0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.23 % Computer : n018.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:29:09 CDT 2018 0.03/0.23 % CPUTime : 0.07/0.27 %----Proving with arithmetic mode 0.07/0.27 ------- cvc4-tfa casc j9 : /export/starexec/sandbox/benchmark/theBenchmark.p at ... 0.07/0.27 --- Run --cbqi-all --purify-triggers --full-saturate-quant at 15... 15.16/15.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15... 30.16/30.82 --- Run --finite-model-find --decision=internal at 15... 45.55/49.49 --- Run --no-e-matching --full-saturate-quant at 15... 45.56/49.70 % SZS status Theorem for theBenchmark 45.56/49.70 % SZS output start Proof for theBenchmark 45.56/49.70 (skolem (let ((_let_0 (power X N))) (forall ((X Int) (N Int) (BOUND_VARIABLE_888 Int) (BOUND_VARIABLE_889 Int) (BOUND_VARIABLE_890 Int)) (or (not (>= N 0)) (not (= _let_0 (* BOUND_VARIABLE_890 (power BOUND_VARIABLE_889 BOUND_VARIABLE_888)))) (not (>= BOUND_VARIABLE_888 0)) (>= BOUND_VARIABLE_888 1) (= BOUND_VARIABLE_890 _let_0)) )) 45.56/49.70 ( skv_2 skv_3 skv_4 skv_5 skv_6 ) 45.56/49.70 ) 45.56/49.70 (instantiation (forall ((A ty) (X bool) (X1 uni) (X2 uni)) (sort A (match_bool A X X1 X2)) ) 45.56/49.70 ( e_ty_8, true, e_uni_9, e_uni_9 ) 45.56/49.70 ( e_ty_8, true, e_uni_9, (contents e_ty_8 e_uni_9) ) 45.56/49.70 ( e_ty_8, true, (contents e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/49.70 ( e_ty_8, false, e_uni_9, e_uni_9 ) 45.56/49.70 ( e_ty_8, false, (contents e_ty_8 e_uni_9), e_uni_9 ) 45.56/49.70 ( (ref e_ty_8), true, e_uni_9, e_uni_9 ) 45.56/49.70 ( (ref e_ty_8), true, e_uni_9, (contents e_ty_8 e_uni_9) ) 45.56/49.70 ( (ref e_ty_8), true, (contents e_ty_8 e_uni_9), e_uni_9 ) 45.56/49.70 ( (ref e_ty_8), true, (contents e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/49.70 ) 45.56/49.70 (instantiation (forall ((A ty) (X uni)) (sort A (contents A X)) ) 45.56/50.15 ( e_ty_8, e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), e_uni_9 ) 45.56/50.15 ( (ref e_ty_8), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), e_uni_9 ) 45.56/50.15 ( (ref (ref e_ty_8)), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty) (X uni)) (sort (ref A) (mk_ref A X)) ) 45.56/50.15 ( e_ty_8, e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), e_uni_9 ) 45.56/50.15 ( (ref e_ty_8), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), e_uni_9 ) 45.56/50.15 ( (ref (ref e_ty_8)), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty)) (sort A (witness A)) ) 45.56/50.15 ( e_ty_8 ) 45.56/50.15 ( (ref e_ty_8) ) 45.56/50.15 ( (ref (ref e_ty_8)) ) 45.56/50.15 ( (ref (ref (ref e_ty_8))) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (= (power X 0) 1) ) 45.56/50.15 ( skv_2 ) 45.56/50.15 ( skv_3 ) 45.56/50.15 ( skv_4 ) 45.56/50.15 ( skv_5 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (+ skv_3 (* skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (div 1 1)) ) 45.56/50.15 ( (* (- 1) (div skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ( (* (- 1) (abs skv_3)) ) 45.56/50.15 ( (+ (* (- 1) (div skv_5 skv_3)) (div (+ skv_5 (* skv_3 skv_3)) skv_3)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (= (mod X 1) 0) ) 45.56/50.15 ( 0 ) 45.56/50.15 ( 1 ) 45.56/50.15 ( 2 ) 45.56/50.15 ( skv_5 