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gad-bv4-no-grammar-0shots

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bv4nogram137

find_inv_ne_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s #x0) (distinct t (bvnot #x0)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr s t))

bv4nogram61

find_inv_bvsge_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram3

find_inv_bvuge_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvshl (bvnot #x0) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram79

find_inv_bvult_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram92

find_inv_bvult_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram84

find_inv_bvslt_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvslt s t) (bvslt #x0 t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvor s #b0111)))

bv4nogram93

find_inv_bvsle_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge t (bvlshr t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram62

find_inv_bvuge_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvnot (bvneg s)) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram54

find_inv_bvuge_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvand (udivtotal (bvmul s t) t) s) s)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram127

find_inv_bvult_bvmul_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvmul (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram39

find_inv_bvult_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram9

find_inv_bvuge_bvashr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvashr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (not (and (bvult s (bvnot s)) (bvult s t)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvand s #b1000))

bv4nogram7

find_inv_bvule_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram58

find_inv_ne_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram24

find_inv_bvsle_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvnot #x0) (bvand (bvneg s) t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvand t #b1000))

bv4nogram35

find_inv_bvule_bvneg_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvneg (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram37

find_inv_bvsle_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvult t min) (bvsge t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvor s #b0111)))

bv4nogram29

find_inv_bvslt_bvashr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvashr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvslt s t) (bvslt #x0 t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvor s #b0111)))

bv4nogram89

find_inv_bvule_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult #x0 (bvor (bvnot s) t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram76

find_inv_bvugt_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t s)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram101

find_inv_bvuge_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge s t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram98

find_inv_ne_bvmul_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvmul (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct t #x0) (distinct s #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvshl #b0111 t))

bv4nogram30

find_inv_bvsle_bvurem1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (uremtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvult t min) (bvsge t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvsub s t))

bv4nogram5

find_inv_bvsge_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvsge (udivtotal (bvnot #x0) s) t) (bvsge (udivtotal max s) t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvshl s (bvor s (bvadd s s)))))

bv4nogram65

find_inv_bvslt_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (=> (bvsle t #x0) (bvslt (udivtotal min s) t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvneg t)))

bv4nogram8

find_inv_bvsgt_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (and (=> (bvslt s #x0) (bvsgt (bvlshr s #x1) t)) (=> (bvsge s #x0) (bvsgt s t)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr s (bvlshr #b0111 (bvsub #b1000 #b0111))))

bv4nogram94

find_inv_bvsge_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvand (bvshl max s) max) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr #b0111 s))

bv4nogram53

find_inv_bvsgt_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt t (bvand s max))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0111)

bv4nogram85

find_inv_bvsgt_bvneg_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvneg (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t max)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram64

find_inv_ne_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvadd s t)))

bv4nogram138

find_inv_bvsgt_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt t (bvand (bvshl max s) max))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr #b0111 s))

bv4nogram25

find_inv_bvsgt_bvashr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvashr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt t (bvlshr max s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0111)

bv4nogram97

find_inv_bvule_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram45

find_inv_bvult_bvshl1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvshl s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram49

find_inv_bvuge_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (not (bvult s t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram50

find_inv_bvugt_bvneg_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvneg (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t (bvnot #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram114

find_inv_bvsle_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge t (bvor s min))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram47

find_inv_eq_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvor t s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram44

find_inv_bvugt_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t (bvnot #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram131

find_inv_bvugt_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t (bvnot #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram1

find_inv_bvsle_bvashr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvashr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvsge t #x0) (bvsge t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvor s #b0111)))

bv4nogram111

find_inv_eq_bvurem1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (uremtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvand (bvsub (bvadd t t) s) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvsub s t))

bv4nogram81

find_inv_bvuge_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram87

find_inv_ne_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s #x0) (distinct t #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram70

find_inv_bvsgt_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t max)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram28

find_inv_bvule_bvmul_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvmul (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram90

find_inv_bvsge_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvsub t s))

bv4nogram110

find_inv_eq_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvsub t s))

bv4nogram56

find_inv_bvuge_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram125

find_inv_eq_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvlshr (bvshl t s) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvshl t s))

bv4nogram77

find_inv_bvslt_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvor (bvnot (bvsub s t)) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram133

find_inv_bvsge_bvashr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvashr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvlshr max s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0111)

bv4nogram105

find_inv_bvult_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram20

find_inv_bvuge_bvneg_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvneg (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvneg t))

bv4nogram21

find_inv_ne_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct t #x0) (bvult s #x4))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvshl #b1000 t))

bv4nogram107

find_inv_bvule_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvneg s))

bv4nogram13

find_inv_bvsgt_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsgt (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvsgt (udivtotal (bvnot #x0) s) t) (bvsgt (udivtotal max s) t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvshl s (bvor s (bvadd s s)))))

bv4nogram83

find_inv_bvslt_bvneg_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvneg (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t min)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram103

find_inv_ne_bvshl1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvshl s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s #x0) (distinct t #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram96

