-
-
Notifications
You must be signed in to change notification settings - Fork 3
Expand file tree
/
Copy pathm.txt
More file actions
116 lines (97 loc) · 7.23 KB
/
Copy pathm.txt
File metadata and controls
116 lines (97 loc) · 7.23 KB
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
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
% Meredith's Axiom (CCCCCpqCNrNsrtCCtpCsp), i.e. ((((0→1)→(¬2→¬3))→2)→4)→((4→0)→(3→0))
% Completeness follows w.r.t. CpCqp,CCpCqrCCpqCpr,CCNpNqCqp and CCpqCCqrCpr,CCNppp,CpCNpq.
%
% Proof system configuration: pmGenerator -c -n -s CCCCCpqCNrNsrtCCtpCsp
% SHA-512/224 hash: 478804cd4793bc7f87041d99326aff4595662146d8a68175dda22bed
%
% Full summary: pmGenerator --transform data/m.txt -f -n -t _
% Step counting: pmGenerator --transform data/m.txt -f -n -t . -p -2 -d
% - all: pmGenerator --transform data/m.txt -f -n -t _ -p -2 -d
% - targets: pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq,CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -p -2 -d
% - 1st PMC: pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -p -2 -d
% - 2nd PMC: pmGenerator --transform data/m.txt -f -n -t CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -p -2 -d
% Compact (2309 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq,CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -j -1 -s CCCppqCrq,CpCqCNpr,CCCpqCqrCsCqr,CCCpqrCqr,CCCpqCrCNNqsCtCrCNNqs,CCpqCCCNCCCCCrsCNtNutvCCvrCurwCNqNNpq,CCCpCNNqqrCsr,CCpqCCCNNprCNqNCsNpq,CCCpNCCCqrCNNqrNstCst,CCCpqrCCCqsCNrNpr,CCCCpqCrqsCps,CpCNCCCqCNNrrsts,CpCCNqNrCrq,CCpqCCCrCsspq,CCpqCCCCrsCNNrsNCptq,CCpCqrCCCpsrCqr,CCCpqrCCpCpqr,CCCCpqCrqCCrpsCtCCrps,CCCpCqrsCCqCCNptrs
% - 1st PMC (680 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -s CCCppqCrq,CCCpqrCqr,CCCpNCCCqrCNNqrNstCst,CCpqCCCrCsspq,CCpqCCCCrsCNNrsNCptq
% - 2nd PMC (2097 bytes): pmGenerator --transform data/m.txt -f -n -t CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -j -1 -s CCCppqCrq,CpCqCNpr,CpCqp,CCCpqrCqr,CCpqCCCNCCCCCrsCNtNutvCCvrCurwCNqNNpq,CCCpCNNqqrCsr,CCCpNCCCqrCNNqrNstCst,CCCpqrCCCqsCNrNpr,CCCCpqCrqsCps,CpCNCCCqCNNrrsts,CCpqCCCrCsspq,CCpqCCCCrsCNNrsNCptq,CCpCqrCCCpsrCqr,CCCpqrCCpCpqr,CCNpqCCqpCrp,CCCCpqCrqsCCrps,CCCCpqCrqCCrpsCtCCrps,CCCpCqrsCCqCCNptrs
