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xamidixamidi
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found 19 shorter proofs for minimal 1-base proof minimization challenge
- solution from #2 (comment) (discussions) - m:(A2:7001↦5401,L1:619↦459) - w1:A2:1925↦1763 - w2:(A2:1264633↦27599,A3:1153↦1007,L1:588991↦11703,L2:405↦367) - w3:(A2:254925↦14557,A3:23321↦4821,L1:16469↦3227,L2:1331↦1283) - w4:(A2:13917↦13819,A3:10779↦10719,L1:12081↦11989,L2:1709↦1703) - w5:(A1:83↦75,A2:157↦153) - w6:(A2:18339↦10343,L1:2743↦1821)
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‎data/m.txt‎

Lines changed: 26 additions & 24 deletions
Original file line numberDiff line numberDiff line change
@@ -7,50 +7,52 @@
77
% Full summary: pmGenerator --transform data/m.txt -f -n -t . -j 1
88
% Step counting: pmGenerator --transform data/m.txt -f -n -t . -p -2 -d
99
% pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -p -2 -d
10-
% Compact (672 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CCCppqCrq,CCCpqrCqr,CCCpNCCCqrCNNqrNstCst,CCpCpqCrCpq,CCCpCqNCCrCNNssNqtCut,CCpqCCrpCrq
11-
% Concrete (8170 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
10+
% Compact (785 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CCCppqCrq,CCCpqrCqr,CpCNNCCqCNNrrss,CCCpNCCCqrCNNqrNstCst,CCpCpqCrCpq,CCpqCCCrCNNssNNpq,CCpqCCrpCrq
11+
% Concrete (6410 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
1212

1313
CCCCCpqCNrNsrtCCtpCsp = 1
1414
[0] CCCCpqCrqCqsCtCqs = D11
1515
[1] CCCpCNqrsCqs = D1[0]
1616
[2] CCCppqCrq = D1[1]
1717
[3] CpCqCrq = D[0][2]
18+
[4] CCCpCqprCsr = D1[3]
1819

1920
% Axiom 1 by Frege (CpCqp), i.e. 0→(1→0) ; 13 steps
20-
[4] CpCqp = D[3]1
21+
[5] CpCqp = D[3]1
2122

22-
[5] CpCqCrr = D[2][2]
23-
[6] CCCpqrCqr = D1D1[5]
23+
[6] CpCqCrr = D[2][2]
24+
[7] CCCpqrCqr = D1D1[6]
2425

2526
% Identity principle (Cpp), i.e. 0→0 ; 19 steps
26-
[7] Cpp = DD[5]11
27+
[8] Cpp = DD[6]11
2728

28-
[8] CpCCpqCrq = D[6]1
29-
[9] CCCpqCrCNNqsCtCrCNNqs = D1D1D[4][1]
30-
[10] CCpqCCCNCCCCCrsCNtNutvCCvrCurwCNqNNpq = DDD1D1DD1[3]111
31-
[11] CpCCCCqrsCNCqrNCCtqCuqCqr = DD1D1[8][0]
29+
[9] CCCCNpNqprCqr = D1[7]
30+
[10] CpCCpqCrq = D[7]1
31+
[11] CCCpqCrCNNqsCtCrCNNqs = D1D1D[5][1]
32+
[12] CCpqCCCNCCCCCrsCNtNutvCCvrCurwCNqNNpq = DDD1D1D[4]111
33+
[13] CpCCCCqrsCNCqrNCCtqCuqCqr = DD1D1[10][0]
3234

3335
% Axiom 3 by Łukasiewicz (CpCNpq), i.e. 0→(¬0→1) ; 41 steps
34-
[12] CpCNpq = DD1[6][6]
36+
[14] CpCNpq = D[9][7]
3537

36-
[13] CCCpNCCCqrCNNqrNstCst = D1D1D[2]D1D[0]D[10]D1D[9]1
37-
[14] CCpCpqCrCpq = DDD1D1D1D[2][13]11
38-
[15] CCCpCqNCCrCNNssNqtCut = D1D1DD1DD1D[11]1D1D1D[2]D1D[0]D[10]D1DD1DD1D1D[2]1[4][0]D[1][0]
38+
[15] CpCNNCCqCNNrrss = D[0]D[12]D1DD1DD1D1D[2]1[5][0]
39+
[16] CCCpNCCCqrCNNqrNstCst = D1D1D[2]D1D[0]D[12]D1D[11]1
40+
[17] CCpCpqCrCpq = DDD1D1D1D[2][16]11
3941

