0.13/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.13 % Command : do_CVC4 %s 0.14/0.34 % Computer : n007.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 180 0.14/0.34 % DateTime : Thu Aug 29 09:23:36 EDT 2019 0.14/0.34 % CPUTime : 0.21/0.47 %----Proving TF0_ARI 0.21/0.48 ------- cvc4-tfa casc 27 : /export/starexec/sandbox/benchmark/theBenchmark.p at 180... 0.21/0.48 --- Run --finite-model-find --decision=internal at 15... 15.37/15.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15... 15.40/15.67 % SZS status Theorem for theBenchmark 15.40/15.67 % SZS output start Proof for theBenchmark 15.40/15.67 (skolem (forall ((N Int) (BOUND_VARIABLE_2907 Int) (BOUND_VARIABLE_2908 Int) (BOUND_VARIABLE_2909 Int) (BOUND_VARIABLE_2910 Int) (BOUND_VARIABLE_2995 Int)) (let ((_let_0 (* (- 1) BOUND_VARIABLE_2908))) (let ((_let_1 (* (- 1) BOUND_VARIABLE_2909))) (let ((_let_2 (div BOUND_VARIABLE_2908 BOUND_VARIABLE_2909))) (let ((_let_3 (* (- 1) BOUND_VARIABLE_2910))) (let ((_let_4 (div N BOUND_VARIABLE_2995))) (or (not (>= N 2)) (not (>= (+ N (* (- 1) BOUND_VARIABLE_2907)) 0)) (not (prime BOUND_VARIABLE_2907)) (not (forall ((I Int)) (or (not (>= I 2)) (not (divides I BOUND_VARIABLE_2908)) (and (>= (+ I (* (- 1) BOUND_VARIABLE_2907)) 0) (divides I N))) )) (not (forall ((I Int)) (or (not (prime I)) (not (divides I N)) (not (>= (+ I (* (- 1) BOUND_VARIABLE_2907)) 1)) (divides I BOUND_VARIABLE_2908)) )) (not (divides BOUND_VARIABLE_2907 N)) (not (>= BOUND_VARIABLE_2907 2)) (not (>= (+ N _let_0) 0)) (not (>= BOUND_VARIABLE_2908 1)) (not (>= BOUND_VARIABLE_2908 2)) (not (divides BOUND_VARIABLE_2908 BOUND_VARIABLE_2908)) (>= (+ BOUND_VARIABLE_2907 _let_0) 1) (not (forall ((I Int)) (or (>= (+ I (* (- 1) BOUND_VARIABLE_2907)) 0) (not (>= I 2)) (not (divides I BOUND_VARIABLE_2908))) )) (>= (+ BOUND_VARIABLE_2907 _let_1) 1) (not (>= (+ BOUND_VARIABLE_2908 _let_1) 0)) (not (divides BOUND_VARIABLE_2909 BOUND_VARIABLE_2908)) (not (forall ((I Int)) (or (>= (+ I _let_1) 0) (not (>= I 2)) (not (divides I BOUND_VARIABLE_2908))) )) (not (prime BOUND_VARIABLE_2909)) (not (>= BOUND_VARIABLE_2909 1)) (not (= BOUND_VARIABLE_2908 (* BOUND_VARIABLE_2909 _let_2))) (not (divides _let_2 BOUND_VARIABLE_2908)) (not (prime BOUND_VARIABLE_2910)) (>= (+ BOUND_VARIABLE_2909 _let_3) 0) (not (divides BOUND_VARIABLE_2910 N)) (>= (+ BOUND_VARIABLE_2907 _let_3) 0) (not (divides BOUND_VARIABLE_2910 BOUND_VARIABLE_2908)) (coprime BOUND_VARIABLE_2909 BOUND_VARIABLE_2910) (not (forall ((I Int)) (or (>= (+ I (* (- 1) BOUND_VARIABLE_2995)) 0) (not (>= I 2)) (not (divides I N))) )) (not (divides BOUND_VARIABLE_2995 N)) (not (>= (+ N (* (- 1) BOUND_VARIABLE_2995)) 0)) (not (>= BOUND_VARIABLE_2995 2)) (not (= N (* BOUND_VARIABLE_2995 _let_4))) (not (divides _let_4 N)) (not (forall ((I Int)) (or (not (divides I N)) (not (>= (+ I (* (- 1) BOUND_VARIABLE_2995)) 1)) (not (prime I)) (and (divides I _let_4) (coprime BOUND_VARIABLE_2995 I))) )))))))) ) 15.40/15.67 ( skv_2 skv_3 skv_4 skv_5 skv_6 skv_7 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((Q Int)) (not (= skv_4 (* Q skv_4))) ) 15.40/15.67 ( skv_13 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((Q Int)) (not (= skv_2 (* Q skv_3))) ) 15.40/15.67 ( skv_14 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((Q Int)) (not (= skv_4 (* Q skv_5))) ) 15.40/15.67 ( skv_15 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((Q Int)) (not (= skv_2 (* Q skv_6))) ) 15.40/15.67 ( skv_16 