BFS-Prover-V2-7B

394

5

license:apache-2.0

by

ByteDance-Seed

Language Model

OTHER

7B params

New

394 downloads

Early-stage

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Edge AI:

Mobile

Laptop

Server

16GB+ RAM

Mobile

Laptop

Server

Quick Summary

BFS-Prover-V2: Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers We introduce BFS-Prover-V2, the state-of-the-art open-sourc...

Device Compatibility

Mobile

4-6GB RAM

Laptop

16GB RAM

Server

GPU

Minimum Recommended

7GB+ RAM

Code Examples

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

Example code for loading and using the tactic generator modelpythontransformers

# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"

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