find_inv_bvsle_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvsge t (bvnot #x0)) (bvsge t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr s (bvlshr #b0111 (bvsub #b1000 #b0111))))

bv4nogram75

find_inv_bvugt_bvashr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvashr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvslt s (bvlshr s (bvnot t))) (bvult t s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvand s #b1000))

bv4nogram6

find_inv_bvugt_bvurem1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (uremtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t s)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram106

find_inv_bvult_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (and (bvult #x0 (bvnot (bvand (bvneg t) s))) (bvult #x0 t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram116

find_inv_bvsge_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (= (bvand s t) t) (bvslt t (bvand (bvsub t s) s)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0111)

bv4nogram100

find_inv_bvult_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (and (bvult #x0 s) (bvult #x0 t))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram38

find_inv_bvule_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram43

find_inv_bvuge_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvlshr (bvshl t s) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot s))

bv4nogram52

find_inv_bvugt_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t (bvnot (bvneg s)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvneg s)))

bv4nogram17

find_inv_bvuge_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram41

find_inv_bvsle_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0111)

bv4nogram33

find_inv_ne_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvand t #b1000))

bv4nogram121

find_inv_bvult_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t #x0)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvneg s))

bv4nogram72

find_inv_eq_bvnot_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvnot (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram124

find_inv_ne_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s #x0) (distinct t #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvneg t))

bv4nogram14

find_inv_bvslt_bvudiv1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (udivtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvslt s t) (bvsge t #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr s (bvlshr #b0111 (bvsub #b1000 #b0111))))

bv4nogram67

find_inv_bvsle_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvlshr t (bvlshr t s)) min)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr t s))

bv4nogram82

find_inv_bvule_bvshl1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvshl s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram23

find_inv_bvugt_bvashr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvashr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t (bvnot #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram18

find_inv_bvule_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge t s)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram122

find_inv_bvsle_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvuge s (bvand t min))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram108

find_inv_ne_bvor_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvor (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s (bvnot #x0)) (distinct t (bvnot #x0)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot t))

bv4nogram10

find_inv_bvslt_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvnot t) (bvor (bvneg s) (bvneg t)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvshl #b1000 (bvshl t t)))

bv4nogram22

find_inv_bvsle_bvudiv0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsle (udivtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (= (udivtotal (bvmul s t) s) t) (=> (bvsle t #x0) (bvslt (udivtotal min s) t)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram63

find_inv_bvule_bvurem1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (uremtotal s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram99

find_inv_bvsge_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (and (=> (bvslt s #x0) (bvsge (bvlshr s #x1) t)) (=> (bvsge s #x0) (bvsge s t)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr s (bvlshr #b0111 (bvsub #b1000 #b0111))))

bv4nogram91

find_inv_bvsge_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvsge (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (bvslt t s) (bvsge #x0 s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) t)

bv4nogram59

find_inv_bvslt_bvand_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvand (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvand (bvnot (bvneg t)) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b1000)

bv4nogram57

find_inv_bvugt_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t (bvshl (bvnot #x0) s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot #b0000))

bv4nogram102

find_inv_ne_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct t #x0) (bvult s #x4))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvshl #b0111 t))

bv4nogram15

find_inv_bvule_bvashr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvashr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) #b0000)

bv4nogram113

find_inv_bvslt_bvadd_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvadd (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct t min)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvsub #b1000 s))

bv4nogram136

find_inv_bvugt_bvlshr0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvugt (bvlshr (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult t (bvlshr (bvnot s) s))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot s))

bv4nogram71

find_inv_bvslt_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (bvslt (bvshl (bvlshr min s) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr #b1000 s))

bv4nogram40

find_inv_bvule_bvlshr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvule (bvlshr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool true) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) s)

bv4nogram129

find_inv_ne_bvurem0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (distinct (uremtotal (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (or (distinct s #x1) (distinct t #x0))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvneg (bvnot t)))

bv4nogram128

find_inv_bvult_bvashr1_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (bvult (bvashr s (inv s t)) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (and (not (and (not (bvult s t)) (bvslt s #x0))) (not (= t #x0)))) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvnot (bvor s #b0111)))

bv4nogram74

find_inv_eq_bvshl0_4bit

You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs. Question: (set-logic BV) (synth-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4)) (declare-var s (BitVec 4)) (declare-var t (BitVec 4)) (define-fun udivtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) #xF (bvudiv a b))) (define-fun uremtotal ((a (BitVec 4)) (b (BitVec 4))) (BitVec 4) (ite (= b #x0) a (bvurem a b))) (define-fun min () (BitVec 4) (bvnot (bvlshr (bvnot #x0) #x1))) (define-fun max () (BitVec 4) (bvnot min)) (define-fun l ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvshl (inv s t) s) t)) (define-fun SC ((s (BitVec 4)) (t (BitVec 4))) Bool (= (bvshl (bvlshr t s) s) t)) (constraint (=> (SC s t) (l s t))) (check-synth) Solution:

(define-fun inv ((s (BitVec 4)) (t (BitVec 4))) (BitVec 4) (bvlshr t s))