TSTP Solution File: NUM510+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM510+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Mon Jul 18 14:26:57 EDT 2022
% Result : Theorem 6.75s 6.93s
% Output : Refutation 7.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM510+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 00:01:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.75/6.93
% 6.75/6.93 SPASS V 3.9
% 6.75/6.93 SPASS beiseite: Proof found.
% 6.75/6.93 % SZS status Theorem
% 6.75/6.93 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.75/6.93 SPASS derived 12108 clauses, backtracked 2406 clauses, performed 39 splits and kept 6936 clauses.
% 6.75/6.93 SPASS allocated 110697 KBytes.
% 6.75/6.93 SPASS spent 0:00:06.56 on the problem.
% 6.75/6.93 0:00:00.04 for the input.
% 6.75/6.93 0:00:00.05 for the FLOTTER CNF translation.
% 6.75/6.93 0:00:00.14 for inferences.
% 6.75/6.93 0:00:00.13 for the backtracking.
% 6.75/6.93 0:00:06.12 for the reduction.
% 6.75/6.93
% 6.75/6.93
% 6.75/6.93 Here is a proof with depth 7, length 281 :
% 6.75/6.93 % SZS output start Refutation
% 6.75/6.93 1[0:Inp] || -> aNaturalNumber0(sz00)*.
% 6.75/6.93 2[0:Inp] || -> aNaturalNumber0(sz10)*.
% 6.75/6.93 3[0:Inp] || -> aNaturalNumber0(xn)*.
% 6.75/6.93 4[0:Inp] || -> aNaturalNumber0(xm)*.
% 6.75/6.93 5[0:Inp] || -> aNaturalNumber0(xp)*.
% 6.75/6.93 6[0:Inp] || -> aNaturalNumber0(skc10)*.
% 6.75/6.93 7[0:Inp] || -> isPrime0(xp)*.
% 6.75/6.93 10[0:Inp] || -> aNaturalNumber0(xk)*.
% 6.75/6.93 12[0:Inp] || -> aNaturalNumber0(xr)*.
% 6.75/6.93 13[0:Inp] || -> isPrime0(xr)*.
% 6.75/6.93 14[0:Inp] || -> aNaturalNumber0(skc15)*.
% 6.75/6.93 15[0:Inp] || -> aNaturalNumber0(skc14)*.
% 6.75/6.93 16[0:Inp] || -> aNaturalNumber0(skc16)*.
% 6.75/6.93 19[0:Inp] || -> aNaturalNumber0(skc19)*.
% 6.75/6.93 23[0:Inp] || -> aNaturalNumber0(skf11(u))*.
% 6.75/6.93 26[0:Inp] || -> doDivides0(xr,xk)*.
% 6.75/6.93 28[0:Inp] || -> doDivides0(xr,xn)*.
% 6.75/6.93 29[0:Inp] || equal(sz10,sz00)** -> .
% 6.75/6.93 33[0:Inp] || equal(xp,sz00)** -> .
% 6.75/6.93 34[0:Inp] || equal(xp,sz10)** -> .
% 6.75/6.93 35[0:Inp] || sdtlseqdt0(xp,xn)* -> .
% 6.75/6.93 37[0:Inp] || equal(xp,xn)** -> .
% 6.75/6.93 41[0:Inp] || equal(xk,sz00)** -> .
% 6.75/6.93 43[0:Inp] || equal(xr,sz00)** -> .
% 6.75/6.93 44[0:Inp] || equal(xr,sz10)** -> .
% 6.75/6.93 45[0:Inp] || equal(xk,xp)** -> .
% 6.75/6.93 47[0:Inp] || -> aNaturalNumber0(sdtsldt0(xn,xr))* SkC1.
% 6.75/6.93 48[0:Inp] isPrime0(u) || -> SkP1(u)*.
% 6.75/6.93 53[0:Inp] || -> equal(sdtpldt0(xr,skc14),xk)**.
% 6.75/6.93 55[0:Inp] || -> equal(sdtpldt0(xk,skc16),xp)**.
% 6.75/6.93 57[0:Inp] || -> equal(sdtasdt0(xr,skc19),xn)**.
% 6.75/6.93 58[0:Inp] || SkC1 -> aNaturalNumber0(sdtsldt0(xn,xr))*.
% 6.75/6.93 61[0:Inp] || sdtlseqdt0(sdtsldt0(xn,xr),xn)* -> SkC1.
% 6.75/6.93 62[0:Inp] || SkC1 -> equal(sdtsldt0(xn,xr),xn)**.
% 6.75/6.93 64[0:Inp] || -> equal(sdtasdt0(xp,skc10),sdtasdt0(xn,xm))**.
% 6.75/6.93 65[0:Inp] || -> equal(sdtasdt0(xp,xk),sdtasdt0(xn,xm))**.
% 6.75/6.93 67[0:Inp] || -> equal(sdtasdt0(xr,skc15),sdtasdt0(xn,xm))**.
% 6.75/6.93 69[0:Inp] || -> SkC1 equal(sdtasdt0(xr,sdtsldt0(xn,xr)),xn)**.
% 6.75/6.93 70[0:Inp] aNaturalNumber0(u) || -> equal(sdtpldt0(u,sz00),u)**.
