added FashionMNIST

xd

19 files changed, 553 insertions, 30 deletions

diff --git a/.gitignore b/.gitignore
index 930f082..08dbf27 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,16 @@
-/nneq/__pycache__
+/inpla
+*/__pycache__
+/vnncomp2025_benchmarks/
+/fashion_mnist/FashionMNIST/raw
+/fashion_mnist/fashion_mnist_a.onnx
+/fashion_mnist/fashion_mnist_a.onnx.data
+/fashion_mnist/fashion_mnist_b.onnx
+/fashion_mnist/fashion_mnist_b.onnx.data
+/fashion_mnist/script_argmax.fish
+/fashion_mnist/script_epsilon.fish
+/fashion_mnist/script_strict.fish
+/xor/xor_a.onnx
+/xor/xor_a.onnx.data
+/xor/xor_b.onnx
+/xor/xor_b.onnx.data
+/fashion_mnist/FashionMNIST/raw
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..ce759eb
--- /dev/null
+++ b/README.md
@@ -0,0 +1,5 @@
+Requires my [fork of Inpla](https://github.com/eric-marin/inpla).
+
+- Clone the fork
+- **make** the executable
+- Copy the **inpla** executable in NNEQ/
diff --git a/fashion_mnist/fashion_mnist.py b/fashion_mnist/fashion_mnist.py
new file mode 100644
index 0000000..1c9dcf7
--- /dev/null
+++ b/fashion_mnist/fashion_mnist.py
@@ -0,0 +1,53 @@
+import torch, torch.nn as nn
+from torchvision.datasets import FashionMNIST
+from torch.utils.data import DataLoader
+from torchvision import transforms
+
+class FashionMNIST_MLP(nn.Module):
+    def __init__(self, hidden_dim):
+        super().__init__()
+        self.layers = nn.Sequential(
+            nn.Flatten(),
+            nn.Linear(6 * 6, hidden_dim),
+            nn.ReLU(),
+            nn.Linear(hidden_dim, 2)
+        )
+    def forward(self, x):
+        return self.layers(x)
+
+transform = transforms.Compose([
+    transforms.Resize((6, 6)),
+    transforms.ToTensor(),
+])
+
+train_dataset = FashionMNIST('./', download=True, transform=transform, train=True)
+tshirts_trousers = [id for id, data in enumerate(train_dataset.targets) if data.item() == 0 or data.item() == 1]
+train_dataset = torch.utils.data.Subset(train_dataset, tshirts_trousers)
+
+trainloader = DataLoader(train_dataset, batch_size=128, shuffle=True)
+
+def train_model(name: str, dim):
+    net = FashionMNIST_MLP(hidden_dim=dim)
+    loss_fn = nn.CrossEntropyLoss()
+    optimizer = torch.optim.Adam(net.parameters(), lr=1e-4)
+
+    print(f"Training {name}...")
+    for epoch in range(100):
+        global loss
+        for data in trainloader:
+            inputs, targets = data
+            optimizer.zero_grad()
+            outputs = net(inputs)
+            loss = loss_fn(outputs, targets)
+            loss.backward()
+            optimizer.step()
+        if (epoch + 1) % 10 == 0:
+            print(f"  Epoch {epoch+1}, Loss: {loss.item():.4f}")
+    return net
+
+if __name__ == "__main__":
+    torch_net_a = train_model("Network A", 6).eval()
+    torch_net_b = train_model("Network B", 12).eval()
+
+    torch.onnx.export(torch_net_a, (torch.randn(1, 1, 6, 6),), "fashion_mnist_a.onnx")
+    torch.onnx.export(torch_net_b, (torch.randn(1, 1, 6, 6),), "fashion_mnist_b.onnx")
diff --git a/fashion_mnist/fashion_mnist_argmax.vnnlib b/fashion_mnist/fashion_mnist_argmax.vnnlib
new file mode 100644
index 0000000..0c4412b
--- /dev/null
+++ b/fashion_mnist/fashion_mnist_argmax.vnnlib
@@ -0,0 +1,133 @@
+; Argmax Equivalence for reduced FashionMNIST
+
+; Constant declaration
+(declare-const X_0 Real)
+(declare-const X_1 Real)
+(declare-const X_2 Real)
+(declare-const X_3 Real)
+(declare-const X_4 Real)
+(declare-const X_5 Real)
+(declare-const X_6 Real)
+(declare-const X_7 Real)
+(declare-const X_8 Real)
+(declare-const X_9 Real)
+(declare-const X_10 Real)
+(declare-const X_11 Real)
+(declare-const X_12 Real)
+(declare-const X_13 Real)
+(declare-const X_14 Real)
+(declare-const X_15 Real)
+(declare-const X_16 Real)
+(declare-const X_17 Real)
+(declare-const X_18 Real)
+(declare-const X_19 Real)
+(declare-const X_20 Real)
+(declare-const X_21 Real)
+(declare-const X_22 Real)
+(declare-const X_23 Real)
+(declare-const X_24 Real)
+(declare-const X_25 Real)
+(declare-const X_26 Real)
+(declare-const X_27 Real)
+(declare-const X_28 Real)
+(declare-const X_29 Real)
+(declare-const X_30 Real)
+(declare-const X_31 Real)
+(declare-const X_32 Real)
+(declare-const X_33 Real)
+(declare-const X_34 Real)
+(declare-const X_35 Real)
+(declare-const Y_0 Real)
+(declare-const Y_1 Real)
+(declare-const Y_2 Real)
+(declare-const Y_3 Real)
+
+; Bounded inputs: X must be within [0, 1]
+(assert (>= X_0 0.0))
+(assert (<= X_0 1.0))
+(assert (>= X_1 0.0))
+(assert (<= X_1 1.0))
+(assert (>= X_2 0.0))
+(assert (<= X_2 1.0))
+(assert (>= X_3 0.0))
+(assert (<= X_3 1.0))
+(assert (>= X_4 0.0))
+(assert (<= X_4 1.0))
+(assert (>= X_5 0.0))
+(assert (<= X_5 1.0))
+(assert (>= X_6 0.0))
+(assert (<= X_6 1.0))
+(assert (>= X_7 0.0))
+(assert (<= X_7 1.0))
+(assert (>= X_8 0.0))
+(assert (<= X_8 1.0))
+(assert (>= X_9 0.0))
+(assert (<= X_9 1.0))
+(assert (>= X_10 0.0))
+(assert (<= X_10 1.0))
+(assert (>= X_11 0.0))
+(assert (<= X_11 1.0))
+(assert (>= X_12 0.0))
+(assert (<= X_12 1.0))
+(assert (>= X_13 0.0))
+(assert (<= X_13 1.0))
+(assert (>= X_14 0.0))
+(assert (<= X_14 1.0))
+(assert (>= X_15 0.0))
+(assert (<= X_15 1.0))
+(assert (>= X_16 0.0))
+(assert (<= X_16 1.0))
+(assert (>= X_17 0.0))