% Concrete (19327 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq,CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -j -1 -e
% - 1st PMC (2116 bytes): pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -e
% - 2nd PMC (17238 bytes): pmGenerator --transform data/m.txt -f -n -t CCpCCNpqrCsCCNtCrtCpt,CpCCqCprCCNrCCNstqCsr,CpCCNqCCNrsCptCCtqCrq,CpCCNqCCNrsCtqCCrtCrq,CCpqCCCrCstCqCNsNpCps,CCCpqCCCNrNsrtCCtpCsp -j -1 -e
CCCCCpqCNrNsrtCCtpCsp = 1
[0] CCCCpqCrqCqsCtCqs = D11
[1] CCCpCNqrsCqs = D1[0]
[2] CCCppqCrq = D1[1]
[3] CpCCCNpqrCsr = D[1]1
[4] CpCqCNpr = D[1][0]
[5] CpCCCCCqrCNsNtsqCtq = D[2]1
[6] CCCpqCNCCCqrCNsNpstCuCNCCCqrCNsNpst = D1D1[3]
[7] CpCqCrq = D[0][2]
[8] CCCpCqprCsr = D1[7]
[9] CCCpqCqrCsCqr = D1D[5]1
[10] CpCqCNCCrqCsqt = D[0][4]
% Axiom 1 by Frege (CpCqp), i.e. 0→(1→0) ; 13 steps
[11] CpCqp = D[7]1
[12] CpCqCNCrCNpst = D[1][4]
[13] CpCqCrr = D[2][2]
[14] CCCpCqqrCsr = D1[13]
[15] CCCpqrCqr = D1[14]
% Identity principle (Cpp), i.e. 0→0 ; 19 steps
[16] Cpp = DD[13]11
[17] CpCCpqCrq = D[15]1
[18] CCCpqCrCNNqsCtCrCNNqs = D1D1D[11][1]
[19] CpCqCNCrqs = D[9][4]
[20] CCpqCCCNCCCCCrsCNtNutvCCvrCurwCNqNNpq = DDD1D1D[8]111
[21] CCCpqCCCqrCNsNpsCtCCCqrCNsNps = D1D1[17]
[22] CCCCpqCNNpqrCsr = D1D[18]1
[23] CpCCCCqrsCNCqrNCCtqCuqCqr = D[21][0]
[24] CCCpqCCNqNrsCrCCNqNrs = D1D1[23]
[25] CCCpqCrNqCsCrNq = D1D1DD1DD1D[8][2]11
[26] CCCpqpCrp = D1D[23]1
[27] CCCpCNNqqrCsr = D1DD1DD1D1[5][11][0]
% Axiom 3 by Łukasiewicz (CpCNpq), i.e. 0→(¬0→1) ; 41 steps
[28] CpCNpq = DD1[15][15]
[29] CpCCCqprCsr = D[15][17]
[30] CCCNCCCCCpqCNrNsrtCCtpCspuCNCvwNNCCxCyywCvw = D[20][14]
[31] CCCNCCCCCpqCNrNsrtCCtpCspuCNCvwNNCCCxyCNNxywCvw = D[20][22]
[32] CCpqCCCNNprCNqNCsNpq = DDD1D1DD1DD1D[8]D1D[6]D1[2]1111
[33] CCCpNCCCqrCNNqrNstCst = D1D1D[2]D1D[0][31]
[34] CCCpqrCCCqsCNrNpr = DDD1D1[29][17]1
[35] CCCpqCNCCprCsrNCCCrtCNuNsuCCprCsr = D[34]1
[36] CCpCpqCrCpq = DDD1D1D1D[2][33]11
[37] CCpCqCprCsCqCpr = DDD1D1D1D[9]D[33][11]11
[38] CCCCpqCrqsCps = D1DD1D1D[2]D1D[26]D1D1D[2]D1D[0]D[20][27]1
[39] CpCNCCCqCNNrrsts = DD[35]D[1]D[19]1[27]
[40] CpCCNqNrCrq = D[37]D[24][11]
% Axiom 3 for Frege by Łukasiewicz (CCNpNqCqp), i.e. (¬0→¬1)→(1→0) ; 157 steps
[41] CCNpNqCqp = D[40]1
% Axiom 2 by Łukasiewicz (CCNppp), i.e. (¬0→0)→0 ; 163 steps
[42] CCNppp = DD[36]DDD1D1D[18][29]111