4042
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 163 steps
41-
[16] CCNppp = DD[14]DDD1D1D[9]D[6][8]111
43+
[18] CCNppp = DD[17]DDD1D1D[11]D[7][10]111
4244

4345
% Axiom 3 for Frege by Łukasiewicz (CCNpNqCqp), i.e. (¬0→¬1)→(1→0) ; 175 steps
44-
[17] CCNpNqCqp = DDDDD1D1D[8]D[6]D[13][1]11DD1D1[11][4]1
46+
[19] CCNpNqCqp = DDDDD1D1D[10]D[7]D[16][1]11DD1D1[13][5]1
4547

46-
[18] CCpCpqCpq = DD[14][14]1
47-
[19] CCpqCCCrCNNssNNpq = D1D[18][15]
48+
[20] CCpCpqCpq = DD[17][17]1
49+
[21] CCpqCCCrCNNssNNpq = DDD1D1DD1DD1D[2][9]111DDDD1D1DD1D1D1D[2]D1D[0]DDDD1D1DD1DD1D[4]D1DD1D1D[1]1D1[2]1111[2]D[1][10]11D[15]1
4850

49-
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 619 steps
50-
[20] CCpqCCqrCpr = DD1D[19][19]1
51+
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 459 steps
52+
[22] CCpqCCqrCpr = DD1D[21][21]1
5153

52-
[21] CCCCpqCrqsCCrps = D[20][20]
53-
[22] CCpqCCrpCrq = DD[20]DD1DD1[15]1[18][21]
54+
[23] CCCCpqCrqsCCrps = D[22][22]
55+
[24] CCpqCCrpCrq = DD[22]DD1DD1D1D1DD1DD1D[13]1D1D1D[2]D1[15]D[1][0]1[20][23]
5456

55-
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 7001 steps
56-
[23] CCpCqrCCpqCpr = DD[22][21]D[21]D[22][18]
57+
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 5401 steps
58+
[25] CCpCqrCCpqCpr = DD[24][23]D[23]D[24][20]

‎data/w1.txt‎

Lines changed: 32 additions & 35 deletions
Original file line numberDiff line numberDiff line change
@@ -7,59 +7,56 @@
77
% Full summary: pmGenerator --transform data/w1.txt -f -n -t . -j 1
88
% Step counting: pmGenerator --transform data/w1.txt -f -n -t . -p -2 -d
99
% pmGenerator --transform data/w1.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -p -2 -d
10-
% Compact (1068 bytes): pmGenerator --transform data/w1.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CCNpCCqrpCrp,CCCCpCCNpqrstCst,CCCpqrCqr,CpCCNqCrqCrq,CpCCNqCCNrsqCrq,CCCCNNpCpNpqrCpr,CCNpCqpCrCCNsCpsCqs,CCCCpqCrqsCCrps,CCCCNpCqpprCqr
11-
% Concrete (3144 bytes): pmGenerator --transform data/w1.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
10+
% Compact (1008 bytes): pmGenerator --transform data/w1.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CCNpCCqrpCrp,CCCCpCCNpqrstCst,CCCpqrCqr,CpCCNqCCNrsqCrq,CCpqCpq,CCCCNNpCpNpqrCpr,CCNpCqpCrCCNsCpsCqs,CCCCNpCqpprCqr
11+
% Concrete (2982 bytes): pmGenerator --transform data/w1.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
1212