+(assert (<= X_17 1.0))
+(assert (>= X_18 0.0))
+(assert (<= X_18 1.0))
+(assert (>= X_19 0.0))
+(assert (<= X_19 1.0))
+(assert (>= X_20 0.0))
+(assert (<= X_20 1.0))
+(assert (>= X_21 0.0))
+(assert (<= X_21 1.0))
+(assert (>= X_22 0.0))
+(assert (<= X_22 1.0))
+(assert (>= X_23 0.0))
+(assert (<= X_23 1.0))
+(assert (>= X_24 0.0))
+(assert (<= X_24 1.0))
+(assert (>= X_25 0.0))
+(assert (<= X_25 1.0))
+(assert (>= X_26 0.0))
+(assert (<= X_26 1.0))
+(assert (>= X_27 0.0))
+(assert (<= X_27 1.0))
+(assert (>= X_28 0.0))
+(assert (<= X_28 1.0))
+(assert (>= X_29 0.0))
+(assert (<= X_29 1.0))
+(assert (>= X_30 0.0))
+(assert (<= X_30 1.0))
+(assert (>= X_31 0.0))
+(assert (<= X_31 1.0))
+(assert (>= X_32 0.0))
+(assert (<= X_32 1.0))
+(assert (>= X_33 0.0))
+(assert (<= X_33 1.0))
+(assert (>= X_34 0.0))
+(assert (<= X_34 1.0))
+(assert (>= X_35 0.0))
+(assert (<= X_35 1.0))
+
+; Violation of argmax equivalence
+(assert (or
+  (and 
+    (> Y_0 Y_1)
+    (or
+      (> Y_3 Y_2)
+    )
+  )
+  (and 
+    (> Y_1 Y_0)
+    (or
+      (> Y_2 Y_3)
+    )
+  )
+))
diff --git a/fashion_mnist/fashion_mnist_epsilon.vnnlib b/fashion_mnist/fashion_mnist_epsilon.vnnlib
new file mode 100644
index 0000000..948e501
--- /dev/null
+++ b/fashion_mnist/fashion_mnist_epsilon.vnnlib
@@ -0,0 +1,124 @@
+; Strict Equivalence for reduced FashionMNIST
+
+; Constant declaration
+(declare-const X_0 Real)
+(declare-const X_1 Real)
+(declare-const X_2 Real)
+(declare-const X_3 Real)
+(declare-const X_4 Real)
+(declare-const X_5 Real)
+(declare-const X_6 Real)
+(declare-const X_7 Real)
+(declare-const X_8 Real)
+(declare-const X_9 Real)
+(declare-const X_10 Real)
+(declare-const X_11 Real)
+(declare-const X_12 Real)
+(declare-const X_13 Real)
+(declare-const X_14 Real)
+(declare-const X_15 Real)
+(declare-const X_16 Real)
+(declare-const X_17 Real)
+(declare-const X_18 Real)
+(declare-const X_19 Real)
+(declare-const X_20 Real)
+(declare-const X_21 Real)
+(declare-const X_22 Real)
+(declare-const X_23 Real)
+(declare-const X_24 Real)
+(declare-const X_25 Real)
+(declare-const X_26 Real)
+(declare-const X_27 Real)
+(declare-const X_28 Real)
+(declare-const X_29 Real)
+(declare-const X_30 Real)
+(declare-const X_31 Real)
+(declare-const X_32 Real)
+(declare-const X_33 Real)
+(declare-const X_34 Real)
+(declare-const X_35 Real)
+(declare-const Y_0 Real)
+(declare-const Y_1 Real)
+(declare-const Y_2 Real)
+(declare-const Y_3 Real)
+
+; Bounded inputs: X must be within [0, 1]
+(assert (>= X_0 0.0))
+(assert (<= X_0 1.0))
+(assert (>= X_1 0.0))
+(assert (<= X_1 1.0))
+(assert (>= X_2 0.0))
+(assert (<= X_2 1.0))
