0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.02/0.24 % Computer : n022.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 04:50:09 CDT 2018 0.02/0.24 % CPUTime : 0.07/0.38 %----Proving without arithmetic mode 0.07/0.39 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.07/0.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 1.01/1.23 % SZS status Theorem for theBenchmark 1.01/1.23 % SZS output start Proof for theBenchmark 1.01/1.23 (skolem (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)))) (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) S_1) _let_1))) (not (hBOOL (hAPP int bool (zcong s1 S_1) _let_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) S_1)))) ))) 1.01/1.23 ( skv_1 ) 1.01/1.23 ) 1.01/1.23 (skolem (let ((_let_0 (bit0 (bit1 pls)))) (forall ((S1 $$unsorted)) (not (hBOOL (hAPP int bool (zcong (hAPP nat int (power_power int S1) (number_number_of nat _let_0)) (number_number_of int min)) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_0))) m)) (one_one int))))) )) 1.01/1.23 ( skv_2 ) 1.01/1.23 ) 1.01/1.23 (skolem (let ((_let_0 (one_one int))) (let ((_let_1 (bit0 (bit1 pls)))) (forall ((T_4 $$unsorted)) (not (= (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat _let_1))) _let_0) (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_1))) m)) _let_0)) T_4))) ))) 1.01/1.23 ( skv_3 ) 1.01/1.23 ) 1.01/1.23 (skolem (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)))) (let ((_let_3 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (zcong s1 X_2) _let_2))) (not (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_3 Y_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y_2) _let_2))) (not (hBOOL (hAPP int bool (zcong s1 Y_2) _let_2))) (= (ti int X_2) (ti int Y_2))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_2) _let_2))) (not (hBOOL (hAPP int bool _let_3 X_2)))) ))))) 1.01/1.23 ( skv_4 ) 1.01/1.23 ) 1.01/1.23 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K1)) (bit1 K2)))) ))) 1.01/1.23 ( pls, min ) 1.01/1.23 ) 1.01/1.23 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K)) (bit0 L)))) ))) 1.01/1.23 ( min, pls ) 1.01/1.23 ) 1.01/1.23 (instantiation (forall ((I_1 $$unsorted) (J_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (plus_plus nat I_1) J_1)) I_1))) ) 1.01/1.23 ( (one_one nat), (one_one nat) ) 1.01/1.23 ) 1.01/1.23 (instantiation (forall ((K_1 $$unsorted)) (not (= pls (bit1 K_1))) ) 1.01/1.23 ( min ) 1.01/1.23 ( pls ) 1.01/1.23 ( (bit1 pls) ) 1.01/1.23 ) 1.01/1.23 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (bit1 K)))) )) 1.01/1.23 ( min ) 1.01/1.23 ( pls ) 1.01/1.23 ( (bit1 pls) ) 1.01/1.23 ) 1.01/1.23 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K1)) (bit1 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))) ))) 1.01/1.23 ( min, min ) 1.01/1.23 ) 1.01/1.23 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K)) pls))) ))) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (bit1 K)) (bit0 L)))) )) 1.01/1.24 ( (zero_zero int), (zero_zero int) ) 1.01/1.24 ( (zero_zero int), (one_one int) ) 1.01/1.24 ( (zero_zero int), min ) 1.01/1.24 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( min, min ) 1.01/1.24 ( min, pls ) 1.01/1.24 ( t, (zero_zero int) ) 1.01/1.24 ( t, (one_one int) ) 1.01/1.24 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.01/1.24 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (number_number_of int K)) (number_number_of int L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 1.01/1.24 ( pls, pls ) 1.01/1.24 ( pls, (bit1 pls) ) 1.01/1.24 ( pls, (bit0 (bit1 pls)) ) 1.01/1.24 ( pls, (bit1 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K)) min))) ))) 1.01/1.24 ( min ) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) (hAPP int int (minus_minus int Z_2) (one_one int))))) )) 1.01/1.24 ( (zero_zero int), (zero_zero int) ) 1.01/1.24 ( (zero_zero int), (one_one int) ) 1.01/1.24 ( (zero_zero int), min ) 1.01/1.24 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( min, min ) 1.01/1.24 ( min, pls ) 1.01/1.24 ( t, (zero_zero int) ) 1.01/1.24 ( t, (one_one int) ) 1.01/1.24 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.01/1.24 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (number_number_of int K)) (number_number_of int L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 1.01/1.24 ( pls, pls ) 1.01/1.24 ( pls, (bit1 pls) ) 1.01/1.24 ) 1.01/1.24 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (zero_zero nat)))) ) 1.01/1.24 ( (zero_zero nat) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Z_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (one_one int)) Z_2))) )) 1.01/1.24 ( (zero_zero int) ) 1.01/1.24 ( (one_one int) ) 1.01/1.24 ( min ) 1.01/1.24 ( t ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (ti T A))) (forall ((T $$unsorted) (A $$unsorted)) (= _let_0 (ti T _let_0)) )) 1.01/1.24 ( int, min ) 1.01/1.24 ( int, pls ) 1.01/1.24 ( int, t ) 1.01/1.24 ( int, m ) 1.01/1.24 ( int, s1 ) 1.01/1.24 ( int, s ) 1.01/1.24 ( (fun int bool), zprime ) 1.01/1.24 ( (fun int bool), twoSqu658283162sum2sq ) 1.01/1.24 ( (fun bool (fun bool bool)), fconj ) 1.01/1.24 ) 1.01/1.24 (instantiation (forall ((V_3 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (number_number_of nat V_3))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) V_3))) ) 1.01/1.24 ( (zero_zero int) ) 1.01/1.24 ( (one_one int) ) 1.01/1.24 ( min ) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (bit1 K)) pls))) )) 1.01/1.24 ( (zero_zero int) ) 1.01/1.24 ( min ) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( t ) 1.01/1.24 ( s ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.01/1.24 ( skv_1 ) 1.01/1.24 ( skv_4 ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (bit0 K)))) )) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (bit0 B_1_1))) (forall ((B_1_1 $$unsorted)) (= _let_0 (ti int _let_0)) )) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (bit0 K)))) )) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (plus_plus int W_1) (one_one int))) Z_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z_2))) )) 1.01/1.24 ( (zero_zero int), (zero_zero int) ) 1.01/1.24 ( (zero_zero int), (one_one int) ) 1.01/1.24 ( (zero_zero int), min ) 1.01/1.24 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( min, min ) 1.01/1.24 ( min, pls ) 1.01/1.24 ( t, (zero_zero int) ) 1.01/1.24 ( t, (one_one int) ) 1.01/1.24 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.01/1.24 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.01/1.24 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) min) (bit0 K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) min) K))) )) 1.01/1.24 ( min ) 1.01/1.24 ( pls ) 1.01/1.24 ( (bit1 pls) ) 1.01/1.24 ( (bit0 (bit1 pls)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (zcong B_2 A_3) Ma)) (hBOOL (hAPP int bool (zcong A_3 B_2) Ma))) ) 1.01/1.24 ( s1, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s1, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s1, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( s, s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (number_number_of int min), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (number_number_of int min), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( skv_1, s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ( skv_4, s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.24 ) 1.01/1.24 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W) W)) ) 1.01/1.24 ( (zero_zero int) ) 1.01/1.24 ( (one_one int) ) 1.01/1.24 ( min ) 1.01/1.24 ) 1.01/1.24 (instantiation (forall ((X_a $$unsorted) (X $$unsorted) (A_6 $$unsorted)) (= (hBOOL (hAPP (fun X_a bool) bool (member X_a X) A_6)) (hBOOL (hAPP X_a bool A_6 X))) ) 1.01/1.24 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls) ) 1.01/1.24 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) t) ) 1.01/1.24 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int))) ) 1.01/1.24 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 1.01/1.24 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) t) ) 1.01/1.24 ( int, min, (hAPP int (fun int bool) (ord_less int) pls) ) 1.01/1.24 ( int, min, (hAPP int (fun int bool) (ord_less int) min) ) 1.01/1.24 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) min) ) 1.01/1.24 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 1.01/1.24 ( int, pls, (hAPP int (fun int bool) (ord_less int) min) ) 1.01/1.24 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min) ) 1.01/1.24 ( int, (number_number_of int (bit0 (bit1 pls))), zprime ) 1.01/1.24 ( int, (number_number_of int (bit0 (bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), zprime ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) t) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (zcong (hAPP nat int (power_power int s) _let_0) (hAPP nat int (power_power int s1) _let_0))) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) s) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 s) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) skv_1) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 skv_1) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 skv_4) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) skv_4) ) 1.01/1.24 ( int, (number_number_of int (bit1 (bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, (number_number_of int min), (quadRes (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) ) 1.01/1.24 