% 6.75/6.93 71[0:Inp] aNaturalNumber0(u) || -> equal(sdtpldt0(sz00,u),u)**.
% 6.75/6.93 72[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(u,sz10),u)**.
% 6.75/6.93 74[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(u,sz00),sz00)**.
% 6.75/6.93 75[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(sz00,u),sz00)**.
% 6.75/6.93 76[0:Inp] || SkC1 -> equal(sdtasdt0(xr,sdtsldt0(xn,xr)),xn)**.
% 6.75/6.93 79[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtpldt0(v,u))*.
% 6.75/6.93 80[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtasdt0(v,u))*.
% 6.75/6.93 84[0:Inp] aNaturalNumber0(u) || equal(sdtpldt0(sdtsldt0(xn,xr),u),xn)** -> SkC1.
% 6.75/6.93 85[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(v,u)* sdtlseqdt0(u,v)*.
% 6.75/6.93 88[0:Inp] || -> SkP1(u) equal(u,sz10) equal(u,sz00) doDivides0(skf11(u),u)*.
% 6.75/6.93 89[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtpldt0(v,u),sdtpldt0(u,v))*.
% 6.75/6.93 90[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtasdt0(v,u),sdtasdt0(u,v))*.
% 6.75/6.93 91[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(u,v) -> sdtlseqdt0(v,u)*.
% 6.75/6.93 95[0:Inp] || equal(skf11(u),sz10)** -> SkP1(u) equal(u,sz10) equal(u,sz00).
% 6.75/6.93 96[0:Inp] || equal(skf11(u),u)** -> SkP1(u) equal(u,sz10) equal(u,sz00).
% 6.75/6.93 97[0:Inp] aNaturalNumber0(u) || doDivides0(u,xp)* -> equal(u,xp) equal(u,sz10).
% 6.75/6.93 98[0:Inp] aNaturalNumber0(u) || doDivides0(u,xr)* -> equal(u,xr) equal(u,sz10).
% 6.75/6.93 99[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(u,v))*.
% 6.75/6.93 105[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> sdtlseqdt0(v,u) equal(u,sz00).
% 6.75/6.93 109[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 6.75/6.93 112[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> sdtlseqdt0(v,u)*.
% 6.75/6.93 114[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(u,sdtasdt0(v,w))*+ -> doDivides0(v,u)*.
% 6.75/6.93 116[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(sdtasdt0(u,v),xp)** -> equal(u,xp) equal(u,sz10).
% 6.75/6.93 120[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)*+ sdtlseqdt0(w,v)* -> sdtlseqdt0(w,u)*.
% 6.75/6.93 124[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || -> equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u)))**.
% 6.75/6.93 125[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> aNaturalNumber0(w)* equal(v,sz00).
% 6.75/6.93 134[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtasdt0(w,v),sdtasdt0(w,u))* -> equal(v,u) equal(w,sz00).
% 6.75/6.93 135[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> equal(v,sz00) equal(u,sdtasdt0(v,w))*.
% 6.75/6.93 142[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || doDivides0(v,w) equal(w,sdtasdt0(v,u))* -> equal(u,sdtsldt0(w,v))* equal(v,sz00).
% 6.75/6.93 146[0:MRR:58.0,47.1] || -> aNaturalNumber0(sdtsldt0(xn,xr))*.
% 6.75/6.93 147[0:Rew:62.1,76.1] || SkC1 -> equal(sdtasdt0(xr,xn),xn)**.
% 6.75/6.93 149[0:MRR:142.3,114.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(u,sdtasdt0(v,w))*+ -> equal(v,sz00) equal(w,sdtsldt0(u,v))*.
% 6.75/6.93 198[0:Res:146.0,97.0] || doDivides0(sdtsldt0(xn,xr),xp)* -> equal(sdtsldt0(xn,xr),xp) equal(sdtsldt0(xn,xr),sz10).
% 6.75/6.93 199[0:Res:146.0,98.0] || doDivides0(sdtsldt0(xn,xr),xr)* -> equal(sdtsldt0(xn,xr),xr) equal(sdtsldt0(xn,xr),sz10).
% 6.75/6.93 309[1:Spt:198.1] || -> equal(sdtsldt0(xn,xr),xp)**.
% 6.75/6.93 336[1:Rew:309.0,62.1] || SkC1* -> equal(xp,xn).
% 6.75/6.93 338[1:Rew:309.0,69.1] || -> SkC1 equal(sdtasdt0(xr,xp),xn)**.
% 6.75/6.93 366[1:MRR:336.1,37.0] || SkC1* -> .
% 6.75/6.93 367[1:MRR:338.0,366.0] || -> equal(sdtasdt0(xr,xp),xn)**.
% 6.75/6.93 532[0:Res:88.3,98.1] aNaturalNumber0(skf11(xr)) || -> SkP1(xr) equal(xr,sz10) equal(xr,sz00) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 6.75/6.93 533[0:SSi:532.0,23.0,13.0,12.0] || -> SkP1(xr) equal(xr,sz10) equal(xr,sz00) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 6.75/6.93 534[0:MRR:533.1,533.2,44.0,43.0] || -> SkP1(xr) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 6.75/6.93 537[0:SpR:534.1,88.3] || -> SkP1(xr) equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00) doDivides0(xr,xr).