+(assert (>= X_3 0.0))
+(assert (<= X_3 1.0))
+(assert (>= X_4 0.0))
+(assert (<= X_4 1.0))
+(assert (>= X_5 0.0))
+(assert (<= X_5 1.0))
+(assert (>= X_6 0.0))
+(assert (<= X_6 1.0))
+(assert (>= X_7 0.0))
+(assert (<= X_7 1.0))
+(assert (>= X_8 0.0))
+(assert (<= X_8 1.0))
+(assert (>= X_9 0.0))
+(assert (<= X_9 1.0))
+(assert (>= X_10 0.0))
+(assert (<= X_10 1.0))
+(assert (>= X_11 0.0))
+(assert (<= X_11 1.0))
+(assert (>= X_12 0.0))
+(assert (<= X_12 1.0))
+(assert (>= X_13 0.0))
+(assert (<= X_13 1.0))
+(assert (>= X_14 0.0))
+(assert (<= X_14 1.0))
+(assert (>= X_15 0.0))
+(assert (<= X_15 1.0))
+(assert (>= X_16 0.0))
+(assert (<= X_16 1.0))
+(assert (>= X_17 0.0))
+(assert (<= X_17 1.0))
+(assert (>= X_18 0.0))
+(assert (<= X_18 1.0))
+(assert (>= X_19 0.0))
+(assert (<= X_19 1.0))
+(assert (>= X_20 0.0))
+(assert (<= X_20 1.0))
+(assert (>= X_21 0.0))
+(assert (<= X_21 1.0))
+(assert (>= X_22 0.0))
+(assert (<= X_22 1.0))
+(assert (>= X_23 0.0))
+(assert (<= X_23 1.0))
+(assert (>= X_24 0.0))
+(assert (<= X_24 1.0))
+(assert (>= X_25 0.0))
+(assert (<= X_25 1.0))
+(assert (>= X_26 0.0))
+(assert (<= X_26 1.0))
+(assert (>= X_27 0.0))
+(assert (<= X_27 1.0))
+(assert (>= X_28 0.0))
+(assert (<= X_28 1.0))
+(assert (>= X_29 0.0))
+(assert (<= X_29 1.0))
+(assert (>= X_30 0.0))
+(assert (<= X_30 1.0))
+(assert (>= X_31 0.0))
+(assert (<= X_31 1.0))
+(assert (>= X_32 0.0))
+(assert (<= X_32 1.0))
+(assert (>= X_33 0.0))
+(assert (<= X_33 1.0))
+(assert (>= X_34 0.0))
+(assert (<= X_34 1.0))
+(assert (>= X_35 0.0))
+(assert (<= X_35 1.0))
+
+; Violation of epsilon equivalence (epsilon = 0.1)
+(define-fun absolute ((x Real)) Real (if (>= x 0) x (- x)))
+(assert (or
+	(> (absolute (- Y_0 Y_2)) 0.1)
+	(> (absolute (- Y_1 Y_3)) 0.1)
+))
diff --git a/fashion_mnist/fashion_mnist_strict.vnnlib b/fashion_mnist/fashion_mnist_strict.vnnlib
new file mode 100644
index 0000000..8242c34
--- /dev/null
+++ b/fashion_mnist/fashion_mnist_strict.vnnlib
@@ -0,0 +1,123 @@
+; Strict Equivalence for reduced FashionMNIST
+
+; Constant declaration
+(declare-const X_0 Real)
+(declare-const X_1 Real)
+(declare-const X_2 Real)
+(declare-const X_3 Real)
+(declare-const X_4 Real)
+(declare-const X_5 Real)
+(declare-const X_6 Real)
+(declare-const X_7 Real)
+(declare-const X_8 Real)
+(declare-const X_9 Real)
+(declare-const X_10 Real)
+(declare-const X_11 Real)
+(declare-const X_12 Real)
+(declare-const X_13 Real)
+(declare-const X_14 Real)
+(declare-const X_15 Real)
+(declare-const X_16 Real)
+(declare-const X_17 Real)
+(declare-const X_18 Real)
+(declare-const X_19 Real)
+(declare-const X_20 Real)
