-
-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathw2.txt
45 lines (37 loc) · 2.47 KB
/
w2.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
% Walsh's 2nd Axiom (CpCCqCprCCNrCCNstqCsr), i.e. 0→((1→(0→2))→((¬2→((¬3→4)→1))→(3→2)))
% TODO: Completeness w.r.t. CpCqp,CCpCqrCCpqCpr,CCNpNqCqp and CCpqCCqrCpr,CCNppp,CpCNpq.
%
% Proof system configuration: pmGenerator -c -n -s CpCCqCprCCNrCCNstqCsr
% SHA-512/224 hash: db25c49b13fec26ecf32e40bde65e4e2273f23b3c022cfd0fa986cff
%
% Full summary: pmGenerator --transform data/w2.txt -f -n -t . -j 1
% Step counting: pmGenerator --transform data/w2.txt -f -n -t . -p -2 -d
% pmGenerator --transform data/w2.txt -f -n -t CpCqp,Cpp,CpCNpq,CCNppp -p -2 -d
% Compact (638 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,Cpp,CpCNpq,CCNppp -j -1 -s CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq,CpCqCrCsCtq,CpCqCrp
% Concrete (1008 bytes): pmGenerator --transform data/w2.txt -f -n -t CpCqp,Cpp,CpCNpq,CCNppp -j -1 -e
CpCCqCprCCNrCCNstqCsr = 1
[0] CCpCCqCCrCqsCCNsCCNturCtsvCCNvCCNwxpCwv = D11
[1] CpCCNCCNqCCNrsCNqCCNtuNpCrqCCNvwtCvCCNqCCNrsCNqCCNtuNpCrq = DD[0]11
[2] CCNCCNpCCNqrCNpCCNstNCuCCvCuwCCNwCCNxyvCxwCqpCCNzasCzCCNpCCNqrCNpCCNstNCuCCvCuwCCNwCCNxyvCxwCqp = D[1]1
[3] CpCCNqCCNrsCNqCCNCCNtCCNuvNpCutwNCxCCyCxzCCNzCCNabyCazCrq = D[2]1
[4] CCCpCCqCprCCNrCCNstqCsruCvu = DD[0][0][3]
% Identity principle (Cpp), i.e. 0→0 ; 35 steps
[5] Cpp = DD[0][4][3]
[6] CCNCCNCpqCCNrsCtCCuCCvCuwCCNwCCNxyvCxwqCrCpqCCNzaCNqCCNpbtCzCCNCpqCCNrsCtCCuCCvCuwCCNwCCNxyvCxwqCrCpq = DD1[0]1
[7] CpCqCrCsCtq = DDDDD1DD[0][6][3]1[3]11
[8] CCpCCqCrCsCtquCCNuCCNvwpCvu = D1D[7]1
% Axiom 1 by Frege (CpCqp), i.e. 0→(1→0) ; 53 steps
[9] CpCqp = DD[8][0]1
[10] CCCNpqrCCNCpsCCNtuCrCCvCCwCvxCCNxCCNyzwCyxsCtCps = D[6][3]
[11] CCNCpCqrCCNstCCNquCNrCCNCvCCwCvxCCNxCCNyzwCyxaNpCsCpCqr = D[0][10]
[12] CCNCpqCCNrsCCtCupCCvCCwCvxCCNxCCNyzwCyxqCrCpq = D[10]D[11][3]
% Axiom 3 by Łukasiewicz (CpCNpq), i.e. 0→(¬0→1) ; 57 steps
[13] CpCNpq = D[12]1
[14] CCpCCqqrCCNrCCNstpCsr = D1[5]
[15] CpCqCrp = DD[0][11][7]
[16] CpCqCCCNCrCCsCrtCCNtCCNuvsCutwNqx = D[11]1
[17] CCpCCqCCNrCCNstCNrCCNCCNuCCNvwNqCvuxNCyCCzCyaCCNaCCNbczCbaCsrdCCNdCCNefpCed = D1[3]
[18] CCNCCNpCCNqrsCqpCCNtuCCNCvCCwCvxCCNxCCNyzwCyxaNsCtCCNpCCNqrsCqp = DD1DD[17][0]11
[19] CpCCNqCCNrsCNqCCNCtpuNCvCCwCvxCCNxCCNyzwCyxCrq = D[2][3]
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 781 steps
[20] CCNppp = DDDD[14]1DDD[0]DDD1[15][0][16]DDD1DDD[0]D1[18][3]DD[0][17][3]DDD1[8]1[3][19]1DDD[0][15]DDD1DD[0]D1[16]DD[0]DDD1DDD1[6]111[3]1DDD1DDD1D[18][3]1[3]1[3][19]1DDD1D[12]DD[0][1]DD[0]DDD1DDD1[4]111[3]1[14]D[4]DD1[9]1