TSTP Solution File: GRP355-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP355-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:59 EDT 2022
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP355-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 05:56:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 962 clauses, backtracked 158 clauses, performed 7 splits and kept 396 clauses.
% 0.22/0.50 SPASS allocated 64055 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.50 0:00:00.03 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.01 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.07 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 4, length 161 :
% 0.22/0.50 % SZS output start Refutation
% 0.22/0.50 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.22/0.50 4[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.22/0.50 5[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.22/0.50 6[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.22/0.50 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.22/0.50 8[0:Inp] || -> equal(multiply(sk_c2,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 9[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 10[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 11[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 12[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.22/0.50 13[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 14[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 15[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.22/0.50 16[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.22/0.50 18[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 19[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.22/0.50 20[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.22/0.50 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 22[0:Inp] || equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(inverse(v),sk_c8) equal(multiply(w,sk_c6),sk_c7)** equal(inverse(w),sk_c6) equal(multiply(sk_c8,x),sk_c6)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.22/0.50 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.50 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.50 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.50 26[0:Con:22.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.22/0.50 27[1:Spt:26.2,26.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.22/0.50 30[2:Spt:18.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 34[3:Spt:11.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 36[3:SpL:34.0,27.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.50 37[3:Obv:36.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 38[3:Rew:30.0,37.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 39[3:Obv:38.0] || -> .
% 0.22/0.50 40[3:Spt:39.0,11.1,34.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.22/0.50 41[3:Spt:39.0,11.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.50 43[3:MRR:9.1,40.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 47[3:MRR:8.1,40.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.22/0.50 58[3:SpL:47.0,27.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.50 59[3:Obv:58.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.22/0.50 60[3:Rew:43.0,59.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 61[3:Obv:60.0] || -> .
% 0.22/0.50 62[2:Spt:61.0,18.1,30.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.50 63[2:Spt:61.0,18.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.50 65[2:MRR:16.1,62.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 69[2:MRR:15.0,62.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.22/0.50 80[2:SpL:69.0,27.1] || equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.50 81[2:Obv:80.1] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.22/0.50 82[2:Rew:65.0,81.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.50 83[2:Obv:82.0] || -> .
% 0.22/0.50 84[1:Spt:83.0,26.0,26.1,26.3,26.4,26.6,26.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c8,w),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.22/0.50 87[2:Spt:4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.22/0.50 88[2:Rew:87.0,84.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),w)* equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c8,w),sk_c6)** equal(sk_c8,sk_c8) -> .
% 0.22/0.50 93[2:Obv:88.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),w)* equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c8,w),sk_c6)** -> .
% 0.22/0.50 95[3:Spt:21.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.50 97[4:Spt:14.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.22/0.50 100[3:SpR:95.0,24.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.22/0.50 105[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.50 110[0:Rew:23.0,105.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.50 113[0:SpR:110.0,110.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.50 116[0:SpR:24.0,110.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.50 119[3:SpR:100.0,110.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.22/0.50 123[0:Rew:113.0,116.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.50 124[3:Rew:123.0,119.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.22/0.50 126[3:SpR:124.0,24.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.22/0.50 129[4:Rew:97.0,126.0] || -> equal(identity,sk_c7)**.
% 0.22/0.50 130[4:Rew:129.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.50 135[4:Rew:129.0,123.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.50 136[4:Rew:130.0,87.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.50 139[4:Rew:136.0,95.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.22/0.50 140[4:Rew:136.0,97.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.22/0.50 142[4:Rew:136.0,93.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),w)* equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c8,w),sk_c6)** -> .
% 0.22/0.50 153[4:Rew:136.0,142.4,136.0,142.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,w),sk_c6)** -> .
% 0.22/0.50 225[4:SpL:140.0,153.2] || equal(inverse(sk_c1),sk_c6) equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.50 226[4:Rew:139.0,225.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.50 227[4:Obv:226.0] || equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.50 512[4:SpL:140.0,227.2] || equal(inverse(sk_c1),sk_c6) equal(sk_c7,u) equal(sk_c7,sk_c7) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.50 515[4:Obv:512.2] || equal(inverse(sk_c1),sk_c6) equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.50 516[4:Rew:139.0,515.0] || equal(sk_c6,sk_c6) equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.50 517[4:Obv:516.0] || equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.50 692[4:SpL:135.0,517.1] || equal(sk_c7,sk_c7) equal(sk_c6,sk_c6)* -> .
% 0.22/0.50 698[4:Obv:692.1] || -> .
% 0.22/0.50 701[4:Spt:698.0,14.1,97.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.22/0.50 702[4:Spt:698.0,14.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.50 703[4:Rew:126.0,701.0] || equal(identity,sk_c7)** -> .
% 0.22/0.50 706[3:Rew:126.0,11.1] || -> equal(inverse(sk_c3),sk_c6)** equal(identity,sk_c7).
% 0.22/0.50 707[4:MRR:706.1,703.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.50 709[3:Rew:126.0,13.1] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(identity,sk_c7).
% 0.22/0.50 710[4:MRR:709.1,703.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.22/0.50 711[3:Rew:126.0,12.1] || -> equal(multiply(sk_c8,sk_c5),sk_c6)** equal(identity,sk_c7).
% 0.22/0.50 712[4:MRR:711.1,703.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.22/0.50 713[3:Rew:126.0,10.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(identity,sk_c7).