+(declare-const X_21 Real)
+(declare-const X_22 Real)
+(declare-const X_23 Real)
+(declare-const X_24 Real)
+(declare-const X_25 Real)
+(declare-const X_26 Real)
+(declare-const X_27 Real)
+(declare-const X_28 Real)
+(declare-const X_29 Real)
+(declare-const X_30 Real)
+(declare-const X_31 Real)
+(declare-const X_32 Real)
+(declare-const X_33 Real)
+(declare-const X_34 Real)
+(declare-const X_35 Real)
+(declare-const Y_0 Real)
+(declare-const Y_1 Real)
+(declare-const Y_2 Real)
+(declare-const Y_3 Real)
+
+; Bounded inputs: X must be within [0, 1]
+(assert (>= X_0 0.0))
+(assert (<= X_0 1.0))
+(assert (>= X_1 0.0))
+(assert (<= X_1 1.0))
+(assert (>= X_2 0.0))
+(assert (<= X_2 1.0))
+(assert (>= X_3 0.0))
+(assert (<= X_3 1.0))
+(assert (>= X_4 0.0))
+(assert (<= X_4 1.0))
+(assert (>= X_5 0.0))
+(assert (<= X_5 1.0))
+(assert (>= X_6 0.0))
+(assert (<= X_6 1.0))
+(assert (>= X_7 0.0))
+(assert (<= X_7 1.0))
+(assert (>= X_8 0.0))
+(assert (<= X_8 1.0))
+(assert (>= X_9 0.0))
+(assert (<= X_9 1.0))
+(assert (>= X_10 0.0))
+(assert (<= X_10 1.0))
+(assert (>= X_11 0.0))
+(assert (<= X_11 1.0))
+(assert (>= X_12 0.0))
+(assert (<= X_12 1.0))
+(assert (>= X_13 0.0))
+(assert (<= X_13 1.0))
+(assert (>= X_14 0.0))
+(assert (<= X_14 1.0))
+(assert (>= X_15 0.0))
+(assert (<= X_15 1.0))
+(assert (>= X_16 0.0))
+(assert (<= X_16 1.0))
+(assert (>= X_17 0.0))
+(assert (<= X_17 1.0))
+(assert (>= X_18 0.0))
+(assert (<= X_18 1.0))
+(assert (>= X_19 0.0))
+(assert (<= X_19 1.0))
+(assert (>= X_20 0.0))
+(assert (<= X_20 1.0))
+(assert (>= X_21 0.0))
+(assert (<= X_21 1.0))
+(assert (>= X_22 0.0))
+(assert (<= X_22 1.0))
+(assert (>= X_23 0.0))
+(assert (<= X_23 1.0))
+(assert (>= X_24 0.0))
+(assert (<= X_24 1.0))
+(assert (>= X_25 0.0))
+(assert (<= X_25 1.0))
+(assert (>= X_26 0.0))
+(assert (<= X_26 1.0))
+(assert (>= X_27 0.0))
+(assert (<= X_27 1.0))
+(assert (>= X_28 0.0))
+(assert (<= X_28 1.0))
+(assert (>= X_29 0.0))
+(assert (<= X_29 1.0))
+(assert (>= X_30 0.0))
+(assert (<= X_30 1.0))
+(assert (>= X_31 0.0))
+(assert (<= X_31 1.0))
+(assert (>= X_32 0.0))
+(assert (<= X_32 1.0))
+(assert (>= X_33 0.0))
+(assert (<= X_33 1.0))
+(assert (>= X_34 0.0))
+(assert (<= X_34 1.0))
+(assert (>= X_35 0.0))
+(assert (<= X_35 1.0))
+
+; Violation of strict equivalence
+(assert (or
+	(not (= Y_0 Y_2))
+	(not (= Y_1 Y_3))
+))
diff --git a/nneq.py b/nneq.py
index 1549878..784002a 100644
--- a/nneq.py
+++ b/nneq.py
@@ -164,6 +164,9 @@ def inpla_export(model: onnx.ModelProto, bounds: Optional[Dict[str, List[float]]
             interactions[in_name] = interactions[out_name]
         yield from []
 
