0.04/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : do_CVC4 %s 0.14/0.35 % Computer : n020.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 11:03:10 EDT 2019 0.14/0.35 % CPUTime : 0.21/0.49 %----Proving TF0_ARI 0.21/0.49 ------- cvc4-tfa casc 27 : /export/starexec/sandbox/benchmark/theBenchmark.p at 180... 0.21/0.49 --- Run --finite-model-find --decision=internal at 15... 15.56/15.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15... 30.59/30.81 --- Run --no-e-matching --full-saturate-quant at 15... 30.62/31.14 % SZS status Theorem for theBenchmark 30.62/31.15 % SZS output start Proof for theBenchmark 30.62/31.15 (skolem (forall ((X Int) (N Int) (BOUND_VARIABLE_964 Int) (BOUND_VARIABLE_965 Int) (BOUND_VARIABLE_966 Int)) (let ((_let_0 (power X N))) (or (not (>= N 0)) (not (= _let_0 (* BOUND_VARIABLE_966 (power BOUND_VARIABLE_965 BOUND_VARIABLE_964)))) (not (>= BOUND_VARIABLE_964 0)) (>= BOUND_VARIABLE_964 1) (= BOUND_VARIABLE_966 _let_0))) ) 30.62/31.15 ( skv_2 skv_3 skv_4 skv_5 skv_6 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (X bool) (X1 uni) (X2 uni)) (sort A (match_bool A X X1 X2)) ) 30.62/31.15 ( e_ty_7, true, e_uni_8, e_uni_8 ) 30.62/31.15 ( e_ty_7, true, e_uni_8, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, true, (mk_ref e_ty_7 e_uni_8), e_uni_8 ) 30.62/31.15 ( e_ty_7, true, (mk_ref e_ty_7 e_uni_8), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, false, e_uni_8, e_uni_8 ) 30.62/31.15 ( e_ty_7, false, e_uni_8, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, false, (mk_ref e_ty_7 e_uni_8), e_uni_8 ) 30.62/31.15 ( e_ty_7, false, (mk_ref e_ty_7 e_uni_8), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), true, e_uni_8, e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), true, e_uni_8, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty)) (sort A (witness A)) ) 30.62/31.15 ( e_ty_7 ) 30.62/31.15 ( (ref e_ty_7) ) 30.62/31.15 ( (ref (ref e_ty_7)) ) 30.62/31.15 ( (ref (ref (ref e_ty_7))) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (X uni)) (sort (ref A) (mk_ref A X)) ) 30.62/31.15 ( e_ty_7, e_uni_8 ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref e_ty_7)), e_uni_8 ) 30.62/31.15 ( (ref (ref e_ty_7)), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((U tuple0)) (= tuple02 U) ) 30.62/31.15 ( e_tuple0_9 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (X uni)) (sort A (contents A X)) ) 30.62/31.15 ( e_ty_7, e_uni_8 ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref (ref e_ty_7)), e_uni_8 ) 30.62/31.15 ( (ref (ref e_ty_7)), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (= (mod X 1) 0) ) 30.62/31.15 ( 0 ) 30.62/31.15 ( 1 ) 30.62/31.15 ( (- 1) ) 30.62/31.15 ( 2 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (* (- 1) (div skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 30.62/31.15 ( (+ skv_5 (* skv_3 skv_3)) ) 30.62/31.15 ( (+ skv_3 (* skv_3 skv_5)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (not (>= X 0)) (>= (mod X Y) 0)) ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= X (mod X Y))) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 0 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_3, skv_3 ) 30.62/31.15 ( skv_3, skv_4 ) 30.62/31.15 ( skv_3, skv_5 ) 30.62/31.15 ( skv_4, skv_4 ) 30.62/31.15 ( skv_6, 0 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (N Int)) (or (not (>= N 1)) (= (power X