% 6.75/6.93 540[0:Obv:537.0] || -> equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00) doDivides0(xr,xr).
% 6.75/6.93 541[0:MRR:540.2,540.3,44.0,43.0] || -> equal(skf11(xr),sz10)** SkP1(xr) doDivides0(xr,xr).
% 6.75/6.93 543[0:SpR:541.0,88.3] || -> SkP1(xr)* doDivides0(xr,xr) SkP1(xr)* equal(xr,sz10) equal(xr,sz00) doDivides0(sz10,xr).
% 6.75/6.93 548[0:Obv:543.0] || -> doDivides0(xr,xr) SkP1(xr)* equal(xr,sz10) equal(xr,sz00) doDivides0(sz10,xr).
% 6.75/6.93 549[0:MRR:548.2,548.3,44.0,43.0] || -> doDivides0(xr,xr) SkP1(xr)* doDivides0(sz10,xr).
% 6.75/6.93 550[2:Spt:549.1] || -> SkP1(xr)*.
% 6.75/6.93 551[0:Res:88.3,97.1] aNaturalNumber0(skf11(xp)) || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 6.75/6.93 552[0:SSi:551.0,23.0,7.0,5.0] || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 6.75/6.93 553[0:MRR:552.1,552.2,34.0,33.0] || -> SkP1(xp) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 6.75/6.93 554[3:Spt:553.0] || -> SkP1(xp)*.
% 6.75/6.93 616[1:SpR:90.2,367.0] aNaturalNumber0(xp) aNaturalNumber0(xr) || -> equal(sdtasdt0(xp,xr),xn)**.
% 6.75/6.93 634[3:SSi:616.1,616.0,13.0,12.0,550.0,7.0,5.0,554.0] || -> equal(sdtasdt0(xp,xr),xn)**.
% 6.75/6.93 651[0:SpR:89.2,55.0] aNaturalNumber0(skc16) aNaturalNumber0(xk) || -> equal(sdtpldt0(skc16,xk),xp)**.
% 6.75/6.93 679[0:SSi:651.1,651.0,10.0,16.0] || -> equal(sdtpldt0(skc16,xk),xp)**.
% 6.75/6.93 732[0:SpR:57.0,99.3] aNaturalNumber0(xr) aNaturalNumber0(skc19) || -> equal(skc19,sz00) sdtlseqdt0(xr,xn)*.
% 6.75/6.93 748[3:SpR:634.0,99.3] aNaturalNumber0(xp) aNaturalNumber0(xr) || -> equal(xr,sz00) sdtlseqdt0(xp,xn)*.
% 6.75/6.93 757[3:SSi:748.1,748.0,13.0,12.0,550.0,7.0,5.0,554.0] || -> equal(xr,sz00) sdtlseqdt0(xp,xn)*.
% 6.75/6.93 758[3:MRR:757.0,757.1,43.0,35.0] || -> .
% 6.75/6.93 766[3:Spt:758.0,553.0,554.0] || SkP1(xp)* -> .
% 6.75/6.93 767[3:Spt:758.0,553.1,553.2] || -> equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 6.75/6.93 783[4:Spt:767.0] || -> equal(skf11(xp),xp)**.
% 6.75/6.93 790[4:SpL:783.0,96.0] || equal(xp,xp) -> SkP1(xp)* equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 793[4:Obv:790.0] || -> SkP1(xp)* equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 794[4:MRR:793.1,793.2,34.0,33.0] || -> SkP1(xp)*.
% 6.75/6.93 795[4:MRR:794.0,766.0] || -> .
% 6.75/6.93 796[4:Spt:795.0,767.0,783.0] || equal(skf11(xp),xp)** -> .
% 6.75/6.93 797[4:Spt:795.0,767.1] || -> equal(skf11(xp),sz10)**.
% 6.75/6.93 804[4:SpL:797.0,95.0] || equal(sz10,sz10) -> SkP1(xp)* equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 808[4:Obv:804.0] || -> SkP1(xp)* equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 809[4:MRR:808.1,808.2,34.0,33.0] || -> SkP1(xp)*.
% 6.75/6.93 810[4:MRR:809.0,766.0] || -> .
% 6.75/6.93 811[2:Spt:810.0,549.1,550.0] || SkP1(xr)* -> .
% 6.75/6.93 812[2:Spt:810.0,549.0,549.2] || -> doDivides0(xr,xr)* doDivides0(sz10,xr).
% 6.75/6.93 816[0:SSi:732.1,732.0,19.0,13.0,12.0] || -> equal(skc19,sz00) sdtlseqdt0(xr,xn)*.
% 6.75/6.93 823[2:Res:48.1,811.0] isPrime0(xr) || -> .
% 6.75/6.93 824[2:SSi:823.0,13.0,12.0] || -> .
% 6.75/6.93 825[1:Spt:824.0,198.1,309.0] || equal(sdtsldt0(xn,xr),xp)** -> .
% 6.75/6.93 826[1:Spt:824.0,198.0,198.2] || doDivides0(sdtsldt0(xn,xr),xp)* -> equal(sdtsldt0(xn,xr),sz10).