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ( (* (- 1) (div skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ( (* (- 1) (abs skv_3)) ) 45.56/50.15 ( (+ skv_5 (* skv_3 skv_3)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (= X (div X 1)) ) 45.56/50.15 ( 0 ) 45.56/50.15 ( 1 ) 45.56/50.15 ( (- 1) ) 45.56/50.15 ( 2 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ( (* (- 1) (div skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ( (* (- 1) (abs skv_3)) ) 45.56/50.15 ( (+ skv_3 (* skv_3 skv_4)) ) 45.56/50.15 ( (+ skv_4 (* skv_3 skv_4)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((U tuple0)) (= tuple02 U) ) 45.56/50.15 ( e_tuple0_7 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= X (mod X Y))) ) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 0 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ( skv_3, skv_3 ) 45.56/50.15 ( skv_3, skv_4 ) 45.56/50.15 ( skv_3, skv_5 ) 45.56/50.15 ( skv_4, skv_4 ) 45.56/50.15 ( skv_6, 0 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= (div X Y) 0)) ) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 0 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ( skv_3, skv_3 ) 45.56/50.15 ( skv_3, skv_4 ) 45.56/50.15 ( skv_3, skv_5 ) 45.56/50.15 ( skv_4, skv_4 ) 45.56/50.15 ( skv_6, 0 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (= X (power X 1)) ) 45.56/50.15 ( skv_2 ) 45.56/50.15 ( skv_3 ) 45.56/50.15 ( skv_4 ) 45.56/50.15 ( skv_5 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ( (+ skv_3 (* skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (div 1 1)) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort A Z)) (= Z (match_bool A true Z Z1))) ) 45.56/50.15 ( e_ty_8, e_uni_9, e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9), e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9), e_uni_9 ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (>= X 1) (not (>= Y 1)) (not (>= (div X Y) 1))) ) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 0 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ( skv_3, skv_3 ) 45.56/50.15 ( skv_6, 0 ) 45.56/50.15 ( skv_6, 1 ) 45.56/50.15 ( skv_6, (- 1) ) 45.56/50.15 ( skv_6, 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int) (N Int)) (or (not (>= N 0)) (= (power (* X Y) N) (* (power X N) (power Y N)))) ) 45.56/50.15 ( skv_2, skv_2, 0 ) 45.56/50.15 ( skv_3, skv_3, 0 ) 45.56/50.15 ( skv_3, skv_3, 1 ) 45.56/50.15 ( skv_3, skv_4, 0 ) 45.56/50.15 ( skv_3, skv_4, 1 ) 45.56/50.15 ( skv_4, skv_3, 0 ) 45.56/50.15 ( skv_4, skv_3, 1 ) 45.56/50.15 ( skv_4, skv_3, 2 ) 45.56/50.15 ( skv_4, skv_4, 0 ) 45.56/50.15 ( skv_4, skv_4, 1 ) 45.56/50.15 ( skv_4, skv_4, 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (= (>= (+ Y (* (- 1) (abs X))) 0) (and (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 0))) ) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ) 45.56/50.15 (instantiation (let ((_let_0 (div X Y))) (forall ((X Int) (Y Int)) (or (not (>= X 0)) (not (>= Y 1)) (and (>= (+ X (* (- 1) _let_0)) 0) (>= _let_0 0))) )) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 0 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (N Int) (M Int)) (or (not (>= N 0)) (not (>= M 0)) (= (power (power X N) M) (power X (* N M)))) ) 45.56/50.15 ( skv_2, 0, 0 ) 45.56/50.15 ( skv_3, 0, 0 ) 