N) (* X (power X (+ (- 1) N))))) ) 30.62/31.15 ( skv_2, 0 ) 30.62/31.15 ( skv_2, 1 ) 30.62/31.15 ( skv_3, 0 ) 30.62/31.15 ( skv_3, 1 ) 30.62/31.15 ( skv_4, 0 ) 30.62/31.15 ( skv_4, 1 ) 30.62/31.15 ( skv_4, 2 ) 30.62/31.15 ( skv_4, 3 ) 30.62/31.15 ( skv_5, 0 ) 30.62/31.15 ( skv_5, 1 ) 30.62/31.15 ( skv_5, 2 ) 30.62/31.15 ( (power skv_2 0), 0 ) 30.62/31.15 ( (power skv_2 0), 1 ) 30.62/31.15 ( (power skv_2 0), 2 ) 30.62/31.15 ( (* skv_2 skv_2), 0 ) 30.62/31.15 ( (* skv_2 skv_2), 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= (+ (abs X) (* (- 1) (abs (* Y (div X Y))))) 0)) ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ) 30.62/31.15 (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)))) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 0 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_6, 0 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (>= X 1) (= Y 0) (not (>= (mod X Y) 1))) ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ( skv_6, (- 1) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int) (N Int)) (or (not (>= N 0)) (= (power (* X Y) N) (* (power X N) (power Y N)))) ) 30.62/31.15 ( skv_2, skv_2, 0 ) 30.62/31.15 ( skv_3, skv_3, 0 ) 30.62/31.15 ( skv_4, skv_4, 0 ) 30.62/31.15 ( skv_4, skv_4, 1 ) 30.62/31.15 ( skv_4, skv_4, 2 ) 30.62/31.15 ( skv_4, (power skv_2 0), 0 ) 30.62/31.15 ( skv_4, (power skv_2 0), 1 ) 30.62/31.15 ( skv_4, (* skv_2 skv_2), 0 ) 30.62/31.15 ( (power skv_2 0), skv_4, 0 ) 30.62/31.15 ( (power skv_2 0), skv_4, 1 ) 30.62/31.15 ( (power skv_2 0), (power skv_2 0), 0 ) 30.62/31.15 ( (power skv_2 0), (power skv_2 0), 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (U uni)) (or (not (sort A U)) (= U (contents A (mk_ref A U)))) ) 30.62/31.15 ( e_ty_7, e_uni_8 ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 (contents e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref (ref e_ty_7))), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort A Z)) (= Z (match_bool A true Z Z1))) ) 30.62/31.15 ( e_ty_7, e_uni_8, e_uni_8 ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8), e_uni_8 ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), e_uni_8 ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 e_uni_8), e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8), e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (>= (+ X (* (- 1) Y)) 0) (= (div X Y) 0)) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 0 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_3, skv_3 ) 30.62/31.15 ( skv_3, skv_4 ) 30.62/31.15 ( skv_3, skv_5 ) 30.62/31.15 ( skv_4, skv_4 ) 30.62/31.15 ( skv_6, 0 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (not (>= X 1)) (not (>= Y 0)) (not (>= Z 0)) (= (mod Z X) (mod (+ Z (* X Y)) X))) ) 30.62/31.15 ( 0, 0, 0 ) 30.62/31.15 ( 0, 0, 1 ) 30.62/31.15 ( 0, 0, (- 1) ) 30.62/31.15 ( 0, 0, 2 ) 30.62/31.15 ( 0, 0, skv_6 ) 30.62/31.15 ( 0, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 0, 0, (* skv_2 skv_2) ) 30.62/31.15 ( 1, 0, 0 ) 30.62/31.15 ( 1, 0, 1 ) 30.62/31.15 ( 1, 0, (- 1) ) 30.62/31.15 ( 1, 0, 2 ) 30.62/31.15 ( 1, 0, skv_6 ) 30.62/31.15 ( 1, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 1, 0, (* skv_2 skv_2) ) 30.62/31.15 ( (- 1), 0, 0 ) 30.62/31.15 ( (- 1), 0, 1 ) 30.62/31.15 ( (- 1), 0, (- 1) ) 30.62/31.15 ( (- 1), 0, 2 ) 30.62/31.15 ( (- 1), 0, skv_6 ) 30.62/31.15 ( (- 1), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (- 