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((Q Int)) (not (= skv_4 (* Q (div skv_4 skv_5)))) ) 15.40/15.67 ( skv_17 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((X Int)) (or (not (divides X skv_2)) (divides X skv_6)) ) 15.40/15.67 ( skv_18 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((X Int)) (or (not (divides X skv_4)) (divides X (div skv_4 skv_5))) ) 15.40/15.67 ( skv_19 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((X Int)) (or (not (divides X skv_4)) (divides X skv_5)) ) 15.40/15.67 ( skv_20 ) 15.40/15.67 ) 15.40/15.67 (skolem (forall ((X Int)) (or (not (divides X skv_2)) (divides X skv_3)) ) 15.40/15.67 ( skv_21 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int)) (= (divides 2 A) (even A)) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_2 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ( (div skv_2 skv_7) ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (divides (gcd A B) A) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (divides (gcd A B) B) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (or (even N) (odd N)) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int)) (= (not (divides 2 A)) (odd A)) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_2 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ( (div skv_2 skv_7) ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (= (= (gcd A B) 1) (coprime A B)) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ( skv_7, 2 ) 15.40/15.67 ( skv_7, 3 ) 15.40/15.67 ( skv_7, skv_3 ) 15.40/15.67 ( skv_7, skv_4 ) 15.40/15.67 ( skv_7, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (= B 0) (= (gcd B (mod A B)) (gcd A B))) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides A B)) (divides A (* (- 1) B))) ) 15.40/15.67 ( 2, skv_2 ) 15.40/15.67 ( skv_3, 0 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* 2 skv_4) ) 15.40/15.67 ( skv_5, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0 ) 15.40/15.67 ( skv_6, skv_2 ) 15.40/15.67 ( skv_6, (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2 ) 15.40/15.67 ( skv_7, (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_3), skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4 ) 15.40/15.67 ( (* (- 1) skv_6), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4 ) 15.40/15.67 ( skv_18, skv_2 ) 15.40/15.67 ( skv_19, skv_4 ) 15.40/15.67 ( skv_20, skv_4 ) 15.40/15.67 ( skv_21, skv_2 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((P Int)) (= (and (forall ((N Int)) (or (not (>= (+ P (* (- 1) N)) 1)) (not (>= N 1)) (coprime N P)) ) (>= P 2)) (prime P)) ) 15.40/15.67 ( 1 ) 15.40/15.67 ( 2 ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_2 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_5 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (or (not (odd N)) (odd (+ 2 N))) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int) (C Int)) (or (not (divides A B)) (not (divides A C)) (divides A (+ B C))) ) 15.40/15.67 ( 2, skv_2, skv_2 ) 15.40/15.67 ( 2, skv_4, skv_4 ) 15.40/15.67 ( skv_2, skv_4, skv_4 ) 15.40/15.67 ( skv_3, 0, 0 ) 15.40/15.67 ( skv_3, skv_2, skv_2 ) 15.40/15.67 ( skv_3, skv_2, skv_4 ) 15.40/15.67 ( skv_3, skv_4, skv_4 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2), (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0, 0 ) 15.40/15.67 ( skv_4, skv_2, skv_2 ) 15.40/15.67 ( skv_4, skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( skv_4, (div skv_4 skv_5), (div skv_4 skv_5) ) 15.40/15.67 ( skv_4, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_5, 0, 0 ) 15.40/15.67 ( skv_5, skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_4, skv_2 ) 15.40/15.67 ( skv_5, skv_4, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4), (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_5, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0, 0 ) 15.40/15.67 ( skv_6, skv_2, skv_2 ) 15.40/15.67 ( skv_6, skv_2, skv_4 ) 15.40/15.67 ( skv_6, skv_4, skv_2 ) 15.40/15.67 ( skv_6, skv_4, skv_4 ) 15.40/15.67 ( skv_6, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2), (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2, skv_2 ) 15.40/15.67 ( skv_7, skv_2, (* 2 skv_2) ) 15.40/15.67 ( skv_7, (* 2 skv_2), skv_2 ) 15.40/15.67 ( (* (- 1) skv_3), skv_2, skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4, skv_4 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4, skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), 0, 0 ) 15.40/15.67 ( (div skv_4 skv_5), skv_2, skv_2 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4, skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( (div skv_4 skv_5), (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( (* (- 1) skv_6), skv_2, skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2, skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2, (* 2 skv_2) ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2), skv_2 ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4, skv_4 ) 15.40/15.67 ( skv_18, skv_2, skv_2 ) 15.40/15.67 ( skv_19, skv_4, skv_4 ) 15.40/15.67 ( skv_19, (div skv_4 skv_5), (div skv_4 skv_5) ) 15.40/15.67 ( skv_20, skv_4, skv_4 ) 15.40/15.67 ( skv_21, skv_2, skv_2 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (mod X Y))) (let ((_let_1 (abs Y))) (or (= Y 0) (and (not (>= (+ _let_0 (* (- 1) _let_1)) 0)) (>= (+ _let_0 _let_1) 1))))) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int) (C Int)) (or (not (divides A B)) (not (divides A C)) (divides A (+ B (* (- 1) C)))) ) 15.40/15.67 ( 2, skv_2, skv_2 ) 15.40/15.67 ( skv_3, 0, 0 ) 15.40/15.67 ( skv_3, skv_2, skv_2 ) 15.40/15.67 ( skv_3, skv_2, (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2), skv_2 ) 15.40/15.67 ( skv_3, (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0, 0 ) 15.40/15.67 ( skv_4, skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( skv_4, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_5, skv_4, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4), (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0, 0 ) 15.40/15.67 ( skv_6, skv_2, skv_2 ) 15.40/15.67 ( skv_6, skv_2, (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2), skv_2 ) 15.40/15.67 ( skv_6, (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4), (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2, skv_2 ) 15.40/15.67 ( skv_7, (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_3), skv_2, skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4, skv_4 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4, skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4, skv_4 ) 15.40/15.67 ( (* (- 1) skv_6), skv_2, skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2, skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4, skv_4 ) 15.40/15.67 ( skv_18, skv_2, skv_2 ) 15.40/15.67 ( skv_19, skv_4, skv_4 ) 15.40/15.67 ( skv_20, skv_4, skv_4 ) 15.40/15.67 ( skv_21, skv_2, skv_2 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (or (not (even N)) (not (odd