1313
CCpCCNpqrCsCCNtCrtCpt = 1
1414
[0] CpCCNqCCCNrCsrCtrqCCtCCNtusq = D11
1515
[1] CpCCNqCCCrCCNrstuqCuq = D1[0]
1616
[2] CpCCNqCCrsqCsq = D1[1]
17-
[3] CCNpCCCqCCNqrstpCtp = D[1]1
18-
[4] CCNpCCqrpCrp = D[2]1
19-
[5] CCCCNpCqpCrpsCCrCCNrtqs = D[4][0]
20-
[6] CCCCpCCNpqrstCst = D[4][1]
21-
[7] CCCpqrCqr = D[4][2]
22-
[8] CCCNCpCCNpqrstCuCCNvCtvCCpCCNpqrv = D[6]1
23-
[9] CCCNpqrCsCCNtCrtCpt = D[7]1
24-
[10] CpCCNqCrqCCNrCCCNsCCCNtCutCvtsCCvCCNvwusrq = D1DD[8][0]1
25-
[11] CpCCNqCrqCCNrCCCNsCCtusCusrq = D1DD[8][2]1
26-
[12] CpCCNqCrqCrq = D1D[7][5]
27-
[13] CpCCNqCCNrsqCrq = D1DDD[9]11[2]
28-
[14] CpCqCCNrCprCCsCCNstur = D[6][8]
17+
[3] CCNpCCqrpCrp = D[2]1
18+
[4] CCCCNpCqpCrpsCCrCCNrtqs = D[3][0]
19+
[5] CCCCpCCNpqrstCst = D[3][1]
20+
[6] CCCpqrCqr = D[3][2]
21+
[7] CCCNCpCCNpqrstCuCCNvCtvCCpCCNpqrv = D[5]1
22+
[8] CCCNpqrCsCCNtCrtCpt = D[6]1
23+
[9] CpCCNqCrqCCNrCCCNsCCCNtCutCvtsCCvCCNvwusrq = D1DD[7][0]1
24+
[10] CpCCNqCrqCrq = D1D[6][4]
25+
[11] CpCCNqCCNrsqCrq = D1DDD[8]11[2]
26+
[12] CpCqCCNrCprCCsCCNstur = D[5][7]
2927

3028
% Axiom 1 by Frege (CpCqp), i.e. 0→(1→0) ; 33 steps
31-
[15] CpCqp = D[7][6]
29+
[13] CpCqp = D[6][5]
3230

33-
[16] CCNpCqpCqp = D[12]1
34-
[17] CCpqCCNpCCCNrCCCNsCtsCusrCCuCCNuvtrpq = D[4][10]
35-
[18] CpCqCCNrCprCsr = D[6][9]
36-
[19] CCpqCpq = D[4][12]
37-
[20] CCCNpqrCpr = D[4][13]
38-
[21] CpCqCCNrCsrCNpr = D[20]1
31+
[14] CCpqCCNpCCCNrCCCNsCtsCusrCCuCCNuvtrpq = D[3][9]
32+
[15] CpCqCCNrCprCsr = D[5][8]
33+
[16] CCpqCpq = D[3][10]
34+
[17] CCCNpqrCpr = D[3][11]
35+
[18] CCCCNpCqpCCrCCNrstpuCqu = D[3]D1[12]
36+
[19] CpCqCCNrCCsprCtr = D[6][15]
3937

4038
% Axiom 3 by Łukasiewicz (CpCNpq), i.e. 0→(¬0→1) ; 87 steps
41-
[22] CpCNpq = D[20][19]
39+
[20] CpCNpq = D[17][16]
4240

43-
[23] CCCCNNpCpNpqrCpr = D[4]D1D[6]D[6]D[5]D[5][7]
44-
[24] CCNpCqpCrCCNsCpsCqs = DD[4]D[9]DD[10]1[10][9]
45-
[25] CpCCpNpq = D[23][7]
41+
[21] CCCCNNpCpNpqrCpr = D[3]D1D[5]D[5]D[4]D[4][6]
42+
[22] CCNpCqpCrCCNsCpsCqs = DD[3]D[8]DD[9]1[9][8]
43+
[23] CpCCpNpq = D[21][6]
44+
[24] CCCCNpCqpCrpsCCNqCrqs = D[3]D1[22]
45+
[25] CCCCNpCqpCrpsCCrqs = D[3]D1D[6][22]
4646

4747
% Identity principle (Cpp), i.e. 0→0 ; 143 steps
48-
[26] Cpp = DD[13]1[25]
48+
[26] Cpp = DD[11]1[23]
4949

5050
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 151 steps
51-
[27] CCpqCCqrCpr = D[7]DD[4]D1[24][7]
51+
[27] CCpqCCqrCpr = D[6]D[24][6]
5252

53-
[28] CNpCpq = D[23]D[4]D[9][15]
54-
[29] CCCCpqCrqsCCrps = D[4]D[9]DD[4][11][27]
55-
[30] CCCCNpCqpCCrCCNrstpuCqu = D[4]D1[14]
56-
[31] CCCCNpCqpprCqr = D[4]D1D[30]D[5]D[4]D[14][28]
53+
[28] CCCCNpCqpprCqr = D[3]D1D[18]D[4]D[3]D[12]D[21]D[3]D[8][13]
5754