1), 0, (* skv_2 skv_2) ) 30.62/31.15 ( 2, 0, 0 ) 30.62/31.15 ( 2, 0, 1 ) 30.62/31.15 ( 2, 0, (- 1) ) 30.62/31.15 ( 2, 0, 2 ) 30.62/31.15 ( 2, 0, skv_6 ) 30.62/31.15 ( 2, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 2, 0, (* skv_2 skv_2) ) 30.62/31.15 ( skv_3, skv_3, skv_3 ) 30.62/31.15 ( skv_3, skv_3, skv_4 ) 30.62/31.15 ( skv_3, skv_3, skv_5 ) 30.62/31.15 ( skv_3, skv_4, skv_3 ) 30.62/31.15 ( skv_3, skv_4, skv_4 ) 30.62/31.15 ( skv_3, skv_5, skv_3 ) 30.62/31.15 ( skv_4, skv_3, skv_3 ) 30.62/31.15 ( skv_4, skv_3, skv_4 ) 30.62/31.15 ( skv_4, skv_4, skv_3 ) 30.62/31.15 ( skv_4, skv_4, skv_4 ) 30.62/31.15 ( skv_6, 0, 0 ) 30.62/31.15 ( skv_6, 0, 1 ) 30.62/31.15 ( skv_6, 0, (- 1) ) 30.62/31.15 ( skv_6, 0, 2 ) 30.62/31.15 ( skv_6, 0, skv_6 ) 30.62/31.15 ( skv_6, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( skv_6, 0, (* skv_2 skv_2) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 0 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 1 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (- 1) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 2 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_2 skv_2) ) 30.62/31.15 ( (* skv_2 skv_2), 0, 0 ) 30.62/31.15 ( (* skv_2 skv_2), 0, 1 ) 30.62/31.15 ( (* skv_2 skv_2), 0, (- 1) ) 30.62/31.15 ( (* skv_2 skv_2), 0, 2 ) 30.62/31.15 ( (* skv_2 skv_2), 0, skv_6 ) 30.62/31.15 ( (* skv_2 skv_2), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2), 0, (* skv_2 skv_2) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (>= (abs X) 0) ) 30.62/31.15 ( 0 ) 30.62/31.15 ( 1 ) 30.62/31.15 ( (- 1) ) 30.62/31.15 ( 2 ) 30.62/31.15 ( skv_3 ) 30.62/31.15 ( skv_4 ) 30.62/31.15 ( skv_5 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (or (not (>= X 0)) (= X (abs X))) ) 30.62/31.15 ( 0 ) 30.62/31.15 ( 1 ) 30.62/31.15 ( (- 1) ) 30.62/31.15 ( 2 ) 30.62/31.15 ( skv_5 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (* (- 1) (div skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (or (>= X 0) (= X (* (- 1) (abs X)))) ) 30.62/31.15 ( 0 ) 30.62/31.15 ( 1 ) 30.62/31.15 ( (- 1) ) 30.62/31.15 ( 2 ) 30.62/31.15 ( skv_3 ) 30.62/31.15 ( skv_4 ) 30.62/31.15 ( skv_5 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (+ skv_3 (* skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (abs skv_3)) ) 30.62/31.15 ) 30.62/31.15 (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)))) ) 30.62/31.15 ( 0, 0, 0 ) 30.62/31.15 ( 0, 0, 1 ) 30.62/31.15 ( 0, 0, (- 1) ) 30.62/31.15 ( 0, 0, 2 ) 30.62/31.15 ( 0, 0, skv_6 ) 30.62/31.15 ( 0, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 0, 0, (* skv_2 skv_2) ) 30.62/31.15 ( 1, 0, 0 ) 30.62/31.15 ( 1, 0, 1 ) 30.62/31.15 ( 1, 0, (- 1) ) 30.62/31.15 ( 1, 0, 2 ) 30.62/31.15 ( 1, 0, skv_6 ) 30.62/31.15 ( 1, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 1, 0, (* skv_2 skv_2) ) 30.62/31.15 ( (- 1), 0, 0 ) 30.62/31.15 ( (- 1), 0, 1 ) 30.62/31.15 ( (- 1), 0, (- 1) ) 30.62/31.15 ( (- 1), 0, 2 ) 30.62/31.15 ( (- 1), 0, skv_6 ) 30.62/31.15 ( (- 1), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (- 1), 0, (* skv_2 skv_2) ) 30.62/31.15 ( 2, 0, 0 ) 30.62/31.15 ( 2, 0, 1 ) 30.62/31.15 ( 2, 0, (- 1) ) 30.62/31.15 ( 2, 0, 2 ) 30.62/31.15 ( 2, 0, skv_6 ) 30.62/31.15 ( 2, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( 2, 0, (* skv_2 skv_2) ) 30.62/31.15 ( skv_3, skv_3, skv_3 ) 30.62/31.15 ( skv_3, skv_3, skv_4 ) 