N))) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((P Int) (A Int) (B Int)) (or (not (prime P)) (not (divides P (* A B))) (divides P A) (divides P B)) ) 15.40/15.67 ( 2, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( 3, skv_2, skv_2 ) 15.40/15.67 ( 3, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_3, skv_3 ) 15.40/15.67 ( skv_2, skv_6, skv_6 ) 15.40/15.67 ( skv_4, (div skv_2 skv_7), (div skv_2 skv_7) ) 15.40/15.67 ( skv_18, skv_6, skv_6 ) 15.40/15.67 ( skv_20, skv_5, skv_5 ) 15.40/15.67 ( skv_21, skv_3, skv_3 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides A B)) (divides (* (- 1) A) B)) ) 15.40/15.67 ( 2, skv_2 ) 15.40/15.67 ( skv_3, 0 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* 2 skv_4) ) 15.40/15.67 ( skv_5, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0 ) 15.40/15.67 ( skv_6, skv_2 ) 15.40/15.67 ( skv_6, (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2 ) 15.40/15.67 ( skv_7, (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_3), skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4 ) 15.40/15.67 ( (* (- 1) skv_6), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4 ) 15.40/15.67 ( skv_18, skv_2 ) 15.40/15.67 ( skv_19, skv_4 ) 15.40/15.67 ( skv_20, skv_4 ) 15.40/15.67 ( skv_21, skv_2 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 15.40/15.67 ( 0, 0, 0 ) 15.40/15.67 ( (- 1), 0, 0 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((P Int) (BOUND_VARIABLE_2030 Int)) (or (not (prime P)) (not (divides BOUND_VARIABLE_2030 P)) (= BOUND_VARIABLE_2030 1) (= P BOUND_VARIABLE_2030) (= P (* (- 1) BOUND_VARIABLE_2030)) (= BOUND_VARIABLE_2030 (- 1))) ) 15.40/15.67 ( 0, skv_3 ) 15.40/15.67 ( 0, skv_4 ) 15.40/15.67 ( 0, skv_6 ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_2, (* (- 1) skv_3) ) 15.40/15.67 ( skv_2, (* (- 1) skv_6) ) 15.40/15.67 ( skv_2, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_18 ) 15.40/15.67 ( skv_2, skv_21 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* (- 1) skv_5) ) 15.40/15.67 ( skv_4, (div skv_4 skv_5) ) 15.40/15.67 ( skv_4, (* (- 1) (div skv_4 skv_5)) ) 15.40/15.67 ( skv_4, skv_19 ) 15.40/15.67 ( skv_4, skv_20 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_4), skv_5 ) 15.40/15.67 ( (div skv_2 skv_7), skv_3 ) 15.40/15.67 ( (div skv_2 skv_7), skv_6 ) 15.40/15.67 ( (* (- 1) skv_2), skv_3 ) 15.40/15.67 ( (* (- 1) skv_2), skv_6 ) 15.40/15.67 ( (* 2 skv_2), skv_3 ) 15.40/15.67 ( (* 2 skv_2), skv_6 ) 15.40/15.67 ( (* 2 skv_2), skv_7 ) 15.40/15.67 ( (* 2 skv_2), (div skv_2 skv_7) ) 15.40/15.67 ( (* 2 skv_4), skv_4 ) 15.40/15.67 ( (* 2 skv_4), skv_5 ) 15.40/15.67 ( (* 2 skv_4), skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides A (* (- 1) B))) (divides A B)) ) 15.40/15.67 ( 2, (div skv_2 skv_7) ) 15.40/15.67 ( 3, skv_2 ) 15.40/15.67 ( 3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, (div skv_2 skv_7) ) 15.40/15.67 ( skv_18, skv_6 ) 15.40/15.67 ( skv_20, skv_5 ) 15.40/15.67 ( skv_21, skv_3 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (= Y 0) (>= (mod X Y) 0)) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((P Int)) (= (and (forall ((N Int)) (or (not (>= (+ P (* (- 1) N)) 1)) (not (>= N 2)) (not (divides N P))) ) (>= P 2)) (prime P)) ) 15.40/15.67 ( 1 ) 15.40/15.67 ( 2 ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_2 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_5 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int) (X Int)) (or (not (divides X