% 6.75/6.93 827[2:Spt:199.1] || -> equal(sdtsldt0(xn,xr),xr)**.
% 6.75/6.93 831[2:Rew:827.0,61.0] || sdtlseqdt0(xr,xn) -> SkC1*.
% 6.75/6.93 832[2:Rew:827.0,62.1] || SkC1* -> equal(xr,xn).
% 6.75/6.93 834[2:Rew:827.0,69.1] || -> SkC1 equal(sdtasdt0(xr,xr),xn)**.
% 6.75/6.93 885[2:Rew:832.1,147.1] || SkC1 -> equal(sdtasdt0(xn,xn),xn)**.
% 6.75/6.93 922[3:Spt:831.0] || sdtlseqdt0(xr,xn)* -> .
% 6.75/6.93 923[3:MRR:816.1,922.0] || -> equal(skc19,sz00)**.
% 6.75/6.93 925[3:Rew:923.0,57.0] || -> equal(sdtasdt0(xr,sz00),xn)**.
% 6.75/6.93 928[3:Res:91.3,922.0] aNaturalNumber0(xn) aNaturalNumber0(xr) || equal(xr,xn)** -> .
% 6.75/6.93 932[3:SSi:928.1,928.0,13.0,12.0,3.0] || equal(xr,xn)** -> .
% 6.75/6.93 933[3:MRR:832.1,932.0] || SkC1* -> .
% 6.75/6.93 934[3:MRR:834.0,933.0] || -> equal(sdtasdt0(xr,xr),xn)**.
% 6.75/6.93 974[3:SpR:925.0,74.1] aNaturalNumber0(xr) || -> equal(xn,sz00)**.
% 6.75/6.93 978[3:SSi:974.0,13.0,12.0] || -> equal(xn,sz00)**.
% 6.75/6.93 992[3:Rew:978.0,922.0] || sdtlseqdt0(xr,sz00)* -> .
% 6.75/6.93 1005[3:Rew:978.0,934.0] || -> equal(sdtasdt0(xr,xr),sz00)**.
% 6.75/6.93 1066[3:SpR:1005.0,99.3] aNaturalNumber0(xr) aNaturalNumber0(xr) || -> equal(xr,sz00) sdtlseqdt0(xr,sz00)*.
% 6.75/6.93 1071[3:Obv:1066.0] aNaturalNumber0(xr) || -> equal(xr,sz00) sdtlseqdt0(xr,sz00)*.
% 6.75/6.93 1072[3:SSi:1071.0,13.0,12.0] || -> equal(xr,sz00) sdtlseqdt0(xr,sz00)*.
% 6.75/6.93 1073[3:MRR:1072.0,1072.1,43.0,992.0] || -> .
% 6.75/6.93 1074[3:Spt:1073.0,831.0,922.0] || -> sdtlseqdt0(xr,xn)*.
% 6.75/6.93 1075[3:Spt:1073.0,831.1] || -> SkC1*.
% 6.75/6.93 1076[3:MRR:832.0,1075.0] || -> equal(xr,xn)**.
% 6.75/6.93 1077[3:Rew:1076.0,13.0] || -> isPrime0(xn)*.
% 6.75/6.93 1080[3:Rew:1076.0,44.0] || equal(xn,sz10)** -> .
% 6.75/6.93 1081[3:Rew:1076.0,43.0] || equal(xn,sz00)** -> .
% 6.75/6.93 1099[3:Rew:1076.0,534.0] || -> SkP1(xn) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 6.75/6.93 1124[3:MRR:885.0,1075.0] || -> equal(sdtasdt0(xn,xn),xn)**.
% 6.75/6.93 1129[3:Rew:1076.0,1099.2,1076.0,1099.1] || -> SkP1(xn) equal(skf11(xn),xn)** equal(skf11(xn),sz10).
% 6.75/6.93 1226[0:SpR:65.0,99.3] aNaturalNumber0(xp) aNaturalNumber0(xk) || -> equal(xk,sz00) sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 6.75/6.93 1229[0:SSi:1226.1,1226.0,10.0,7.0,5.0] || -> equal(xk,sz00) sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 6.75/6.93 1230[0:MRR:1229.0,41.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 6.75/6.93 1379[0:SpL:553.1,96.0] || equal(xp,xp) -> SkP1(xp) equal(skf11(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 1381[0:Obv:1379.1] || -> equal(skf11(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00).
% 6.75/6.93 1382[0:MRR:1381.0,1381.2,1381.3,95.0,34.0,33.0] || -> SkP1(xp)*.
% 6.75/6.93 1388[3:SpL:1129.1,96.0] || equal(xn,xn) -> SkP1(xn) equal(skf11(xn),sz10)** SkP1(xn) equal(xn,sz10) equal(xn,sz00).
% 6.75/6.93 1390[3:Obv:1388.1] || -> equal(skf11(xn),sz10)** SkP1(xn) equal(xn,sz10) equal(xn,sz00).
% 6.75/6.93 1391[3:MRR:1390.0,1390.2,1390.3,95.0,1080.0,1081.0] || -> SkP1(xn)*.
% 6.75/6.93 1883[0:Res:1230.0,109.2] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 6.75/6.93 1957[0:EqR:112.3] aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 6.75/6.93 1958[0:SpL:55.0,112.3] aNaturalNumber0(u) aNaturalNumber0(xk) aNaturalNumber0(skc16) || equal(xp,u) -> sdtlseqdt0(xk,u)*.