30.62/31.15 ( skv_3, skv_3, skv_5 ) 30.62/31.15 ( skv_3, skv_4, skv_3 ) 30.62/31.15 ( skv_3, skv_4, skv_4 ) 30.62/31.15 ( skv_3, skv_5, skv_3 ) 30.62/31.15 ( skv_4, skv_3, skv_3 ) 30.62/31.15 ( skv_4, skv_3, skv_4 ) 30.62/31.15 ( skv_4, skv_4, skv_3 ) 30.62/31.15 ( skv_4, skv_4, skv_4 ) 30.62/31.15 ( skv_6, 0, 0 ) 30.62/31.15 ( skv_6, 0, 1 ) 30.62/31.15 ( skv_6, 0, (- 1) ) 30.62/31.15 ( skv_6, 0, 2 ) 30.62/31.15 ( skv_6, 0, skv_6 ) 30.62/31.15 ( skv_6, 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( skv_6, 0, (* skv_2 skv_2) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 0 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 1 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (- 1) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, 2 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)), 0, (* skv_2 skv_2) ) 30.62/31.15 ( (* skv_2 skv_2), 0, 0 ) 30.62/31.15 ( (* skv_2 skv_2), 0, 1 ) 30.62/31.15 ( (* skv_2 skv_2), 0, (- 1) ) 30.62/31.15 ( (* skv_2 skv_2), 0, 2 ) 30.62/31.15 ( (* skv_2 skv_2), 0, skv_6 ) 30.62/31.15 ( (* skv_2 skv_2), 0, (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2), 0, (* skv_2 skv_2) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (U uni)) (or (not (sort (ref A) U)) (= U (mk_ref A (contents A U)))) ) 30.62/31.15 ( e_ty_7, e_uni_8 ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), e_uni_8 ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref (ref e_ty_7)), e_uni_8 ) 30.62/31.15 ( (ref (ref e_ty_7)), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref (ref e_ty_7)), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref (ref (ref e_ty_7))), e_uni_8 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (= X (power X 1)) ) 30.62/31.15 ( skv_2 ) 30.62/31.15 ( skv_3 ) 30.62/31.15 ( skv_4 ) 30.62/31.15 ( skv_5 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (power skv_2 0) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (+ skv_3 (* skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 30.62/31.15 ( (* (- 1) (abs skv_3)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (= (>= (+ Y (* (- 1) (abs X))) 0) (and (>= (+ X Y) 0) (not (>= (+ X (* (- 1) Y)) 1)))) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (N Int)) (or (not (>= N 0)) (= (power X (+ 1 N)) (* X (power X N)))) ) 30.62/31.15 ( skv_2, 0 ) 30.62/31.15 ( skv_3, 0 ) 30.62/31.15 ( skv_4, 0 ) 30.62/31.15 ( skv_4, 1 ) 30.62/31.15 ( skv_4, 2 ) 30.62/31.15 ( skv_5, 0 ) 30.62/31.15 ( (power skv_2 0), 0 ) 30.62/31.15 ( (power skv_2 0), 1 ) 30.62/31.15 ( (power skv_2 0), 2 ) 30.62/31.15 ( (* skv_2 skv_2), 0 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (= X (+ (mod X Y) (* Y (div X Y))))) ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 30.62/31.15 ( 0, 0, 0 ) 30.62/31.15 ( (- 1), 0, 0 ) 30.62/31.15 ( (- 1), 0, 1 ) 30.62/31.15 ( (- 1), (- 1), 1 ) 30.62/31.15 ( (- 2), (- 2), 1 ) 30.62/31.15 ( (- 2), (- 2), 2 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (not (>= Y 1)) (>= X 1) (not (>= (div X Y) 1))) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 0 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_3, skv_3 ) 30.62/31.15 ( skv_6, 0 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ( skv_6, (- 1) ) 30.62/31.15 ( skv_6, 2 ) 30.62/31.15 ( skv_6, skv_6 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (N Int) (M Int)) (or (not (>= N 0)) (not (>= M 0)) (= (power (power