left_inverse associativity
% 0.19/0.47
%------------------------------------------------------------------------------