% 6.75/6.93 1968[0:SSi:1957.0,79.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 6.75/6.93 1969[0:SSi:1958.2,1958.1,16.0,10.0] aNaturalNumber0(u) || equal(xp,u) -> sdtlseqdt0(xk,u)*.
% 6.75/6.93 3068[0:SpL:72.1,149.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(u) aNaturalNumber0(sz10) || equal(v,u) -> equal(u,sz00) equal(sdtsldt0(v,u),sz10)**.
% 6.75/6.93 3078[0:SpL:64.0,149.3] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(skc10) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),skc10)**.
% 6.75/6.93 3079[0:SpL:65.0,149.3] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(xk) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xk)**.
% 6.75/6.93 3096[0:SSi:3079.2,3079.1,10.0,7.0,5.0,1382.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xk)**.
% 6.75/6.93 3097[0:MRR:3096.2,33.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(sdtsldt0(u,xp),xk)**.
% 6.75/6.93 3098[0:Rew:3097.2,3078.5] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(skc10) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(xk,skc10).
% 6.75/6.93 3099[0:SSi:3098.2,3098.1,6.0,7.0,5.0,1382.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(xk,skc10).
% 6.75/6.93 3100[0:MRR:3099.2,33.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(xk,skc10).
% 6.75/6.93 3104[0:Obv:3068.0] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(sz10) || equal(u,v) -> equal(v,sz00) equal(sdtsldt0(u,v),sz10)**.
% 6.75/6.93 3105[0:SSi:3104.2,2.0] aNaturalNumber0(u) aNaturalNumber0(v) || equal(u,v) -> equal(v,sz00) equal(sdtsldt0(u,v),sz10)**.
% 6.75/6.93 3168[3:SpL:1124.0,134.3] aNaturalNumber0(xn) aNaturalNumber0(u) aNaturalNumber0(xn) || equal(sdtasdt0(xn,u),xn)** -> equal(u,xn) equal(xn,sz00).
% 6.75/6.93 3178[3:Obv:3168.0] aNaturalNumber0(u) aNaturalNumber0(xn) || equal(sdtasdt0(xn,u),xn)** -> equal(u,xn) equal(xn,sz00).
% 6.75/6.93 3179[3:SSi:3178.1,3.0,1077.0,1391.0] aNaturalNumber0(u) || equal(sdtasdt0(xn,u),xn)** -> equal(u,xn) equal(xn,sz00).
% 6.75/6.93 3180[3:MRR:3179.3,1081.0] aNaturalNumber0(u) || equal(sdtasdt0(xn,u),xn)** -> equal(u,xn).
% 6.75/6.93 4733[0:SpR:71.1,1968.2] aNaturalNumber0(u) aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 6.75/6.93 4748[0:Obv:4733.0] aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 6.75/6.93 4749[0:SSi:4748.0,1.0] aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 6.75/6.93 4768[0:Res:4749.1,109.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 6.75/6.93 4772[0:Obv:4768.0] aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 6.75/6.93 4773[0:SSi:4772.1,1.0] aNaturalNumber0(u) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 6.75/6.93 5943[0:SpR:679.0,1968.2] aNaturalNumber0(skc16) aNaturalNumber0(xk) || -> sdtlseqdt0(skc16,xp)*.
% 6.75/6.93 5958[0:SSi:5943.1,5943.0,10.0,16.0] || -> sdtlseqdt0(skc16,xp)*.
% 6.75/6.93 5963[0:Res:5958.0,120.3] aNaturalNumber0(xp) aNaturalNumber0(skc16) aNaturalNumber0(u) || sdtlseqdt0(u,skc16)* -> sdtlseqdt0(u,xp).
% 6.75/6.93 5966[0:SSi:5963.1,5963.0,16.0,7.0,5.0,1382.0] aNaturalNumber0(u) || sdtlseqdt0(u,skc16)* -> sdtlseqdt0(u,xp).
% 6.75/6.93 7694[0:Res:85.2,5966.1] aNaturalNumber0(skc16) aNaturalNumber0(u) aNaturalNumber0(u) || -> sdtlseqdt0(skc16,u)* sdtlseqdt0(u,xp)*.
% 6.75/6.93 7708[0:Obv:7694.1] aNaturalNumber0(skc16) aNaturalNumber0(u) || -> sdtlseqdt0(skc16,u)* sdtlseqdt0(u,xp)*.
% 6.75/6.93 7709[0:SSi:7708.0,16.0] aNaturalNumber0(u) || -> sdtlseqdt0(skc16,u)* sdtlseqdt0(u,xp)*.
% 6.75/6.93 8710[3:SpL:72.1,3180.1] aNaturalNumber0(xn) aNaturalNumber0(sz10) || equal(xn,xn)* -> equal(xn,sz10).
% 6.75/6.93 8727[3:Obv:8710.2] aNaturalNumber0(xn) aNaturalNumber0(sz10) || -> equal(xn,sz10)**.
% 6.75/6.93 8728[3:SSi:8727.1,8727.0,2.0,3.0,1077.0,1391.0] || -> equal(xn,sz10)**.
