MIP solver reports feasible MIP as infeasible

[odow]

Found by jump-dev/HiGHS.jl#104

MPS file (note the big-M constraint):

NAME        
ROWS
 N  COST
 E  R0      
 L  R1      
COLUMNS
    MARK0000  'MARKER'                 'INTORG'
    C0        R1        -1000000
    MARK0001  'MARKER'                 'INTEND'
    C1        R0        1
    C1        R1        1
RHS
    RHS_V     R0        1
BOUNDS
 BV BOUND     C0      
 FR BOUND     C1      
ENDATA

Output

julia> using HiGHS_jll

julia> HiGHS_jll.highs() do exe
           run(`$(exe) bug.mps`)
       end
Running HiGHS 1.2.1 [date: , git hash: ]
Copyright (c) 2022 ERGO-Code under MIT licence terms
Number of BV entries in BOUNDS section is 1
MIP  bug has 2 rows; 2 cols; 3 nonzeros; 1 integer variables
Presolving model
0 rows, 0 cols, 0 nonzeros
0 rows, 0 cols, 0 nonzeros
Presolve: Optimal
WARNING: Untransformed solution with objective 0 is violated by 1 for the original model

Solving report
  Status            Optimal
  Primal bound      0
  Dual bound        0
  Gap               0% (tolerance: 0.01%)
  Solution status   infeasible
                    0 (objective)
                    0 (bound viol.)
                    0 (int. viol.)
                    1 (row viol.)
  Timing            0.00 (total)
                    0.00 (presolve)
                    0.00 (postsolve)
  Nodes             0
  LP iterations     0 (total)
                    0 (strong br.)
                    0 (separation)
                    0 (heuristics)
ERROR:   MIP solver claims optimality, but with num/sum/max primal(1/1/1) and dual(-1/inf/inf) infeasibilities

[jajhall]

I see. The MIP is feasible, but if presolve is used it identifies infeasibility. If presolve is not used, then all is fine

[jajhall]

It also exposes a minor reporting issue that I've fixed, so branch fix-771 has been created