A)) (not (divides X B)) (divides X (gcd A B))) ) 15.40/15.67 ( skv_2, skv_2, 3 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (or (not (odd N)) (even (+ 1 N))) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (= (gcd Y X) (gcd X Y)) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ( skv_6, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= (div X Y) 0)) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (>= (gcd A B) 0) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((P Int)) (or (not (prime P)) (not (>= P 3)) (odd P)) ) 15.40/15.67 ( 2 ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_5 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (= B 0) (not (= (mod A B) 0)) (divides B A)) ) 15.40/15.67 ( skv_2, 3 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, skv_21 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_5, skv_20 ) 15.40/15.67 ( skv_6, skv_2 ) 15.40/15.67 ( skv_6, skv_18 ) 15.40/15.67 ( (div skv_2 skv_7), 2 ) 15.40/15.67 ( (div skv_2 skv_7), 3 ) 15.40/15.67 ( (div skv_2 skv_7), skv_4 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (= (not (forall ((K Int)) (not (= N (+ 1 (* 2 K)))) )) (odd N)) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= X 1) (not (>= (mod X Y) 1))) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int)) (>= (abs X) 0) ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ( (* skv_5 (div skv_4 skv_5)) ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (= B 0) (not (divides B A)) (= (mod A B) 0)) ) 15.40/15.67 ( 0, skv_3 ) 15.40/15.67 ( 0, skv_4 ) 15.40/15.67 ( 0, skv_6 ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_2, (* (- 1) skv_3) ) 15.40/15.67 ( skv_2, (* (- 1) skv_6) ) 15.40/15.67 ( skv_2, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_18 ) 15.40/15.67 ( skv_2, skv_21 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* (- 1) skv_5) ) 15.40/15.67 ( skv_4, (div skv_4 skv_5) ) 15.40/15.67 ( skv_4, (* (- 1) (div skv_4 skv_5)) ) 15.40/15.67 ( skv_4, skv_19 ) 15.40/15.67 ( skv_4, skv_20 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_4), skv_5 ) 15.40/15.67 ( (div skv_2 skv_7), skv_3 ) 15.40/15.67 ( (div skv_2 skv_7), skv_6 ) 15.40/15.67 ( (* (- 1) skv_2), skv_3 ) 15.40/15.67 ( (* (- 1) skv_2), skv_6 ) 15.40/15.67 ( (* 2 skv_2), skv_3 ) 15.40/15.67 ( (* 2 skv_2), skv_6 ) 15.40/15.67 ( (* 2 skv_2), skv_7 ) 15.40/15.67 ( (* 2 skv_2), (div skv_2 skv_7) ) 15.40/15.67 ( (* 2 skv_4), skv_4 ) 15.40/15.67 ( (* 2 skv_4), skv_5 ) 15.40/15.67 ( (* 2 skv_4), skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (= (gcd A B) (gcd (* (- 1) A) B)) ) 15.40/15.67 ( skv_2, skv_2 ) 15.40/15.67 ( skv_5, skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int) (C Int)) (or (not (divides A B)) (not (divides B C)) (divides A C)) ) 15.40/15.67 ( skv_3, skv_2, skv_4 ) 15.40/15.67 ( skv_3, skv_2, (* (- 1) skv_4) ) 15.40/15.67 ( skv_3, (div skv_2 skv_7), skv_2 ) 15.40/15.67 ( skv_4, skv_4, skv_4 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( skv_6, skv_2, (* 2 skv_4) ) 15.40/15.67 ( skv_6, (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.67 ( skv_7, skv_2, 0 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= (+ (abs X) (* (- 1) (abs (* Y (div X Y))))) 0)) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (>= X 1) (not (>= Y 1)) (not (>= (div X Y) 1))) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((D Int) (N Int)) (= (divides D N) (not (forall ((Q Int)) (not (= N (* D Q))) ))) ) 15.40/15.67 ( 2, skv_2 ) 15.40/15.67 ( 2, (div skv_2 skv_7) ) 15.40/15.67 ( 3, skv_2 ) 15.40/15.67 ( 3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_3, 0 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (div skv_2 skv_7) ) 15.40/15.67 ( skv_4, (* 2 skv_4) ) 15.40/15.67 ( skv_5, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0 ) 15.40/15.67 ( skv_6, skv_2 ) 15.40/15.67 ( skv_6, (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2 ) 15.40/15.67 ( skv_7, (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_3), skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4 ) 15.40/15.67 ( (* (- 1) skv_6), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4 ) 15.40/15.67 ( skv_18, skv_2 ) 15.40/15.67 ( skv_18, skv_6 ) 15.40/15.67 ( skv_19, skv_4 ) 15.40/15.67 ( skv_20, skv_4 ) 15.40/15.67 ( skv_20, skv_5 ) 15.40/15.67 ( skv_21, skv_2 ) 15.40/15.67 ( skv_21, skv_3 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides (* (- 1) A) B)) (divides A B)) ) 15.40/15.67 ( 2, (div skv_2 skv_7) ) 15.40/15.67 ( 3, skv_2 ) 15.40/15.67 ( 3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_4, (div skv_2 skv_7) ) 15.40/15.67 ( skv_18, skv_6 ) 15.40/15.67 ( skv_20, skv_5 ) 15.40/15.67 ( skv_21, skv_3 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (div X Y))) (or (not (>= Y 1)) (not (>= X 0)) (and (>= _let_0 0) (>= (+ X (* (- 1) _let_0)) 0)))) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (= X (+ (mod X Y) (* Y (div X Y))))) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((N Int)) (= (not (forall ((K Int)) (not (= N (* 2 K))) )) (even N)) ) 15.40/15.67 ( 3 ) 15.40/15.67 ( skv_3 ) 15.40/15.67 ( skv_6 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (not (>= Y 1)) (>= (div X Y) 0)) ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides A B)) (not (divides B A)) (= A (* (- 1) B)) (= A B)) ) 15.40/15.67 ( 0, skv_3 ) 15.40/15.67 ( 0, skv_4 ) 15.40/15.67 ( 0, skv_6 ) 15.40/15.67 ( 2, skv_2 ) 15.40/15.67 ( skv_2, 2 ) 15.40/15.67 ( skv_2, skv_3 ) 15.40/15.67 ( skv_2, skv_6 ) 15.40/15.67 ( skv_2, skv_7 ) 15.40/15.67 ( skv_2, (* (- 1) skv_3) ) 15.40/15.67 ( skv_2, (* (- 1) skv_6) ) 15.40/15.67 ( skv_2, (div skv_2 skv_7) ) 15.40/15.67 ( skv_2, skv_18 ) 15.40/15.67 ( skv_2, skv_21 ) 15.40/15.67 ( skv_3, 0 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7) ) 15.40/15.67 ( skv_3, (* (- 1) skv_2) ) 15.40/15.67 ( skv_3, (* 2 skv_2) ) 15.40/15.67 ( skv_4, 0 ) 15.40/15.67 ( skv_4, skv_4 ) 15.40/15.67 ( skv_4, skv_5 ) 15.40/15.67 ( skv_4, (* (- 1) skv_4) ) 15.40/15.67 ( skv_4, (* (- 1) skv_5) ) 15.40/15.67 ( skv_4, (div skv_4 skv_5) ) 15.40/15.67 ( skv_4, (* (- 1) (div skv_4 skv_5)) ) 15.40/15.67 ( skv_4, (* 2 skv_4) ) 15.40/15.67 ( skv_4, skv_19 ) 15.40/15.67 ( skv_4, skv_20 ) 15.40/15.67 ( skv_5, skv_4 ) 15.40/15.67 ( skv_5, (* (- 1) skv_4) ) 15.40/15.67 ( skv_5, (* 2 skv_4) ) 15.40/15.67 ( skv_6, 0 ) 15.40/15.67 ( skv_6, skv_2 ) 15.40/15.67 ( skv_6, (div skv_2 skv_7) ) 15.40/15.67 ( skv_6, (* (- 1) skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_2) ) 15.40/15.67 ( skv_6, (* 2 skv_4) ) 15.40/15.67 ( skv_7, skv_2 ) 15.40/15.67 ( skv_7, (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_3), skv_2 ) 15.40/15.67 ( (* (- 1) skv_4), skv_4 ) 15.40/15.67 ( (* (- 1) skv_4), skv_5 ) 15.40/15.67 ( (* (- 1) skv_5), skv_4 ) 15.40/15.67 ( (div skv_4 skv_5), skv_4 ) 15.40/15.67 ( (* (- 1) skv_6), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_2 ) 15.40/15.67 ( (div skv_2 skv_7), skv_3 ) 15.40/15.67 ( (div