% 6.75/6.93 8729[3:MRR:8728.0,1080.0] || -> .
% 6.75/6.93 8738[2:Spt:8729.0,199.1,827.0] || equal(sdtsldt0(xn,xr),xr)** -> .
% 6.75/6.93 8739[2:Spt:8729.0,199.0,199.2] || doDivides0(sdtsldt0(xn,xr),xr)* -> equal(sdtsldt0(xn,xr),sz10).
% 6.75/6.93 8762[0:SSi:1883.1,1883.0,7.0,5.0,1382.2,80.0,3.0,4.0] || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 6.75/6.93 8813[3:Spt:84.0,84.1] aNaturalNumber0(u) || equal(sdtpldt0(sdtsldt0(xn,xr),u),xn)** -> .
% 6.75/6.93 8815[3:SpL:70.1,8813.1] aNaturalNumber0(sdtsldt0(xn,xr)) aNaturalNumber0(sz00) || equal(sdtsldt0(xn,xr),xn)** -> .
% 6.75/6.93 8818[3:SSi:8815.1,1.0] aNaturalNumber0(sdtsldt0(xn,xr)) || equal(sdtsldt0(xn,xr),xn)** -> .
% 6.75/6.93 8819[3:MRR:8818.0,146.0] || equal(sdtsldt0(xn,xr),xn)** -> .
% 6.75/6.93 8820[3:MRR:62.1,8819.0] || SkC1* -> .
% 7.85/8.06 8821[3:MRR:61.1,8820.0] || sdtlseqdt0(sdtsldt0(xn,xr),xn)* -> .
% 7.85/8.06 8822[3:MRR:69.0,8820.0] || -> equal(sdtasdt0(xr,sdtsldt0(xn,xr)),xn)**.
% 7.85/8.06 8896[0:Res:26.0,105.2] aNaturalNumber0(xk) aNaturalNumber0(xr) || -> sdtlseqdt0(xr,xk)* equal(xk,sz00).
% 7.85/8.06 8897[0:SSi:8896.1,8896.0,12.0,13.0,10.0] || -> sdtlseqdt0(xr,xk)* equal(xk,sz00).
% 7.85/8.06 8898[0:MRR:8897.1,41.0] || -> sdtlseqdt0(xr,xk)*.
% 7.85/8.06 8916[0:Res:8898.0,109.2] aNaturalNumber0(xk) aNaturalNumber0(xr) || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 7.85/8.06 8917[0:SSi:8916.1,8916.0,12.0,13.0,10.0] || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 7.85/8.06 8978[0:SpR:53.0,124.3] aNaturalNumber0(u) aNaturalNumber0(skc14) aNaturalNumber0(xr) || -> equal(sdtpldt0(xk,u),sdtpldt0(xr,sdtpldt0(skc14,u)))**.
% 7.85/8.06 8993[0:SSi:8978.2,8978.1,12.0,13.0,15.0] aNaturalNumber0(u) || -> equal(sdtpldt0(xk,u),sdtpldt0(xr,sdtpldt0(skc14,u)))**.
% 7.85/8.06 9031[0:SpL:57.0,149.3] aNaturalNumber0(u) aNaturalNumber0(xr) aNaturalNumber0(skc19) || equal(u,xn) -> equal(xr,sz00) equal(sdtsldt0(u,xr),skc19)**.
% 7.85/8.06 9045[0:SSi:9031.2,9031.1,19.0,12.0,13.0] aNaturalNumber0(u) || equal(u,xn) -> equal(xr,sz00) equal(sdtsldt0(u,xr),skc19)**.
% 7.85/8.06 9046[0:MRR:9045.2,43.0] aNaturalNumber0(u) || equal(u,xn) -> equal(sdtsldt0(u,xr),skc19)**.
% 7.85/8.06 9737[3:SpL:8822.0,149.3] aNaturalNumber0(u) aNaturalNumber0(xr) aNaturalNumber0(sdtsldt0(xn,xr)) || equal(u,xn) -> equal(xr,sz00) equal(sdtsldt0(xn,xr),sdtsldt0(u,xr))*.
% 7.85/8.06 9804[0:SpL:67.0,116.2] aNaturalNumber0(xr) aNaturalNumber0(skc15) || equal(sdtasdt0(xn,xm),xp)** -> equal(xr,xp) equal(xr,sz10).
% 7.85/8.06 9814[0:SSi:9804.1,9804.0,14.0,12.0,13.0] || equal(sdtasdt0(xn,xm),xp)** -> equal(xr,xp) equal(xr,sz10).
% 7.85/8.06 9815[0:MRR:9814.2,44.0] || equal(sdtasdt0(xn,xm),xp)** -> equal(xr,xp).
% 7.85/8.06 10114[0:SpL:534.1,96.0] || equal(xr,xr) -> SkP1(xr) equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00).
% 7.85/8.06 10121[0:Obv:10114.1] || -> equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00).
% 7.85/8.06 10122[0:MRR:10121.0,10121.2,10121.3,95.0,44.0,43.0] || -> SkP1(xr)*.
% 7.85/8.06 10389[0:Res:1969.2,8917.0] aNaturalNumber0(xr) || equal(xr,xp) -> equal(xk,xr)**.