5855
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 323 steps
59-
[32] CCNppp = D[4]D[31][19]
56+
[29] CCNppp = D[3]D[28][16]
6057

6158
% Axiom 3 for Frege by Łukasiewicz (CCNpNqCqp), i.e. (¬0→¬1)→(1→0) ; 343 steps
62-
[33] CCNpNqCqp = DDD1DD[4]D1D[7][24]D[4]DD[7][18][25]1[13]
59+
[30] CCNpNqCqp = DDD1D[25]D[3]D[19][23]1[11]
6360

64-
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 1925 steps
65-
[34] CCpCqrCCpqCpr = DD[29]D[4]D1D[30]DD[4]D[9]D[17][7]D[5]D[4]D[18][28]D[29]DD[16]DD[4]D[3]DD[4]D1DDD[18]D[6]D[7]D[5][22]1[11]D[7]D[7][21]D[31][7]DD[4]D[3]DD[4]D[9]D[4]D1DD[4]D1[18]DDD[9]D[4]D[9]D[16]D[20][17]1[0][21]D[6]D[6]DD[4]D1DD[4]D[8]DD[4]D1D[17]1[7]1[7]
61+
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 1763 steps
62+
[31] CCpCqrCCpqCpr = DD[25]D[3]D1D[28]D[6]D[5]D[6]D[4]D[3]D[15][2]DD[3]D[8]DD[3]D1DD[7][2]1[27]DDDD1D[6]D[24]D[3]D[19][20]1D[18]D[4]DD[3]D1D[3]DD[6][12]D[6][13][16]DD[3]DD[1]1DD[3]D[8]D[3]D1DD[3]D1[15]DDD[8]D[3]D[8]DD[10]1D[17][14]1[0]D[17]1D[5]D[5]DD[3]D1DD[3]D[7]DD[3]D1D[14]1[6]1[6]

‎data/w2.txt‎

Lines changed: 48 additions & 94 deletions
Original file line numberDiff line numberDiff line change
@@ -7,119 +7,73 @@
77
% Full summary: pmGenerator --transform data/w2.txt -f -n -t . -j 1
88
% Step counting: pmGenerator --transform data/w2.txt -f -n -t . -p -2 -d
99
% pmGenerator --transform data/w2.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -p -2 -d
10-
% Compact (3083 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq,CCCNpqrCCNCpsCCNtuCrCCvCCwCvxCCNxCCNyzwCyxsCtCps,CpCqCrCsCtq,CpCqCrCNps,CCCNpqrCCNCpsCCNtuNrCtCps,CpCCNqCCNrsCNqCCNCtCCuCtvCCNvCCNwxuCwvyNzCzCrq,CpCqCrp,CpCqCrCsCtp,CpCNCqCNprs,CpCCNqCCNCCNrCCNstNCNpuCsrvNCwwq,CCNCpCqrrCpCqr,CNCpCqNrCsCtCur,CNNpCqCrCsp,CCNpCCNNqrqCNqp,CCNCCpqqCCNrspCrCCpqq,CNCpCqrCsNr,CCNCpCqrCCNstCNrCCNquCprCsCpCqr,CCpqCpCrq,CCNCCNCpqCpqqCCNrspCrCCNCpqCpqq,CCNCCpqqpCCpqq,CCNppCCpqq,CCCpqrCqr,CCpCqCprCqCpr,CCCpqCrpCrp,CCpCqCrNpCqCrNp,CCNpCqCrpCqCrp,CCpCNCpqrCNCpqr,CCpCNNpqCNNpq,CCNNCpqpp,CpCCpqCrq,CpCqCCprCsr,CCNpCCpqqCCpqq,CCpNqCpCqr,CNCCpqCprq,CCpqCpCCqrr,CCNCpqrCCrqCpq
11-
% Concrete (1855466 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
10+
% Compact (1620 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq,CCCNpqrCCNCpsCCNtuCrCCvCCwCvxCCNxCCNyzwCyxsCtCps,CCpCCqCrCsCtquCCNuCCNvwpCvu,CpCCNqCCNrsCNqCCNCtCCuCtvCCNvCCNwxuCwvyNzCzCrq,CpCCNqCCNCrCNpstNCuCCvCuwCCNwCCNxyvCxwq,CpCCNqCCNrsCpqCrq,CCpCCqCCNrCCNCsCNqtuNCvCwCCxCwyCCNyCCNzaxCzyrbCCNbCCNcdpCcb,CNCpCqNrCsCtCur,CCNCCpqCrqCCNstCNqCCNrupCsCCpqCrq,CCNCCpqqpCCpqq,CCpCqCprCqCpr,CCpqCCNppq,CCpCqrCCqpCqr,CCpCqrCpCqCsr
11+
% Concrete (40960 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
1212