% 0.22/0.50 714[4:MRR:713.1,703.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.22/0.50 746[4:SpR:710.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.22/0.50 748[4:Rew:702.0,746.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.22/0.51 749[4:Rew:712.0,748.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.51 751[4:Rew:749.0,124.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.22/0.51 754[4:Rew:749.0,126.0] || -> equal(multiply(sk_c1,sk_c6),identity)**.
% 0.22/0.51 762[4:Rew:749.0,712.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.22/0.51 783[4:SpR:714.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.22/0.51 785[4:Rew:707.0,783.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.22/0.51 801[4:SpR:762.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.22/0.51 803[4:Rew:754.0,801.0,751.0,801.0] || -> equal(identity,sk_c5)**.
% 0.22/0.51 804[4:Rew:803.0,703.0] || equal(sk_c5,sk_c7)** -> .
% 0.22/0.51 805[4:Rew:803.0,754.0] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.22/0.51 826[4:SpR:785.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.22/0.51 828[4:Rew:751.0,826.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.22/0.51 829[4:Rew:805.0,828.0] || -> equal(sk_c5,sk_c7)**.
% 0.22/0.51 830[4:MRR:829.0,804.0] || -> .
% 0.22/0.51 831[3:Spt:830.0,21.1,95.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.51 832[3:Spt:830.0,21.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.51 833[3:MRR:16.1,831.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 834[3:MRR:18.1,831.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.51 835[3:MRR:20.0,831.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.22/0.51 836[3:MRR:19.0,831.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.22/0.51 837[3:MRR:17.0,831.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.22/0.51 838[3:MRR:15.0,831.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.22/0.51 849[3:SpR:835.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.22/0.51 851[3:Rew:832.0,849.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.22/0.51 852[3:Rew:836.0,851.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.51 854[3:Rew:852.0,833.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.22/0.51 860[3:Rew:852.0,836.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.22/0.51 861[3:Rew:852.0,838.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.51 862[3:Rew:852.0,93.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),w)* equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c8,w),sk_c6)** -> .
% 0.22/0.51 870[3:Rew:852.0,862.4,852.0,862.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,w),sk_c6)** -> .
% 0.22/0.51 877[3:SpR:837.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.22/0.51 879[3:Rew:834.0,877.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.22/0.51 888[3:SpR:860.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.22/0.51 890[3:Rew:24.0,888.0] || -> equal(identity,sk_c5)**.
% 0.22/0.51 891[3:Rew:890.0,123.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.22/0.51 895[3:Rew:890.0,24.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.22/0.51 904[3:SpR:879.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.22/0.51 906[3:Rew:895.0,904.0] || -> equal(sk_c5,sk_c7)**.
% 0.22/0.51 909[3:Rew:906.0,891.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.51 1111[3:SpL:861.0,870.2] || equal(inverse(sk_c2),sk_c6) equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.51 1115[3:Rew:854.0,1111.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.51 1116[3:Obv:1115.0] || equal(inverse(u),sk_c6) equal(sk_c7,v) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(sk_c6,v),sk_c6)** -> .
% 0.22/0.51 1415[3:SpL:861.0,1116.2] || equal(inverse(sk_c2),sk_c6) equal(sk_c7,u) equal(sk_c7,sk_c7) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.51 1418[3:Obv:1415.2] || equal(inverse(sk_c2),sk_c6) equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.51 1419[3:Rew:854.0,1418.0] || equal(sk_c6,sk_c6) equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.51 1420[3:Obv:1419.0] || equal(sk_c7,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.22/0.51 1497[3:SpL:909.0,1420.1] || equal(sk_c7,sk_c7) equal(sk_c6,sk_c6)* -> .
% 0.22/0.51 1503[3:Obv:1497.1] || -> .
% 0.22/0.51 1506[2:Spt:1503.0,4.1,87.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.22/0.51 1507[2:Spt:1503.0,4.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.22/0.51 1510[2:MRR:7.1,1506.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.51 1511[2:MRR:6.1,1506.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.22/0.51 1512[2:MRR:5.1,1506.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.22/0.51 1513[2:MRR:3.1,1506.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.22/0.51 1530[2:SpR:1511.0,110.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.22/0.51 1532[2:Rew:1510.0,1530.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.22/0.51 1533[2:Rew:1512.0,1532.0] || -> equal(sk_c8,sk_c6)**.
% 0.22/0.51 1537[2:Rew:1533.0,1506.0] || equal(multiply(sk_c7,sk_c6),sk_c6)** -> .
% 0.22/0.51 1538[2:Rew:1533.0,1512.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.22/0.51 1549[2:SpR:1513.0,110.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.22/0.51 1551[2:Rew:1507.0,1549.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.22/0.51 1557[2:SpR:1538.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.22/0.51 1559[2:Rew:24.0,1557.0] || -> equal(identity,sk_c5)**.
% 0.22/0.51 1560[2:Rew:1559.0,23.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.22/0.51 1562[2:Rew:1559.0,24.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.22/0.51 1575[2:SpR:1551.0,110.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.22/0.51 1577[2:Rew:1562.0,1575.0] || -> equal(sk_c5,sk_c7)**.
% 0.22/0.51 1580[2:Rew:1577.0,1560.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.51 1584[2:UnC:1580.0,1537.0] || -> .
% 0.22/0.51 % SZS output end Refutation
% 0.22/0.51 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_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 left_identity left_inverse associativity
% 0.22/0.51
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