X N) M) (power X (* N M)))) ) 30.62/31.15 ( skv_2, 0, 0 ) 30.62/31.15 ( skv_3, 0, 0 ) 30.62/31.15 ( skv_4, 0, 0 ) 30.62/31.15 ( skv_4, 0, 1 ) 30.62/31.15 ( skv_4, 1, 0 ) 30.62/31.15 ( skv_4, 1, 1 ) 30.62/31.15 ( (power skv_2 0), 0, 0 ) 30.62/31.15 ( (power skv_2 0), 0, 1 ) 30.62/31.15 ( (power skv_2 0), 1, 0 ) 30.62/31.15 ( (power skv_2 0), 1, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (= (power X 0) 1) ) 30.62/31.15 ( skv_2 ) 30.62/31.15 ( skv_3 ) 30.62/31.15 ( skv_4 ) 30.62/31.15 ( skv_5 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (+ skv_3 (* skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (div skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 30.62/31.15 ( (* (- 1) (abs skv_3)) ) 30.62/31.15 ( (+ (* (- 1) (div skv_5 skv_3)) (div (+ skv_5 (* skv_3 skv_3)) skv_3)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort A Z1)) (= Z1 (match_bool A false Z Z1))) ) 30.62/31.15 ( e_ty_7, e_uni_8, e_uni_8 ) 30.62/31.15 ( e_ty_7, e_uni_8, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, e_uni_8, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( e_ty_7, e_uni_8, (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( e_ty_7, (mk_ref e_ty_7 e_uni_8), (contents e_ty_7 e_uni_8) ) 30.62/31.15 ( e_ty_7, (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)) ) 30.62/31.15 ( (ref e_ty_7), e_uni_8, (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (mk_ref e_ty_7 e_uni_8), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ( (ref e_ty_7), (contents e_ty_7 (mk_ref e_ty_7 e_uni_8)), (mk_ref e_ty_7 e_uni_8) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (abs Y))) (let ((_let_1 (mod X Y))) (or (= Y 0) (and (>= (+ _let_0 _let_1) 1) (>= (+ _let_0 (* (- 1) _let_1)) 1))))) ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ) 30.62/31.15 (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)))) ) 30.62/31.15 ( skv_2, 0, 0 ) 30.62/31.15 ( skv_3, 0, 0 ) 30.62/31.15 ( skv_4, 0, 0 ) 30.62/31.15 ( skv_4, 0, 1 ) 30.62/31.15 ( skv_4, 0, 2 ) 30.62/31.15 ( skv_4, 1, 0 ) 30.62/31.15 ( skv_4, 1, 1 ) 30.62/31.15 ( skv_4, 1, 2 ) 30.62/31.15 ( (power skv_2 0), 0, 0 ) 30.62/31.15 ( (power skv_2 0), 0, 1 ) 30.62/31.15 ( (power skv_2 0), 1, 0 ) 30.62/31.15 ( (power skv_2 0), 1, 1 ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int)) (= X (div X 1)) ) 30.62/31.15 ( 0 ) 30.62/31.15 ( 1 ) 30.62/31.15 ( (- 1) ) 30.62/31.15 ( 2 ) 30.62/31.15 ( skv_6 ) 30.62/31.15 ( (* skv_6 (power skv_5 skv_4)) ) 30.62/31.15 ( (* skv_2 skv_2) ) 30.62/31.15 ( (* (- 1) (div 1 1)) ) 30.62/31.15 ( (* (- 1) (div skv_3 skv_3)) ) 30.62/31.15 ( (* (- 1) (* skv_2 (power skv_2 0))) ) 30.62/31.15 ( (* (- 1) (abs skv_3)) ) 30.62/31.15 ) 30.62/31.15 (instantiation (forall ((X Int) (Y Int)) (or (not (>= Y 1)) (not (>= X 0)) (>= (div X Y) 0)) ) 30.62/31.15 ( 0, 0 ) 30.62/31.15 ( 0, 1 ) 30.62/31.15 ( 0, (- 1) ) 30.62/31.15 ( 0, 2 ) 30.62/31.15 ( 0, skv_6 ) 30.62/31.15 ( 1, 0 ) 30.62/31.15 ( 1, 1 ) 30.62/31.15 ( 1, (- 1) ) 30.62/31.15 ( 1, 2 ) 30.62/31.15 ( 1, skv_6 ) 30.62/31.15 ( (- 1), 0 ) 30.62/31.15 ( (- 1), 1 ) 30.62/31.15 ( (- 1), (- 1) ) 30.62/31.15 ( (- 1), 2 ) 30.62/31.15 ( (- 1), skv_6 ) 30.62/31.15 ( 2, 0 ) 30.62/31.15 ( 2, 1 ) 30.62/31.15 ( 2, (- 1) ) 30.62/31.15 ( 2, 2 ) 30.62/31.15 ( 2, skv_6 ) 30.62/31.15 ( skv_6, 0 ) 30.62/31.15 ( skv_6, 1 ) 30.62/31.15 ) 30.62/31.15 % SZS output end Proof for theBenchmark 30.62/31.15 EOF