1313
CpCCqCprCCNrCCNstqCsr = 1
1414
[0] CCpCCqCCrCqsCCNsCCNturCtsvCCNvCCNwxpCwv = D11
1515
[1] CCNCCNCCNpCCNqrsCqpCCNtuvCtCCNpCCNqrsCqpCCNwxCsCvpCwCCNCCNpCCNqrsCqpCCNtuvCtCCNpCCNqrsCqp = D[0]1
1616
[2] CCNCpqCCNrsCCCNtCCNuvNpCutCCwCCxCwyCCNyCCNzaxCzyqCrCpq = D[0][0]
1717
[3] CCNCCNCpqCCNrsCtCCuCCvCuwCCNwCCNxyvCxwqCrCpqCCNzaCNqCCNpbtCzCCNCpqCCNrsCtCCuCCvCuwCCNwCCNxyvCxwqCrCpq = DD1[0]1
1818
[4] CpCCNCCNqCCNrsCNqCCNtuNpCrqCCNvwtCvCCNqCCNrsCNqCCNtuNpCrq = D[1]1
19-
[5] CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq = DD[4]11
20-
[6] CCpCCqCCNrCCNstCNrCCNCCNuCCNvwNqCvuxNCyCCzCyaCCNaCCNbczCbaCsrdCCNdCCNefpCed = D1[5]
21-
[7] CCNCpqCCNrsCCtpCCuCCvCuwCCNwCCNxyvCxwqCrCpq = D[6][0]
22-
[8] CCpqCCNCCNqCCNrstCrqCCNuvpCuCCNqCCNrstCrq = D[1][5]
23-
[9] CCCpCCqCprCCNrCCNstqCsruCvu = D[2][5]
24-
[10] CCCNpqrCCNCpsCCNtuCrCCvCCwCvxCCNxCCNyzwCyxsCtCps = D[3][5]
25-
[11] CCNpCCNqrCCsCCtCsuCCNuCCNvwtCvupCqp = D[0][9]
26-
[12] CCNCpCqrCCNstCCNquCNrCCNCvCCwCvxCCNxCCNyzwCyxaNpCsCpCqr = D[0][10]
27-
[13] CCNCCNCpCqrCCNstCCNquvCsCpCqrCCNwxCNCqrCCNpyCvCCzCCaCzbCCNbCCNcdaCcbrCwCCNCpCqrCCNstCCNquvCsCpCqr = DD1[10]1
28-
[14] CCNCCNpCCNqrsCqpCCNtuCCNCvCCwCvxCCNxCCNyzwCyxaNsCtCCNpCCNqrsCqp = DD1D[7]11
19+
[5] CCNCCNpCCNqrCNpCCNstNCuCCvCuwCCNwCCNxyvCxwCqpCCNzasCzCCNpCCNqrCNpCCNstNCuCCvCuwCCNwCCNxyvCxwCqp = D[4]1
20+
[6] CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq = D[5]1
21+
[7] CCpCCqCCNrCCNstCNrCCNCCNuCCNvwNqCvuxNCyCCzCyaCCNaCCNbczCbaCsrdCCNdCCNefpCed = D1[6]
22+
[8] CCNCpqCCNrsCCtpCCuCCvCuwCCNwCCNxyvCxwqCrCpq = D[7][0]
23+
[9] CCpqCCNCCNqCCNrstCrqCCNuvpCuCCNqCCNrstCrq = D[1][6]
24+
[10] CCCNpqrCCNCpsCCNtuCrCCvCCwCvxCCNxCCNyzwCyxsCtCps = D[3][6]
25+
[11] CCNCpCqrCCNstCCNquCNrCCNCvCCwCvxCCNxCCNyzwCyxaNpCsCpCqr = D[0][10]
26+
[12] CCNCCNpCCNqrsCqpCCNtuCCNCvCCwCvxCCNxCCNyzwCyxaNsCtCCNpCCNqrsCqp = DD1D[8]11
2927