45.56/50.15 ( skv_3, 0, 1 ) 45.56/50.15 ( skv_3, 1, 0 ) 45.56/50.15 ( skv_3, 1, 1 ) 45.56/50.15 ( skv_4, 0, 0 ) 45.56/50.15 ( skv_4, 0, 1 ) 45.56/50.15 ( skv_4, 1, 0 ) 45.56/50.15 ( skv_4, 1, 1 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (>= (abs X) 0) ) 45.56/50.15 ( 0 ) 45.56/50.15 ( 1 ) 45.56/50.15 ( (- 1) ) 45.56/50.15 ( 2 ) 45.56/50.15 ( skv_3 ) 45.56/50.15 ( skv_4 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (N Int) (M Int)) (or (not (>= N 0)) (not (>= M 0)) (= (power X (+ N M)) (* (power X N) (power X M)))) ) 45.56/50.15 ( skv_2, 0, 0 ) 45.56/50.15 ( skv_3, 0, 0 ) 45.56/50.15 ( skv_3, 0, 1 ) 45.56/50.15 ( skv_3, 1, 0 ) 45.56/50.15 ( skv_3, 1, 1 ) 45.56/50.15 ( skv_4, 0, 0 ) 45.56/50.15 ( skv_4, 0, 1 ) 45.56/50.15 ( skv_4, 0, 2 ) 45.56/50.15 ( skv_4, 1, 0 ) 45.56/50.15 ( skv_4, 1, 1 ) 45.56/50.15 ( skv_4, 1, 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= (+ (abs X) (* (- 1) (abs (* Y (div X Y))))) 0)) ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (let ((_let_0 (abs Y))) (let ((_let_1 (mod X Y))) (forall ((X Int) (Y Int)) (or (= Y 0) (and (>= (+ _let_0 _let_1) 1) (>= (+ _let_0 (* (- 1) _let_1)) 1))) ))) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (or (not (>= X 0)) (= X (abs X))) ) 45.56/50.15 ( 0 ) 45.56/50.15 ( 1 ) 45.56/50.15 ( (- 1) ) 45.56/50.15 ( 2 ) 45.56/50.15 ( skv_5 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ( (* (- 1) (abs skv_3)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int)) (or (>= X 0) (= X (* (- 1) (abs X)))) ) 45.56/50.15 ( 0 ) 45.56/50.15 ( 1 ) 45.56/50.15 ( (- 1) ) 45.56/50.15 ( 2 ) 45.56/50.15 ( skv_3 ) 45.56/50.15 ( skv_4 ) 45.56/50.15 ( skv_5 ) 45.56/50.15 ( skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2) ) 45.56/50.15 ( (+ skv_3 (* skv_3 skv_3)) ) 45.56/50.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (not (>= Y 1)) (>= (div X Y) 0)) ) 45.56/50.15 ( 0, 0 ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 0 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 0 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 0 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 45.56/50.15 ( 0, 0, 0 ) 45.56/50.15 ( 0, 0, 1 ) 45.56/50.15 ( 0, 0, 2 ) 45.56/50.15 ( (- 1), 0, 0 ) 45.56/50.15 ( (- 1), 0, 1 ) 45.56/50.15 ( (- 1), (- 1), 0 ) 45.56/50.15 ( (- 1), (- 1), 1 ) 45.56/50.15 ( (- 2), (- 2), 1 ) 45.56/50.15 ( (- 2), (- 2), 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (not (>= Y 0)) (not (>= Z 0)) (not (>= X 1)) (= (mod Z X) (mod (+ Z (* X Y)) X))) ) 45.56/50.15 ( 0, 0, 0 ) 45.56/50.15 ( 0, 0, 1 ) 45.56/50.15 ( 0, 0, (- 1) ) 45.56/50.15 ( 0, 0, 2 ) 45.56/50.15 ( 0, 0, skv_6 ) 45.56/50.15 ( 0, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 0, 0, (* skv_2 skv_2) ) 45.56/50.15 ( 1, 0, 0 ) 45.56/50.15 ( 1, 0, 1 ) 45.56/50.15 ( 1, 0, (- 1) ) 45.56/50.15 ( 1, 0, 2 ) 45.56/50.15 ( 1, 0, skv_6 ) 45.56/50.15 ( 1, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 1, 0, (* skv_2 skv_2) ) 45.56/50.15 ( (- 1), 0, 0 ) 45.56/50.15 ( (- 1), 0, 1 ) 45.56/50.15 ( (- 1), 0, (- 1) ) 45.56/50.15 ( (- 1), 0, 2 ) 45.56/50.15 ( (- 1), 0, skv_6 ) 45.56/50.15 ( (- 1), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (- 1), 0, (* skv_2 skv_2) ) 45.56/50.15 ( 2, 0, 0 ) 45.56/50.15 ( 2, 0, 1 ) 45.56/50.15 ( 2, 0, (- 1) ) 