skv_2 skv_7), skv_6 ) 15.40/15.67 ( (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.67 ( (* (- 1) skv_2), skv_3 ) 15.40/15.67 ( (* (- 1) skv_2), skv_6 ) 15.40/15.67 ( (* (- 1) (div skv_4 skv_5)), skv_4 ) 15.40/15.67 ( (* 2 skv_2), skv_3 ) 15.40/15.67 ( (* 2 skv_2), skv_6 ) 15.40/15.67 ( (* 2 skv_2), skv_7 ) 15.40/15.67 ( (* 2 skv_2), (div skv_2 skv_7) ) 15.40/15.67 ( (* 2 skv_4), skv_4 ) 15.40/15.67 ( (* 2 skv_4), skv_5 ) 15.40/15.67 ( (* 2 skv_4), skv_6 ) 15.40/15.67 ( skv_18, skv_2 ) 15.40/15.67 ( skv_19, skv_4 ) 15.40/15.67 ( skv_20, skv_4 ) 15.40/15.67 ( skv_21, skv_2 ) 15.40/15.67 ) 15.40/15.67 (instantiation (forall ((A Int) (B Int)) (or (not (divides A B)) (= B 0) (not (>= (+ (abs A) (* (- 1) (abs B))) 1))) ) 15.40/15.67 ( 2, skv_2 ) 15.40/15.67 ( skv_3, 0 ) 15.40/15.67 ( skv_3, skv_2 ) 15.40/15.67 ( skv_3, (div skv_2 skv_7) ) 15.40/15.68 ( skv_3, (* (- 1) skv_2) ) 15.40/15.68 ( skv_3, (* 2 skv_2) ) 15.40/15.68 ( skv_4, 0 ) 15.40/15.68 ( skv_4, skv_4 ) 15.40/15.68 ( skv_4, (* (- 1) skv_4) ) 15.40/15.68 ( skv_4, (* 2 skv_4) ) 15.40/15.68 ( skv_5, skv_4 ) 15.40/15.68 ( skv_5, (* (- 1) skv_4) ) 15.40/15.68 ( skv_5, (* 2 skv_4) ) 15.40/15.68 ( skv_6, 0 ) 15.40/15.68 ( skv_6, skv_2 ) 15.40/15.68 ( skv_6, (div skv_2 skv_7) ) 15.40/15.68 ( skv_6, (* (- 1) skv_2) ) 15.40/15.68 ( skv_6, (* 2 skv_2) ) 15.40/15.68 ( skv_6, (* 2 skv_4) ) 15.40/15.68 ( skv_7, skv_2 ) 15.40/15.68 ( skv_7, (* 2 skv_2) ) 15.40/15.68 ( (* (- 1) skv_3), skv_2 ) 15.40/15.68 ( (* (- 1) skv_4), skv_4 ) 15.40/15.68 ( (* (- 1) skv_5), skv_4 ) 15.40/15.68 ( (div skv_4 skv_5), skv_4 ) 15.40/15.68 ( (* (- 1) skv_6), skv_2 ) 15.40/15.68 ( (div skv_2 skv_7), skv_2 ) 15.40/15.68 ( (div skv_2 skv_7), (* 2 skv_2) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)), skv_4 ) 15.40/15.68 ( skv_18, skv_2 ) 15.40/15.68 ( skv_19, skv_4 ) 15.40/15.68 ( skv_20, skv_4 ) 15.40/15.68 ( skv_21, skv_2 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((A Int) (B Int) (D Int)) (or (not (>= D 0)) (not (divides D A)) (not (divides D B)) (not (forall ((X Int)) (or (not (divides X A)) (not (divides X B)) (divides X D)) )) (= D (gcd A B))) ) 15.40/15.68 ( 0, 0, skv_3 ) 15.40/15.68 ( 0, 0, skv_4 ) 15.40/15.68 ( 0, 0, skv_6 ) 15.40/15.68 ( skv_2, skv_2, 2 ) 15.40/15.68 ( skv_2, skv_2, skv_3 ) 15.40/15.68 ( skv_2, skv_2, skv_6 ) 15.40/15.68 ( skv_2, skv_2, skv_7 ) 15.40/15.68 ( skv_2, skv_2, (* (- 1) skv_3) ) 15.40/15.68 ( skv_2, skv_2, (* (- 1) skv_6) ) 15.40/15.68 ( skv_2, skv_2, (div skv_2 skv_7) ) 15.40/15.68 ( skv_2, skv_2, skv_18 ) 15.40/15.68 ( skv_2, skv_2, skv_21 ) 15.40/15.68 ( skv_2, (* (- 1) skv_2), skv_3 ) 15.40/15.68 ( skv_2, (* (- 1) skv_2), skv_6 ) 15.40/15.68 ( skv_4, skv_4, skv_4 ) 15.40/15.68 ( skv_4, skv_4, skv_5 ) 15.40/15.68 ( skv_4, skv_4, (* (- 1) skv_4) ) 15.40/15.68 ( skv_4, skv_4, (* (- 1) skv_5) ) 15.40/15.68 ( skv_4, skv_4, (div skv_4 skv_5) ) 15.40/15.68 ( skv_4, skv_4, (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_4, skv_4, skv_19 ) 15.40/15.68 ( skv_4, skv_4, skv_20 ) 15.40/15.68 ( skv_4, (* (- 1) skv_4), skv_4 ) 15.40/15.68 ( (* (- 1) skv_4), skv_4, skv_4 ) 15.40/15.68 ( (* (- 1) skv_4), (* (- 1) skv_4), skv_5 ) 15.40/15.68 ( (div skv_2 skv_7), (div skv_2 skv_7), skv_3 ) 15.40/15.68 ( (div skv_2 skv_7), (div skv_2 skv_7), skv_6 ) 15.40/15.68 ( (* (- 1) skv_2), skv_2, skv_3 ) 15.40/15.68 ( (* (- 1) skv_2), skv_2, skv_6 ) 15.40/15.68 ( (* 2 skv_2), (* 2 skv_2), skv_3 ) 15.40/15.68 ( (* 2 skv_2), (* 2 skv_2), skv_6 ) 15.40/15.68 ( (* 2 skv_2), (* 2 skv_2), skv_7 ) 15.40/15.68 ( (* 2 skv_2), (* 2 skv_2), (div skv_2 skv_7) ) 15.40/15.68 ( (* 2 skv_4), (* 2 skv_4), skv_4 ) 15.40/15.68 ( (* 2 skv_4), (* 2 skv_4), skv_5 ) 15.40/15.68 ( (* 2 skv_4), (* 2 skv_4), skv_6 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((P Int)) (or (not (>= P 2)) (not (forall ((D Int)) (let ((_let_0 (* D D))) (or (not (>= D 2)) (not (prime D)) (not (>= _let_0 2)) (not (>= (+ P (* (- 1) _let_0)) 0)) (not (divides D P)))) )) (prime P)) ) 15.40/15.68 ( 1 ) 15.40/15.68 ( skv_2 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((X Int)) (or (>= X 0) (= X (* (- 1) (abs X)))) ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( (* skv_5 (div skv_4 skv_5)) ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((X Int)) (or (not (>= X 0)) (= X (abs X))) ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( (* skv_5 (div skv_4 skv_5)) ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= X (mod X Y))) ) 15.40/15.68 ( skv_2, skv_3 ) 15.40/15.68 ( skv_2, skv_6 ) 15.40/15.68 ( skv_4, skv_4 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((P Int)) (or (not (prime P)) (not (even P)) (= P 2)) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( 3 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((X Int) (Y Int) (Z Int)) (= (gcd X (gcd Y Z)) (gcd (gcd X Y) Z)) ) 15.40/15.68 ( skv_2, skv_2, skv_2 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (not (>= I 2)) (not (divides I skv_4)) (and (>= (+ I (* (- 1) skv_3)) 0) (divides I skv_2))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( 3 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (not (prime I)) (not (divides I skv_2)) (not (>= (+ I (* (- 1) skv_3)) 1)) (divides I skv_4)) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( 3 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (>= (+ I (* (- 1) skv_3)) 0) (not (>= I 2)) (not (divides I skv_4))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (>= (+ I (* (- 1) skv_5)) 0) (not (>= I 2)) (not (divides I skv_4))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (>= (+ I (* (- 1) skv_7)) 0) (not (>= I 2)) (not (divides I skv_2))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((I Int)) (or (not (divides I skv_2)) (not (>= (+ I (* (- 1) skv_7)) 1)) (not (prime I)) (and (divides I (div skv_2 skv_7)) (coprime skv_7 I))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( 3 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (div skv_4 skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((N Int)) (or (>= N 2) (not (>= N 1)) (coprime N 2)) ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((N Int)) (or (>= N 3) (not (>= N 1)) (coprime N 3)) ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((N Int)) (or (>= (+ N (* (- 1) skv_6)) 0) (not (>= N 1)) (coprime N skv_6)) ) 15.40/15.68 ( skv_5 ) 15.40/15.68 ) 15.40/15.68 (instantiation (forall ((X Int)) (or (not (divides X skv_4)) (divides X (div skv_4 skv_5))) ) 15.40/15.68 ( 2 ) 15.40/15.68 ( 3 ) 15.40/15.68 ( skv_3 ) 15.40/15.68 ( skv_4 ) 15.40/15.68 ( skv_6 ) 15.40/15.68 ( skv_7 ) 15.40/15.68 ( (* (- 1) skv_3) ) 15.40/15.68 ( (* (- 1) skv_4) ) 15.40/15.68 ( (* (- 1) skv_5) ) 15.40/15.68 ( (* (- 1) skv_6) ) 15.40/15.68 ( (div skv_2 skv_7) ) 15.40/15.68 ( (* (- 1) (div skv_4 skv_5)) ) 15.40/15.68 ( skv_18 ) 15.40/15.68 ( skv_19 ) 15.40/15.68 ( skv_20 ) 15.40/15.68 ( skv_21 ) 15.40/15.68 ) 15.40/15.68 % SZS output end Proof for theBenchmark 15.40/15.68 EOF