3028
% Identity principle (Cpp), i.e. 0→0 ; 35 steps
31-
[15] Cpp = D[11][5]
29+
[13] Cpp = DD[0]D[2][6][6]
3230

33-
[16] CCNpCCNCqCCrCqsCCNsCCNturCtsvNwCwCxp = D[12][5]
34-
[17] CCCNpqCrCCsCCtCsuCCNuCCNvwtCvuxCCNCpCyxCCNzaCCNybrCzCpCyx = D[13][5]
35-
[18] CNpCCNqCCNrspCrq = D[14][5]
36-
[19] CCpCCqqrCCNrCCNstpCsr = D1[15]
37-
[20] CCNCCNpCCNqrCspCqpCCNtusCtCCNpCCNqrCspCqp = D[19]1
38-
[21] CpCqCCCNqrsCts = DD[17]11
39-
[22] CCNCCNpCCNqrCspCqpCCNtuCNCCNpCCNqrCspCqpCCNCvCCwCvxCCNxCCNyzwCyxasCtCCNpCCNqrCspCqp = D[0][20]
40-
[23] CpCqCrCsCtq = DDDDD1DD[0][3][5]1[5]11
41-
[24] CCpCCqCrCsCtquCCNuCCNvwpCvu = D1D[23]1
42-
[25] CpCqCrCNps = D[2][21]
43-
[26] CCNCpCNqrCCNstqCsCpCNqr = D[0][25]
44-
[27] CCCNpqrCCNCpsCCNtuNrCtCps = DDD1[18]1[5]
45-
[28] CpCCNqCCNrsCNqCCNCtCCuCtvCCNvCCNwxuCwvyNzCzCrq = D[7]DD[0]DDD1DDD1[3]111[5]1
31+
[14] CCNpCCNCqCCrCqsCCNsCCNturCtsvNwCwCxp = D[11][6]
32+
[15] CCCNpqCrCCsCCtCsuCCNuCCNvwtCvuxCCNCpCyxCCNzaCCNybrCzCpCyx = DDD1[10]1[6]
33+
[16] CNpCCNqCCNrspCrq = D[12][6]
34+
[17] CCpCCqqrCCNrCCNstpCsr = D1[13]
35+
[18] CCNCCNpCCNqrCspCqpCCNtusCtCCNpCCNqrCspCqp = D[17]1
36+
[19] CpCqCrCsCtq = DDDDD1DD[0][3][6]1[6]11
37+
[20] CCpCCqCrCsCtquCCNuCCNvwpCvu = D1D[19]1
38+
[21] CCNCpCNqrCCNstqCsCpCNqr = D[0]D[2]DD[15]11
39+
[22] CCCNpqrCCNCpsCCNtuNrCtCps = DDD1[16]1[6]
40+
[23] CpCCNqCCNrsCNqCCNCtCCuCtvCCNvCCNwxuCwvyNzCzCrq = D[8]DD[0]DDD1DDD1[3]111[6]1
4641

4742
% Axiom 1 by Frege (CpCqp), i.e. 0→(1→0) ; 53 steps
48-
[29] CpCqp = DD[24][0]1
43+
[24] CpCqp = DD[20][0]1
4944

50-
[30] CCpCCqCrqsCCNsCCNtupCts = D1[29]
51-
[31] CCCNCpCCqCprCCNrCCNstqCsruvCCNwCCNxyCvwCxw = D[22][5]
52-
[32] CCNCpqCCNrsCCtCupCCvCCwCvxCCNxCCNyzwCyxqCrCpq = D[10][16]
45+
[25] CCNCpqCCNrsCCtCupCCvCCwCvxCCNxCCNyzwCyxqCrCpq = D[10][14]
5346

5447
% Axiom 3 by Łukasiewicz (CpCNpq), i.e. 0→(¬0→1) ; 57 steps
55-
[33] CpCNpq = D[32]1
48+
[26] CpCNpq = D[25]1
5649