% 7.85/8.06 10390[0:SSi:10389.0,12.0,13.0,10122.0] || equal(xr,xp) -> equal(xk,xr)**.
% 7.85/8.06 10406[0:SpL:10390.1,45.0] || equal(xr,xp)** equal(xr,xp)** -> .
% 7.85/8.06 10418[0:Obv:10406.0] || equal(xr,xp)** -> .
% 7.85/8.06 10420[0:MRR:9815.1,10418.0] || equal(sdtasdt0(xn,xm),xp)** -> .
% 7.85/8.06 10423[0:MRR:8762.1,10420.0] || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> .
% 7.85/8.06 10985[0:EqR:3100.1] aNaturalNumber0(sdtasdt0(xn,xm)) || -> equal(xk,skc10)**.
% 7.85/8.06 10986[0:SSi:10985.0,80.0,3.0,4.2] || -> equal(xk,skc10)**.
% 7.85/8.06 10991[0:Rew:10986.0,45.0] || equal(skc10,xp)** -> .
% 7.85/8.06 10998[0:Rew:10986.0,53.0] || -> equal(sdtpldt0(xr,skc14),skc10)**.
% 7.85/8.06 11107[0:Rew:10986.0,8993.1] aNaturalNumber0(u) || -> equal(sdtpldt0(xr,sdtpldt0(skc14,u)),sdtpldt0(skc10,u))**.
% 7.85/8.06 12038[0:Rew:10986.0,55.0] || -> equal(sdtpldt0(skc10,skc16),xp)**.
% 7.85/8.06 12111[3:Rew:9046.2,9737.5] aNaturalNumber0(u) aNaturalNumber0(xr) aNaturalNumber0(sdtsldt0(xn,xr)) || equal(u,xn)* -> equal(xr,sz00) equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 12112[3:SSi:12111.1,12.0,13.0,10122.0] aNaturalNumber0(u) aNaturalNumber0(sdtsldt0(xn,xr)) || equal(u,xn)* -> equal(xr,sz00) equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 12113[3:MRR:12112.3,43.0] aNaturalNumber0(u) aNaturalNumber0(sdtsldt0(xn,xr)) || equal(u,xn)* -> equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 12114[3:MRR:12113.1,146.0] aNaturalNumber0(u) || equal(u,xn)*+ -> equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 13532[0:Res:7709.2,10423.0] aNaturalNumber0(sdtasdt0(xn,xm)) || -> sdtlseqdt0(skc16,sdtasdt0(xn,xm))*.
% 7.85/8.06 13533[0:SSi:13532.0,80.0,3.0,4.2] || -> sdtlseqdt0(skc16,sdtasdt0(xn,xm))*.
% 7.85/8.06 14399[3:EqR:12114.1] aNaturalNumber0(xn) || -> equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 14400[3:SSi:14399.0,3.0] || -> equal(sdtsldt0(xn,xr),skc19)**.
% 7.85/8.06 14404[3:Rew:14400.0,8821.0] || sdtlseqdt0(skc19,xn)* -> .
% 7.85/8.06 14534[3:SpL:14400.0,135.3] aNaturalNumber0(xn) aNaturalNumber0(xr) || doDivides0(xr,xn) equal(u,skc19) -> equal(xr,sz00) equal(sdtasdt0(xr,u),xn)**.
% 7.85/8.06 14535[3:SpL:14400.0,125.3] aNaturalNumber0(xn) aNaturalNumber0(xr) || doDivides0(xr,xn)* equal(u,skc19) -> aNaturalNumber0(u)* equal(xr,sz00).
% 7.85/8.06 14537[3:SSi:14535.1,14535.0,12.0,13.0,10122.0,3.0] || doDivides0(xr,xn)* equal(u,skc19) -> aNaturalNumber0(u)* equal(xr,sz00).
% 7.85/8.06 14538[3:MRR:14537.0,14537.3,28.0,43.0] || equal(u,skc19) -> aNaturalNumber0(u)*.
% 7.85/8.06 14541[3:SSi:14534.1,14534.0,12.0,13.0,10122.0,3.0] || doDivides0(xr,xn) equal(u,skc19) -> equal(xr,sz00) equal(sdtasdt0(xr,u),xn)**.
% 7.85/8.06 14542[3:MRR:14541.0,14541.2,28.0,43.0] || equal(u,skc19) -> equal(sdtasdt0(xr,u),xn)**.
% 7.85/8.06 14684[3:SpR:14542.1,90.2] aNaturalNumber0(u) aNaturalNumber0(xr) || equal(u,skc19) -> equal(sdtasdt0(u,xr),xn)**.
% 7.85/8.06 14728[3:SSi:14684.1,12.0,13.0,10122.0] aNaturalNumber0(u) || equal(u,skc19) -> equal(sdtasdt0(u,xr),xn)**.
% 7.85/8.06 14729[3:MRR:14728.0,14538.1] || equal(u,skc19) -> equal(sdtasdt0(u,xr),xn)**.
% 7.85/8.06 15089[0:SpR:70.1,11107.1] aNaturalNumber0(skc14) aNaturalNumber0(sz00) || -> equal(sdtpldt0(skc10,sz00),sdtpldt0(xr,skc14))**.