+    def op_reshape(node):
+        return op_flatten(node)
+
     graph, initializers = model.graph, get_initializers(model.graph)
     var_gen, wire_gen = NameGen("v"), NameGen("w")
     interactions: Dict[str, List[List[str]]] = {}
@@ -172,6 +175,7 @@ def inpla_export(model: onnx.ModelProto, bounds: Optional[Dict[str, List[float]]
         "Gemm": op_gemm,
         "Relu": op_relu,
         "Flatten": op_flatten,
+        "Reshape": op_reshape,
         "MatMul": op_matmul
     }
 
@@ -258,7 +262,7 @@ def z3_evaluate(model: str, X):
 
 def net(model: onnx.ModelProto, X, bounds: Optional[Dict[str, List[float]]] = None):
     model_hash = hashlib.sha256(model.SerializeToString()).hexdigest()
-    bounds_key = tuple(sorted(bounds.items())) if bounds else None
+    bounds_key = tuple(sorted((k, tuple(v)) for k, v in bounds.items())) if bounds else None
     cache_key = (model_hash, bounds_key)
 
     if cache_key not in _INPLA_CACHE:
diff --git a/notes.norg b/notes.norg
index 9d05485..ed823b3 100644
--- a/notes.norg
+++ b/notes.norg
@@ -4,16 +4,37 @@ description: WIP tool to prove NNEQ using Interaction Nets as pre-processor fo m
 authors: ericmarin
 categories: research
 created: 2026-03-14T09:21:24
-updated: 2026-03-21T11:53:27
+updated: 2026-03-25T09:32:43
 version: 1.1.1
 @end
 
 * TODO
-	- (?) Scalability: Added cache for already processed NN. Inpla is the bottleneck but now I removed most of the limits.
-	- (x) Soundness of translated NN: {:proof.norg:}[PROOF]
-	- (x) Compatibility with other types of NN: Added support for ONNX format. For now only GEMM and ReLU operations are implemented.
-	- ( ) Comparison with other tool ({https://github.com/NeuralNetworkVerification/Marabou}[Marabou], {https://github.com/guykatzz/ReluplexCav2017}[Reluplex])
-	- ( ) Add Range agent to enable ReLU optimization
+	- (!) Scalability: 
+			 Added cache for already processed NN.
+			 Removed limits from Inpla, but it runs slow on big NN because of parsing overhead.
+			 *I should write a Reduction Engine in Rust with a Work Stealing Queue to be more flexible.*
+
+	- (x) Soundness of translated NN:
+			 Translation from NN to IN and the Interaction Rules are proved {:proof.norg:}[here].
+
+	- (x) Compatibility with other types of NN:
+			 Added support for ONNX format.
+			 Operations: Gemm, ReLU, Flatten, Reshape, Matmul.
+
+	- (+) Comparison with other tool ({https://github.com/NeuralNetworkVerification/Marabou}[Marabou], {https://github.com/guykatzz/ReluplexCav2017}[Reluplex]):
+			 My tool is just a pre-processor that takes an NN, optimizes it using IN and converts in a format for SMT solvers.
+			 Marabou and Reluplex are solvers and this tool could be used WITH them.
+			 DeePoly/Marabou-Preprocessor: numeric bound tightening, lossy and heuristic.
+			 ONNX-Simplifier: just folds constants.
+			 Neurify: symbolic bound tightening (similar to the Range agent). Doesn't use a solver
+
+	- (!) Add Range agent to enable ReLU optimization:
+
+	- ( ) Merging Linear packets of the same variable when Adding:
+
+	~ Completare passo induttivo dimostrazione
+	~ 2 Reti uguali NOTE
+	~ 1 Rete grande NOTE
 
 * Agents
 ** Built-in
diff --git a/proof.norg b/proof.norg
index 7f35c1e..8ae8490 100644
--- a/proof.norg
+++ b/proof.norg
@@ -2,21 +2,21 @@
 title: proof
 description: 
 authors: ericmarin
-categories: 
+categories: research
 created: 2026-03-16T11:34:52
-updated: 2026-03-17T18:59:09
+updated: 2026-03-25T08:18:04
 version: 1.1.1
 @end
 