57-
[34] CCpCCqCrCNsCCNtCCNuvsCutwCCNwCCNxypCxw = D1DD[0]DD[8][14][5]1
58-
[35] CCpCCqCCrCqsCCNsCCNturCtsvCpCwCxv = DD[6][17][5]
59-
[36] CpCqCNCrps = D[26][5]
60-
[37] CCNCNCpqrCCNstqCsCNCpqr = D[0][36]
61-
[38] CpCqCrp = DD[0][12][23]
62-
[39] CCNpCCNqrNsCsCqp = DD[0][31][5]
63-
[40] CpCqCrCsCtp = DD[0]DDD1DDD1D[21]1111[5][5]
64-
[41] CpCNCqCNprs = D[11]DD[6]DDD1[25]111
65-
[42] CpCCNqCCNrsCpqCrq = D[22][28]
66-
[43] CCNCNpqCCNrspCrCNpq = D[0]DDD1[38][0]D[12]1
67-
[44] CpCCNqCCNCCNrCCNstNCNpuCsrvNCwwq = D[32]DD[0][4]DD[0]DDD1DDD1[9]111[5]1
68-
[45] CCpCCqCCNrCCNCCNsCCNtuNCNqvCtswNCxxryCCNyCCNzapCzy = D1[44]
69-
[46] CCNCpCqrrCpCqr = DD[0]DDD[6]DD[0][13][5][5]DD[0]DD[0]D[8]1[5][5][5]
70-
[47] CNCpCqNrCsCtCur = DD[34]DDD1[24]1[5][5]
71-
[48] CNNpCqCrCsp = DD[34]DDD1[30]1[5][5]
72-
[49] CCNpCCNNqrqCNqp = DDDD1[41]1[29]1
73-
[50] CCNCCpqqCCNrspCrCCpqq = D[45][42]
74-
[51] CNCpCqrCsNr = DD[43][47]1
75-
[52] CpCCpqq = D[50][44]
76-
[53] CCNCpCqrCCNstCNrCCNquCprCsCpCqr = D[45]DDD1[42]1[44]
77-
[54] CCpqCpCrq = D[53][28]
50+
[27] CpCCNqCCNCrCNpstNCuCCvCuwCCNwCCNxyvCxwq = D[25]DDD[0][7][6][5]
51+
[28] CpCCNqCCNrsCpqCrq = DD[0][18][23]
52+
[29] CCpCCqCCNrCCNCsCNqtuNCvCwCCxCwyCCNyCCNzaxCzyrbCCNbCCNcdpCcb = D1D[25]DD[0]DD[7]DDD1[4]1[6]11
53+
[30] CNCpCqNrCsCtCur = DDD1DD[0]DD[9][12][6]1DDD1[20]1[6][6]
54+
[31] CCNCCpqqCCNrspCrCCpqq = D[29][28]
55+
[32] CCNCpCqrCCNstCNrCCNquCprCsCpCqr = D[29]DDD1[28]1[27]
7856

79-
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 405 steps
80-
[55] CCNppp = DDD[20][51]1[44]
57+
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 367 steps
58+
[33] CCNppp = DDD[18]DDD[0]D[2]DDD1[19]DDD1[11]111[30]11[27]
8159

82-
[56] CCNCCNCpqCpqqCCNrspCrCCNCpqCpqq = D[45]DDD1[55]1[44]
83-
[57] CpCCNCpqCpqq = D[56][44]
84-
[58] CCpqCrCpCsq = D[54][54]
85-
[59] CpCCNCNqqCNqqq = D[56]DDD[0]DD[0][26][5][47]1
86-
[60] CpCCNCNqCrqCNqCrqCrq = D[56][51]
87-
[61] CCNpNqCCNpCCNrsqCrp = DDD1DDD1[57][15]11[44]
88-
[62] CCNCCpqqpCCpqq = D[50][57]
89-
[63] CCNppCCpqq = D[50][59]
90-
[64] CCCpqrCqr = DDD[45][19][44]DDDDDD1DDD1[6]1[5]1[5]1[5][57]
91-
[65] CpCCNqqCCqrr = D[29][63]
92-
[66] CCpCqCprCqCpr = D[62]DD[37]DD[0]DDD1[27]1[5][5]1
60+
[34] CCNCCNCpqCpqqCCNrspCrCCNCpqCpqq = D[29]DDD1[33]1[27]
61+
[35] CCNCCpqCrqCCNstCNqCCNrupCsCCpqCrq = D[29]DDD1DDD1D[31][27]1[27]1[27]
62+
[36] CCCNpqrCCrsCps = D[35][6]
63+
[37] CpCCNCpqCpqq = D[34][27]
64+
[38] CCNpCCNqrsCCspCqp = D[35][27]
65+
[39] CCNCCpqqpCCpqq = D[31][37]
9366