45.56/50.15 ( 2, 0, 2 ) 45.56/50.15 ( 2, 0, skv_6 ) 45.56/50.15 ( 2, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 2, 0, (* skv_2 skv_2) ) 45.56/50.15 ( skv_3, skv_3, skv_3 ) 45.56/50.15 ( skv_3, skv_3, skv_4 ) 45.56/50.15 ( skv_3, skv_3, skv_5 ) 45.56/50.15 ( skv_3, skv_4, skv_3 ) 45.56/50.15 ( skv_3, skv_4, skv_4 ) 45.56/50.15 ( skv_4, skv_3, skv_3 ) 45.56/50.15 ( skv_4, skv_3, skv_4 ) 45.56/50.15 ( skv_4, skv_4, skv_3 ) 45.56/50.15 ( skv_4, skv_4, skv_4 ) 45.56/50.15 ( skv_6, 0, 0 ) 45.56/50.15 ( skv_6, 0, 1 ) 45.56/50.15 ( skv_6, 0, (- 1) ) 45.56/50.15 ( skv_6, 0, 2 ) 45.56/50.15 ( skv_6, 0, skv_6 ) 45.56/50.15 ( skv_6, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( skv_6, 0, (* skv_2 skv_2) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 0 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 1 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (- 1) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 2 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_2 skv_2) ) 45.56/50.15 ( (* skv_2 skv_2), 0, 0 ) 45.56/50.15 ( (* skv_2 skv_2), 0, 1 ) 45.56/50.15 ( (* skv_2 skv_2), 0, (- 1) ) 45.56/50.15 ( (* skv_2 skv_2), 0, 2 ) 45.56/50.15 ( (* skv_2 skv_2), 0, skv_6 ) 45.56/50.15 ( (* skv_2 skv_2), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2), 0, (* skv_2 skv_2) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (N Int)) (or (not (>= N 1)) (= (power X N) (* X (power X (+ (- 1) N))))) ) 45.56/50.15 ( skv_2, 0 ) 45.56/50.15 ( skv_2, 1 ) 45.56/50.15 ( skv_3, 0 ) 45.56/50.15 ( skv_3, 1 ) 45.56/50.15 ( skv_3, 2 ) 45.56/50.15 ( skv_3, 3 ) 45.56/50.15 ( skv_4, 0 ) 45.56/50.15 ( skv_4, 1 ) 45.56/50.15 ( skv_4, 2 ) 45.56/50.15 ( skv_4, 3 ) 45.56/50.15 ( skv_5, 0 ) 45.56/50.15 ( skv_5, 1 ) 45.56/50.15 ( skv_5, 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (N Int)) (or (not (>= N 0)) (= (power X (+ 1 N)) (* X (power X N)))) ) 45.56/50.15 ( skv_2, 0 ) 45.56/50.15 ( skv_3, 0 ) 45.56/50.15 ( skv_3, 1 ) 45.56/50.15 ( skv_3, 2 ) 45.56/50.15 ( skv_4, 0 ) 45.56/50.15 ( skv_4, 1 ) 45.56/50.15 ( skv_4, 2 ) 45.56/50.15 ( skv_5, 0 ) 45.56/50.15 ( skv_5, 1 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort A Z1)) (= Z1 (match_bool A false Z Z1))) ) 45.56/50.15 ( e_ty_8, e_uni_9, e_uni_9 ) 45.56/50.15 ( e_ty_8, e_uni_9, (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 e_uni_9), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), e_uni_9, (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), e_uni_9, (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ( (ref e_ty_8), (contents e_ty_8 e_uni_9), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty) (U uni)) (or (not (sort (ref A) U)) (= U (mk_ref A (contents A U)))) ) 45.56/50.15 ( e_ty_8, e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), e_uni_9 ) 45.56/50.15 ( (ref e_ty_8), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), e_uni_9 ) 45.56/50.15 ( (ref (ref e_ty_8)), (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (= X (+ (mod X Y) (* Y (div X Y))))) ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((A ty) (U uni)) (or (not (sort A U)) (= U (contents A (mk_ref A U)))) ) 45.56/50.15 ( e_ty_8, e_uni_9 ) 45.56/50.15 ( e_ty_8, (contents e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( e_ty_8, (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref e_ty_8), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 e_uni_9) ) 45.56/50.15 ( (ref (ref e_ty_8)), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ( (ref (ref (ref e_ty_8))), (mk_ref e_ty_8 (contents e_ty_8 e_uni_9)) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (= Y 0) (>= (mod X Y) 0)) ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (not (>= Y 0)) (not (>= Z 0)) (not (>= X 1)) (= Y (+ (* (- 1) (div Z X)) (div (+ Z (* X Y)) X)))) ) 45.56/50.15 ( 0, 0, 0 ) 45.56/50.15 ( 0, 0, 1 ) 45.56/50.15 ( 0, 0, (- 1) ) 45.56/50.15 ( 0, 0, 2 ) 45.56/50.15 ( 0, 0, skv_6 ) 45.56/50.15 ( 0, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 0, 0, (* skv_2 skv_2) ) 45.56/50.15 ( 1, 0, 0 ) 45.56/50.15 ( 1, 0, 1 ) 45.56/50.15 ( 1, 0, (- 1) ) 45.56/50.15 ( 1, 0, 2 ) 45.56/50.15 ( 1, 0, skv_6 ) 45.56/50.15 ( 1, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 1, 0, (* skv_2 skv_2) ) 45.56/50.15 ( (- 1), 0, 0 ) 45.56/50.15 ( (- 1), 0, 1 ) 45.56/50.15 ( (- 1), 0, (- 1) ) 45.56/50.15 ( (- 1), 0, 2 ) 45.56/50.15 ( (- 1), 0, skv_6 ) 45.56/50.15 ( (- 1), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (- 1), 0, (* skv_2 skv_2) ) 45.56/50.15 ( 2, 0, 0 ) 45.56/50.15 ( 2, 0, 1 ) 45.56/50.15 ( 2, 0, (- 1) ) 45.56/50.15 ( 2, 0, 2 ) 45.56/50.15 ( 2, 0, skv_6 ) 45.56/50.15 ( 2, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( 2, 0, (* skv_2 skv_2) ) 45.56/50.15 ( skv_3, skv_3, skv_3 ) 45.56/50.15 ( skv_3, skv_3, skv_4 ) 45.56/50.15 ( skv_3, skv_3, skv_5 ) 45.56/50.15 ( skv_3, skv_4, skv_3 ) 45.56/50.15 ( skv_3, skv_4, skv_4 ) 45.56/50.15 ( skv_4, skv_3, skv_3 ) 45.56/50.15 ( skv_4, skv_3, skv_4 ) 45.56/50.15 ( skv_4, skv_4, skv_3 ) 45.56/50.15 ( skv_4, skv_4, skv_4 ) 45.56/50.15 ( skv_6, 0, 0 ) 45.56/50.15 ( skv_6, 0, 1 ) 45.56/50.15 ( skv_6, 0, (- 1) ) 45.56/50.15 ( skv_6, 0, 2 ) 45.56/50.15 ( skv_6, 0, skv_6 ) 45.56/50.15 ( skv_6, 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( skv_6, 0, (* skv_2 skv_2) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 0 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 1 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (- 1) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, 2 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, skv_6 ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_2 skv_2) ) 45.56/50.15 ( (* skv_2 skv_2), 0, 0 ) 45.56/50.15 ( (* skv_2 skv_2), 0, 1 ) 45.56/50.15 ( (* skv_2 skv_2), 0, (- 1) ) 45.56/50.15 ( (* skv_2 skv_2), 0, 2 ) 45.56/50.15 ( (* skv_2 skv_2), 0, skv_6 ) 45.56/50.15 ( (* skv_2 skv_2), 0, (* skv_6 (power skv_5 skv_4)) ) 45.56/50.15 ( (* skv_2 skv_2), 0, (* skv_2 skv_2) ) 45.56/50.15 ) 45.56/50.15 (instantiation (forall ((X Int) (Y Int)) (or (>= X 1) (= Y 0) (not (>= (mod X Y) 1))) ) 45.56/50.15 ( 0, 1 ) 45.56/50.15 ( 0, (- 1) ) 45.56/50.15 ( 0, 2 ) 45.56/50.15 ( 0, skv_6 ) 45.56/50.15 ( 1, 1 ) 45.56/50.15 ( 1, (- 1) ) 45.56/50.15 ( 1, 2 ) 45.56/50.15 ( 1, skv_6 ) 45.56/50.15 ( (- 1), 1 ) 45.56/50.15 ( (- 1), (- 1) ) 45.56/50.15 ( (- 1), 2 ) 45.56/50.15 ( (- 1), skv_6 ) 45.56/50.15 ( 2, 1 ) 45.56/50.15 ( 2, (- 1) ) 45.56/50.15 ( 2, 2 ) 45.56/50.15 ( 2, skv_6 ) 45.56/50.15 ( skv_6, 1 ) 45.56/50.15 ) 45.56/50.15 % SZS output end Proof for theBenchmark 45.56/50.15 EOF