 * Mathematical Definitions
-	- Linear(x, q, r) ~ out => out = q*x + r %with q,r Real%
-	- Concrete(k) ~ out => out = k %with k Real%
+	- Linear(x, q, r) ~ out => out = q*x + r
+	- Concrete(k) ~ out => out = k
 	- Add(out, b) ~ a => out = a + b
-	- AddCheckLinear(out, x, q, r) ~ b => out = q*x + (r + b) %with q,r Real%
-	- AddCheckConcrete(out, k) ~ b => out = k + b %with k Real%
+	- AddCheckLinear(out, x, q, r) ~ b => out = q*x + (r + b)
+	- AddCheckConcrete(out, k) ~ b => out = k + b
 	- Mul(out, b) ~ a => out = a * b
-	- MulCheckLinear(out, x, q, r) ~ b => out = q*b*x + r*b %with q,r Real%
-	- MulCheckConcrete(out, k) ~ b => out = k*b %with k Real%
+	- MulCheckLinear(out, x, q, r) ~ b => out = q*b*x + r*b
+	- MulCheckConcrete(out, k) ~ b => out = k*b
 	- ReLU(out) ~ x => out = IF (x > 0) THEN x ELSE 0
 	- Materialize(out) ~ x => out = x
 
@@ -47,10 +47,13 @@ version: 1.1.1
 	 /Y = alpha * A * B + beta * C/
 
 ** Flatten
-	 Just identity mapping
+	 Just identity mapping.
 
 ** MatMul
-	 Equal to Gemm with alpha=1 and beta=0
+	 Equal to Gemm with alpha=1 and beta=0.
+
+** Reshape
+	 Just identity mapping.
 
 * Proof for the Interaction Rules
 ** Materialize
diff --git a/verify_fashion_mnist.py b/verify_fashion_mnist.py
new file mode 100644
index 0000000..48c8bc1
--- /dev/null
+++ b/verify_fashion_mnist.py
@@ -0,0 +1,32 @@
+import z3
+import nneq
+
+def check_property(onnx_a, onnx_b, vnnlib):
+    solver = nneq.Solver()
+    
+    print(f"--- Checking {vnnlib} ---")
+    
+    solver.load_onnx(onnx_a)
+    solver.load_onnx(onnx_b)
+    solver.load_vnnlib(vnnlib)
+    
+    result = solver.check()
+    
+    if result == z3.unsat:
+        print("VERIFIED (UNSAT): The networks are equivalent under this property.")
+    elif result == z3.sat:
+        print("FAILED (SAT): The networks are NOT equivalent.")
+        print("Counter-example input:")
+        print(solver.model())
+        # m = solver.model()
+        # sorted_symbols = sorted([s for s in m.decls() if s.name().startswith("X_")], key=lambda s: s.name())
+        # for s in sorted_symbols:
+            # print(f"  {s.name()} = {m[s]}")
+    else:
+        print("UNKNOWN")
+    print("")
+
+if __name__ == "__main__":
+    check_property("./fashion_mnist/fashion_mnist_a.onnx", "./fashion_mnist/fashion_mnist_b.onnx", "./fashion_mnist/fashion_mnist_strict.vnnlib")
+    check_property("./fashion_mnist/fashion_mnist_a.onnx", "./fashion_mnist/fashion_mnist_b.onnx", "./fashion_mnist/fashion_mnist_epsilon.vnnlib")
+    check_property("./fashion_mnist/fashion_mnist_a.onnx", "./fashion_mnist/fashion_mnist_b.onnx", "./fashion_mnist/fashion_mnist_argmax.vnnlib")
diff --git a/verify_xor.py b/verify_xor.py
index 7328229..90623a0 100644
--- a/verify_xor.py
+++ b/verify_xor.py
@@ -1,7 +1,7 @@
 import z3
 import nneq
 
-def check_equivalence(onnx_a, onnx_b, vnnlib):
+def check_property(onnx_a, onnx_b, vnnlib):
     solver = nneq.Solver()
     
     print(f"--- Checking {vnnlib} ---")
@@ -17,15 +17,16 @@ def check_equivalence(onnx_a, onnx_b, vnnlib):
     elif result == z3.sat:
         print("FAILED (SAT): The networks are NOT equivalent.")
         print("Counter-example input:")
-        m = solver.model()
-        sorted_symbols = sorted([s for s in m.decls() if s.name().startswith("X_")], key=lambda s: s.name())
-        for s in sorted_symbols:
-            print(f"  {s.name()} = {m[s]}")
+        print(solver.model())
+        # m = solver.model()
+        # sorted_symbols = sorted([s for s in m.decls() if s.name().startswith("X_")], key=lambda s: s.name())
+        # for s in sorted_symbols:
+            # print(f"  {s.name()} = {m[s]}")
     else:
         print("UNKNOWN")
     print("")
 