% 7.85/8.06 15103[0:Rew:10998.0,15089.2] aNaturalNumber0(skc14) aNaturalNumber0(sz00) || -> equal(sdtpldt0(skc10,sz00),skc10)**.
% 7.85/8.06 15104[0:SSi:15103.1,15103.0,1.0,15.0] || -> equal(sdtpldt0(skc10,sz00),skc10)**.
% 7.85/8.06 16061[3:SpR:14729.1,99.3] aNaturalNumber0(u) aNaturalNumber0(xr) || equal(u,skc19) -> equal(xr,sz00) sdtlseqdt0(u,xn)*.
% 7.85/8.06 16096[3:SSi:16061.1,12.0,13.0,10122.0] aNaturalNumber0(u) || equal(u,skc19) -> equal(xr,sz00) sdtlseqdt0(u,xn)*.
% 7.85/8.06 16097[3:MRR:16096.0,16096.2,14538.1,43.0] || equal(u,skc19) -> sdtlseqdt0(u,xn)*.
% 7.85/8.06 16164[3:Res:16097.1,14404.0] || equal(skc19,skc19)* -> .
% 7.85/8.06 16167[3:Obv:16164.0] || -> .
% 7.85/8.06 16181[3:Spt:16167.0,84.2] || -> SkC1*.
% 7.85/8.06 16182[3:MRR:62.0,16181.0] || -> equal(sdtsldt0(xn,xr),xn)**.
% 7.85/8.06 16187[3:MRR:147.0,16181.0] || -> equal(sdtasdt0(xr,xn),xn)**.
% 7.85/8.06 16326[3:SpL:16182.0,125.3] aNaturalNumber0(xn) aNaturalNumber0(xr) || doDivides0(xr,xn)* equal(u,xn) -> aNaturalNumber0(u)* equal(xr,sz00).
% 7.85/8.06 16387[3:SSi:16326.1,16326.0,12.0,13.0,10122.0,3.0] || doDivides0(xr,xn)* equal(u,xn) -> aNaturalNumber0(u)* equal(xr,sz00).
% 7.85/8.06 16388[3:MRR:16387.0,16387.3,28.0,43.0] || equal(u,xn) -> aNaturalNumber0(u)*.
% 7.85/8.06 16447[3:SpR:16187.0,90.2] aNaturalNumber0(xn) aNaturalNumber0(xr) || -> equal(sdtasdt0(xn,xr),xn)**.
% 7.85/8.06 16474[3:SSi:16447.1,16447.0,12.0,13.0,10122.0,3.0] || -> equal(sdtasdt0(xn,xr),xn)**.
% 7.85/8.06 16631[3:SpL:16474.0,149.3] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(xr) || equal(u,xn) -> equal(xn,sz00) equal(sdtsldt0(u,xn),xr)**.
% 7.85/8.06 16640[3:Rew:3105.4,16631.5] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(xr) || equal(u,xn)* -> equal(xn,sz00) equal(xr,sz10)**.
% 7.85/8.06 16641[3:SSi:16640.2,16640.1,12.0,13.0,10122.0,3.0] aNaturalNumber0(u) || equal(u,xn)* -> equal(xn,sz00) equal(xr,sz10)**.
% 7.85/8.06 16642[3:MRR:16641.3,44.0] aNaturalNumber0(u) || equal(u,xn)* -> equal(xn,sz00)**.
% 7.85/8.06 16643[3:MRR:16642.0,16388.1] || equal(u,xn)* -> equal(xn,sz00)**.
% 7.85/8.06 17514[3:AED:29.0,16643.0] || -> equal(xn,sz00)**.
% 7.85/8.06 17530[3:Rew:17514.0,13533.0] || -> sdtlseqdt0(skc16,sdtasdt0(sz00,xm))*.
% 7.85/8.06 18016[3:SpR:75.1,17530.0] aNaturalNumber0(xm) || -> sdtlseqdt0(skc16,sz00)*.
% 7.85/8.06 18019[3:SSi:18016.0,4.0] || -> sdtlseqdt0(skc16,sz00)*.
% 7.85/8.06 18031[3:Res:18019.0,4773.1] aNaturalNumber0(skc16) || -> equal(skc16,sz00)**.
% 7.85/8.06 18032[3:SSi:18031.0,16.0] || -> equal(skc16,sz00)**.
% 7.85/8.06 18035[3:Rew:18032.0,12038.0] || -> equal(sdtpldt0(skc10,sz00),xp)**.
% 7.85/8.06 18077[3:Rew:15104.0,18035.0] || -> equal(skc10,xp)**.
% 7.85/8.06 18078[3:MRR:18077.0,10991.0] || -> .
% 7.85/8.06 % SZS output end Refutation
% 7.85/8.06 Formulae used in the proof : mSortsC mSortsC_01 m__1837 m__1860 m__2306 m__2342 m__2362 m__2377 m__2487 m__1799 m__1870 m__2287 m__2327 m__ m_AddZero m_MulUnit m_MulZero mSortsB mSortsB_02 mLETotal mAddComm mMulComm mMonMul2 mDivLE mLEAsym mDefLE mDefDiv mLETran mAddAsso mDefQuot mMulCanc
% 7.85/8.06
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