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+// Simple 32-bit ALU supporting addition and subtraction (sel=0/1).
+// Outputs are registered. Overflow/underflow detected via 33-bit extended arithmetic.
+// Active-low synchronous reset. Used as a sandbox for formal verification.
+module simple_alu (
+
+    //inputs
+    input logic        clk,
+    input logic [31:0] a,
+    input logic [31:0] b,
+    input logic        sel,         //sel = 0 -> ADD, sel = 1 -> SUB
+    input logic        rst,         //active LOW sync reset
+
+    //outputs
+    output logic [31:0] y,
+    output logic        overflow
+);
+
+    logic [32:0] sum;
+    logic [32:0] diff;
+
+    always_comb begin
+        sum  = {1'b0, a} + {1'b0, b};
+        diff = {1'b0, a} - {1'b0, b};
+    end
+
+    always_ff @(posedge clk) begin
+    if (~rst) begin
+        y <= '0;
+        overflow <= '0;
+    end
+    else begin
+        case (sel)
+        0:  begin
+                y <= sum[31:0];
+                overflow <= sum[32];
+        end
+        1:  begin
+                y <= diff[31:0];
+                overflow <= diff[32];
+        end
+        endcase
+    end
+    end
+endmodule