diff --git a/Tests/test_RuleMap/test_sparse_lut.py b/Tests/test_RuleMap/test_sparse_lut.py
index 2a9c5bd7..9ec2ba10 100644
--- a/Tests/test_RuleMap/test_sparse_lut.py
+++ b/Tests/test_RuleMap/test_sparse_lut.py
@@ -1,4 +1,3 @@
-from networkx.generators.random_graphs import fast_gnp_random_graph
 from pynars.NARS.DataStructures._py.Link import LinkType
 from pynars.NARS.RuleMap import Interface_SyllogisticRules, RuleMap
 from pynars.Narsese import Budget
diff --git a/pynars/NAL/Functions/ExtendedBooleanFunctions.py b/pynars/NAL/Functions/ExtendedBooleanFunctions.py
index d0fb68b8..fd953f08 100644
--- a/pynars/NAL/Functions/ExtendedBooleanFunctions.py
+++ b/pynars/NAL/Functions/ExtendedBooleanFunctions.py
@@ -1,10 +1,12 @@
-import numpy as np
+from functools import reduce
+from statistics import mean
+from operator import mul
 
 Not = lambda x: (1-x)
 
-And = lambda *x: np.prod(x)
-Or  = lambda *x: 1 - np.prod(1-np.array(x))
-Average = lambda *x: np.mean(x)
+And = lambda *x: reduce(mul, x, 1)
+Or  = lambda *x: 1 - reduce(mul, (1 - xi for xi in x), 1)
+Average = lambda *x: mean(x)
 
 def Scalar(x): 
     x = 0.5 + 4*(x-0.5)**3 
diff --git a/pynars/NARS/RuleMap/add_rule.py b/pynars/NARS/RuleMap/add_rule.py
index 94c5d5e3..70cd9ed8 100644
--- a/pynars/NARS/RuleMap/add_rule.py
+++ b/pynars/NARS/RuleMap/add_rule.py
@@ -8,8 +8,6 @@
 from typing_extensions import Protocol
 from collections import OrderedDict
 
-from numpy import product
-
 from pynars.Config import Enable
 from pynars.NARS.RuleMap.Interface import Interface_CompositionalRules, Interface_SyllogisticRules, Interface_DecompositionalRules, Interface_TransformRules, Interface_ConditionalRules, Interface_TemporalRules, Interface_VariableRules
 from pynars.Narsese import Copula, Task
diff --git a/pynars/Narsese/_py/Compound.py b/pynars/Narsese/_py/Compound.py
index 8a6b50d7..58ee94d5 100644
--- a/pynars/Narsese/_py/Compound.py
+++ b/pynars/Narsese/_py/Compound.py
@@ -10,7 +10,6 @@
 from ordered_set import OrderedSet
 from typing import Set
 from pynars.utils.tools import list_contains
-import numpy as np
 from pynars.Global import States
 
 
@@ -358,9 +357,13 @@ def equal(self, o: Type['Compound']) -> bool:
                 set2: Iterable[Term] = o.terms - self.terms
                 if len(set1) == len(set2) == 0:
                     return True
-                eq_array = np.array([[term1.equal(term2)
-                                    for term2 in set2] for term1 in set1])
-                if np.prod(eq_array.sum(axis=0)) > 0 and np.prod(eq_array.sum(axis=1)) > 0:
+                # ChatGPT: directly returns the result of the logical AND condition, 
+                # checking if all column sums and all row sums are greater than zero. 
+                # This uses the built-in all() function to ensure every sum in each direction (column and row) 
+                # is greater than zero. The zip(*eq_array) unpacks each row of eq_array into columns.
+                eq_array = [[term1.equal(term2)
+                             for term2 in set2] for term1 in set1]
+                if all(sum(col) > 0 for col in zip(*eq_array)) and all(sum(row) > 0 for row in eq_array):
                     return True
                 else:
                     return False
diff --git a/pynars/Narsese/_py/Term.py b/pynars/Narsese/_py/Term.py
index 7d91f11e..ddd8cb47 100644
--- a/pynars/Narsese/_py/Term.py
+++ b/pynars/Narsese/_py/Term.py
@@ -4,7 +4,6 @@
 from typing import Iterable, List, Set, Type
 from enum import Enum
 from pynars.utils.IndexVar import IndexVar
-from numpy import prod
 from ordered_set import OrderedSet
 # from pynars.utils.tools import find_pos_with_pos, find_var_with_pos
 from copy import copy, deepcopy
diff --git a/pynars/Narsese/_py/Truth.py b/pynars/Narsese/_py/Truth.py
index 653e1717..9f1ff4cb 100644
--- a/pynars/Narsese/_py/Truth.py
+++ b/pynars/Narsese/_py/Truth.py
@@ -1,6 +1,5 @@
 from pynars.Config import Config
 from typing import Type
-import numpy as np
 
 class Truth:
     # analytic: Type['Truth']
diff --git a/pynars/utils/IndexVar.py b/pynars/utils/IndexVar.py
index 2e6503d2..037580c0 100644
--- a/pynars/utils/IndexVar.py
+++ b/pynars/utils/IndexVar.py
@@ -5,8 +5,6 @@
 from ordered_set import OrderedSet
 from bidict import bidict
 
-from numpy import prod
-
 class IntVar:
     def __init__(self, num: int) -> None:
         self.num = int(num)
diff --git a/pynars/utils/tools.py b/pynars/utils/tools.py
index e8860214..74758548 100644
--- a/pynars/utils/tools.py
+++ b/pynars/utils/tools.py
@@ -49,8 +49,8 @@ def rand_seed(x: int):
     import random
     random.seed(x)
     
-    import numpy as np
-    np.random.seed(x)
+    # import numpy as np
+    # np.random.seed(x)
 
     # if using pytorch, set its seed!
     # # import torch
diff --git a/requirements-min.txt b/requirements-min.txt
new file mode 100644
index 00000000..2b02b515
--- /dev/null
+++ b/requirements-min.txt
@@ -0,0 +1,15 @@
+# ale-py>=0.7.3
+# git+git://github.com/mila-iqia/atari-representation-learning.git
+# AutoROM>=0.4.2
+# AutoROM.accept-rom-license>=0.4.2
+bidict>=0.21.2
+depq>=1.5.5
+jstyleson>=0.0.2
+lark==0.12.0
+ordered-set>=4.0.2
+sty>=1.0.0rc2
+tqdm<=3.1.4
+typing>=3.7.4.3
+typing_extensions>=4.0.1
+sparse-lut>=1.0.0
+miniKanren>=1.0.3
\ No newline at end of file