 if __name__ == "__main__":
-    check_equivalence("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_strict.vnnlib")
-    check_equivalence("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_epsilon.vnnlib")
-    check_equivalence("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_argmax.vnnlib")
+    check_property("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_strict.vnnlib")
+    check_property("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_epsilon.vnnlib")
+    check_property("./xor/xor_a.onnx", "./xor/xor_b.onnx", "./xor/xor_argmax.vnnlib")
diff --git a/vnncomp2025_benchmarks b/vnncomp2025_benchmarks
deleted file mode 160000
-Subproject 8b7b811b78ce6a329dc96f04ae6652da3c24594
diff --git a/xor/xor_a.onnx b/xor/xor_a.onnx
deleted file mode 100644
index 9c13609..0000000
--- a/xor/xor_a.onnx
+++ /dev/null
diff --git a/xor/xor_a.onnx.data b/xor/xor_a.onnx.data
deleted file mode 100644
index e69de29..0000000
--- a/xor/xor_a.onnx.data
+++ /dev/null
diff --git a/xor/xor_argmax.vnnlib b/xor/xor_argmax.vnnlib
index 3043d70..d38bc31 100644
--- a/xor/xor_argmax.vnnlib
+++ b/xor/xor_argmax.vnnlib
@@ -1,11 +1,14 @@
+; Argmax Equivalence for XOR
+
+; Constant declaration
 (declare-const X_0 Real)
 (declare-const X_1 Real)
 (declare-const Y_0 Real)
 (declare-const Y_1 Real)
 
-; Discrete inputs: X must be 0 or 1
+; Bounded inputs: X must be 0 or 1
 (assert (or (= X_0 0) (= X_0 1)))
 (assert (or (= X_1 0) (= X_1 1)))
 
-; Violation of argmax equivalence (threshold 0.5)
+; Violation of argmax equivalence
 (assert (not (= (> Y_0 0.5) (> Y_1 0.5))))
diff --git a/xor/xor_b.onnx b/xor/xor_b.onnx
deleted file mode 100644
index fb18840..0000000
--- a/xor/xor_b.onnx
+++ /dev/null
diff --git a/xor/xor_b.onnx.data b/xor/xor_b.onnx.data
deleted file mode 100644
index e69de29..0000000
--- a/xor/xor_b.onnx.data
+++ /dev/null
diff --git a/xor/xor_epsilon.vnnlib b/xor/xor_epsilon.vnnlib
index d4e9bb7..427243e 100644
--- a/xor/xor_epsilon.vnnlib
+++ b/xor/xor_epsilon.vnnlib
@@ -1,9 +1,12 @@
+; Epsilon Equivalence for XOR
+
+; Constant declaration
 (declare-const X_0 Real)
 (declare-const X_1 Real)
 (declare-const Y_0 Real)
 (declare-const Y_1 Real)
 
-; Discrete inputs: X must be 0 or 1
+; Bounded inputs: X must be 0 or 1
 (assert (or (= X_0 0) (= X_0 1)))
 (assert (or (= X_1 0) (= X_1 1)))
 
diff --git a/xor/xor_strict.vnnlib b/xor/xor_strict.vnnlib
index fcf364e..bead476 100644
--- a/xor/xor_strict.vnnlib
+++ b/xor/xor_strict.vnnlib
@@ -1,9 +1,12 @@
+; Strict Equivalence for XOR
+
+; Constant declaration
 (declare-const X_0 Real)
 (declare-const X_1 Real)
 (declare-const Y_0 Real)
 (declare-const Y_1 Real)
 
-; Discrete inputs: X must be 0 or 1
+; Bounded inputs: X must be 0 or 1
 (assert (or (= X_0 0) (= X_0 1)))
 (assert (or (= X_1 0) (= X_1 1)))