[43] CCpqCCCrCsspq = D1D[30][39]
[44] CCCCpqCrqsCCCCCqtCNuNrups = D1D[43]1
[45] CCpqCCCCrsCNNrsNCptq = D[35]D[33]DDDDD1D1DD1D[9][12][6]11[15]1
[46] CCpCqrCCCpsrCqr = DDDDD1D1D[11]D1D1D1D[11]D1DD1D1DD1D[2]D1D1D[2]D1D[0][30][9]1111DD1D1D1D[21]DD1[27][4]1
[47] CCCCCNpqrCsrCptCuCpt = D1D[45][3]
[48] CCCpqrCCpCpqr = D1DD[20][36][39]
% Axiom 1 by Łukasiewicz (CCpqCCqrCpr), i.e. (0→1)→((1→2)→(0→2)) ; 371 steps
[49] CCpqCCqrCpr = DD1D[43][43]1
[50] CCNpqCCqpCrp = DD1D[43]D1D[31][39]1
[51] CCCCCCpqCNNpqNCrstCCrtuCvCCrtu = D1D[45][45]
[52] CCCCpqCrqsCCrps = D1D[43][49]
[53] CCCCpqCrqCCrpsCtCCrps = D1D[45][49]
[54] CCpqCCrpCsCrq = D[38][52]
[55] CCpqCrCCspCsq = D[38][53]
[56] CCCCpqCprsCCqrs = D1DD[20][55][39]
[57] CCCpCqrsCCqCCNptrs = D1D[43]DD[51]D[44][47]1
% Walsh's 6th Axiom (CCCpqCCCNrNsrtCCtpCsp), i.e. ((0→1)→(((¬2→¬3)→2)→4))→((4→0)→(3→0)) ; 1085 steps
[58] CCCpqCCCNrNsrtCCtpCsp = DD1D[43]D1D1D1D[2]D1D[0]D[32][22]D[44]D[46]DD1D[43]D1DD1D1D[2]D1D[0]D[20]DD1D1D[2]D1D[0]D[20]D1D1D[24][4][1]D[15]D[20][15]1
% Axiom 2 by Frege (CCpCqrCCpqCpr), i.e. (0→(1→2))→((0→1)→(0→2)) ; 1213 steps
[59] CCpCqrCCpqCpr = DD[51]D[44][53]1
% Walsh's 4th Axiom (CpCCNqCCNrsCtqCCrtCrq), i.e. 0→((¬1→((¬2→3)→(4→1)))→((2→4)→(2→1))) ; 1679 steps
[60] CpCCNqCCNrsCtqCCrtCrq = DD1DD1[35]D1D[11]D1DD1D1D1D[2]D1D[0]D[32][27]DDDD[35]D[15]D[15]D[10]1[49]1[55]D1DD[20]DDD1D1D[18]DD1D1DD1[10][25]111[39]
% Walsh's 5th Axiom (CCpqCCCrCstCqCNsNpCps), i.e. (0→1)→(((2→(3→4))→(1→(¬3→¬0)))→(0→3)) ; 2105 steps
[61] CCpqCCCrCstCqCNsNpCps = DD1D[43]D[52]D1DD[20]DD[34][29]D[26]DDDDD1D1DD1D[0][12][6]1111[39]DD[53]D1DD1[40]D1DD[20]DDD1D1DD1DD1D[2]D1DD1[19][25]1111[39]1
% Walsh's 1st Axiom (CCpCCNpqrCsCCNtCrtCpt), i.e. (0→((¬0→1)→2))→(3→((¬4→(2→4))→(0→4))) ; 2201 steps
[62] CCpCCNpqrCsCCNtCrtCpt = DD1DD[20]D[52][47][39]D[48]DD[53]D[38]D1D[11]D1DD[20]DDD1D1D[18]D[15][29]11[39]1
% Walsh's 2nd Axiom (CpCCqCprCCNrCCNstqCsr), i.e. 0→((1→(0→2))→((¬2→((¬3→4)→1))→(3→2))) ; 4649 steps
[63] CpCCqCprCCNrCCNstqCsr = DD1D[43]D[38]D[48][54]DD[53]D1D[11]D[43]DD1D[43]DD[37][50]1D[56][57]1
% Walsh's 3rd Axiom (CpCCNqCCNrsCptCCtqCrq), i.e. 0→((¬1→((¬2→3)→(0→4)))→((4→1)→(2→1))) ; 5315 steps
[64] CpCCNqCCNrsCptCCtqCrq = DD1D[43]DD1D[43]D[38]D[48]D[56][54][57]DD[53]D1D[11]D[43]D[52]D[46][50]1