94-
% Axiom 3 for Frege by Łukasiewicz (CCNpNqCqp), i.e. (¬0→¬1)→(1→0) ; 1153 steps
95-
[67] CCNpNqCqp = DD[45][61][44]
67+
% Axiom 3 for Frege by Łukasiewicz (CCNpNqCqp), i.e. (¬0→¬1)→(1→0) ; 1007 steps
68+
[40] CCNpNqCqp = DD[29]DDD1DDD1[37][13]11[27][27]
9669

97-
[68] CCCpqCrpCrp = D[62]DDD1DD[0][8][5]D[27][16][28]
98-
[69] CCpCqCrNpCqCrNp = D[62]D[49][40]
99-
[70] CCNpCqCrpCqCrp = D[62]D[49]D[35][48]
100-
[71] CCpCqNpCqNp = D[69][52]
101-
[72] CCpCNCpqrCNCpqr = D[62]D[68][41]
102-
[73] CCCCpqqCprCpr = D[66]D[50][65]
103-
[74] CCpCNNpqCNNpq = DDD[0][29][60]D[50]DDD[0][38][60]D[50]DDDD[0]DD[8]D[0][18][5][38]1DDD1[36][31][5]
104-
[75] CCNNCpqpp = D[68]D[50]D[39]D[56]D[29]DD[0]DD[0]D[30][18][28][59]
105-
[76] CpCCpqCrq = D[73][58]
106-
[77] CpCqCCprCsr = D[54][76]
107-
[78] CCNpCCpqqCCpqq = D[62]D[71]D[37][65]
108-
[79] CNCpqCCNCprCprr = D[56]D[29][75]
109-
[80] CCpqCpCNqr = D[26][79]
110-
[81] CNNpCCpqCrq = D[74][77]
111-
[82] CCpqCNCprq = D[66]D[72][77]
112-
[83] CCpNqCpCqr = D[70]D[82]D[39][79]
113-
[84] CNCCpqCprq = DD[78]DDD[0][40][79]DD[43][57]D[69]D[80]DD[53][5][75]D[80][83]
114-
[85] CNCCpqCprCsq = D[54][84]
115-
[86] CNCCpqCprCsCtq = D[35][85]
116-
[87] CCpqCpCCqrr = D[46]DD[64][50]D[78]D[74][86]
117-
[88] CCNCpqrCCrqCpq = D[70]DDDDD[53][44][57][76]DDD[66][81]D[46]D[87]D[67]DD[64]D[0]DDD1[48][0]1DD[66]DD[66][63][77]DD[66]D[73][77][83]DDD[69]D[49][85]D[69]D[49][86]D[49]D[54]DD[66]D[50]D[29]D[71]DDD[6][61][44]D[49]D[54][52]D[72]D[54][82][77]
118-
[89] CCpCqrCCqpCqr = D[88][84]
119-
[90] CCpCqrCpCqCsr = D[89][58]
70+
[41] CCpCqCprCqCpr = D[39]DDD[0]D[21][6]DD[0]DDD1[22]1[6][6]1
71+
[42] CCpqCCNppq = D[38]D[34]DDD[0]DD[0][21][6][30]1
72+
[43] CCpCqrCCqpCqr = D[38]D[34]D[24]DD[39]DDD1DD[0][9][6]D[22][14][23]D[31]D[24]DDD[29][17][27]D[39]DD[8]DDD[0][15][6]D[20][16]1
73+
[44] CCpCqrCpCqCsr = D[43]DD[0]DD[9]D[32][27][6][6]
12074

121-
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 588991 steps
122-
[91] CCpqCCqrCpr = D[66]D[90]DD[88]D[72][58][89]
75+
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 11703 steps
76+
[45] CCpqCCqrCpr = D[41]D[44]DD[36]D[42]D[32][23][43]
12377

124-
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 1264633 steps
125-
[92] CCpCqrCCpqCpr = DD[91]D[66]D[90]DD[66]DDD[62]D[71]DD[62]DD[27][29][44]D[26][28]D[87][81][77][89][89]
78+
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 27599 steps
79+
[46] CCpCqrCCpqCpr = DD[45]D[41]D[44]DD[36]D[42]D[35][23][43][43]

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