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) ) 1.01/1.24 ( int, (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t), twoSqu658283162sum2sq ) 1.01/1.24 ( int, (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int (fun int bool) (ord_less int) (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t)) ) 1.01/1.24 ( int, skv_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.24 ( int, skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.01/1.25 ( nat, (number_number_of nat (bit0 (bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W))) ))) 1.01/1.25 ( (zero_zero int), (zero_zero int) ) 1.01/1.25 ( (zero_zero int), (one_one int) ) 1.01/1.25 ( (zero_zero int), min ) 1.01/1.25 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.25 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.01/1.25 ( (zero_zero int), s ) 1.01/1.25 ( (zero_zero int), skv_1 ) 1.01/1.25 ( (zero_zero int), skv_4 ) 1.01/1.25 ( (one_one int), (zero_zero int) ) 1.01/1.25 ( (one_one int), t ) 1.01/1.25 ( min, (zero_zero int) ) 1.01/1.25 ( min, min ) 1.01/1.25 ( min, pls ) 1.01/1.25 ( pls, min ) 1.01/1.25 ( (number_number_of int (bit0 (bit1 pls))), (zero_zero int) ) 1.01/1.25 ( t, (one_one int) ) 1.01/1.25 ( (number_number_of int (bit1 (bit1 pls))), (zero_zero int) ) 1.01/1.25 ( s, (zero_zero int) ) 1.01/1.25 ( skv_1, (zero_zero int) ) 1.01/1.25 ( skv_4, (zero_zero int) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K)) (bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 1.01/1.25 ( pls, pls ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) min)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (bit0 K)) min))) )) 1.01/1.25 ( (zero_zero int) ) 1.01/1.25 ( (one_one int) ) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ( (bit0 (bit1 pls)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (dvd_dvd nat) K))) (forall ((K $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (plus_plus nat N) K))) (hBOOL (hAPP nat bool _let_0 N))) )) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 W_1)) _let_2))) )))) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ( (bit0 (bit1 pls)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (or (hBOOL (hAPP nat bool _let_0 N)) (hBOOL (hAPP nat bool _let_0 Ma))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (plus_plus nat Ma) N)))) )) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Ma) (hAPP int int (minus_minus int A_3) B_2))) (hBOOL (hAPP int bool (zcong A_3 B_2) Ma))) ) 1.01/1.25 ( s1, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( s1, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( s1, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((V_3 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V_3) pls)) (= (zero_zero nat) (number_number_of nat V_3))) ) 1.01/1.25 ( (zero_zero int) ) 1.01/1.25 ( (one_one int) ) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ( (bit0 (bit1 pls)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K1)) (bit0 K2)))) ))) 1.01/1.25 ( pls, pls ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((X $$unsorted) (P_2 $$unsorted)) (= (hBOOL (hAPP int bool (zcong X (zero_zero int)) P_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) P_2) X))) ) 1.01/1.25 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K)) min)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min))) ))) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N)) (and (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N)) (not (= Ma N)))) )) 1.01/1.25 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N $$unsorted)) (= (not (= _let_0 N)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) )) 1.01/1.25 ( (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) (hAPP nat nat (plus_plus nat M) N_1))) ) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (twoSqu1929807760sum2sq B_1_1))) (forall ((B_1_1 $$unsorted)) (= _let_0 (ti int _let_0)) )) 1.01/1.25 ( (product_Pair int int s (one_one int)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X_1) (hAPP nat int (power_power int X_1) (number_number_of nat (bit0 (bit1 pls)))))) ) 1.01/1.25 ( (zero_zero int) ) 1.01/1.25 ( (one_one int) ) 1.01/1.25 ( min ) 1.01/1.25 ( s1 ) 1.01/1.25 ( s ) 1.01/1.25 ( skv_2 ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K)) min))) ))) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ( (bit0 (bit1 pls)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (bit0 K))) (hBOOL (hAPP int bool _let_0 K))) )) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ( (bit0 (bit1 pls)) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) (hAPP nat nat (plus_plus nat N_1) M))) ) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) min))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 (bit1 K))) (hBOOL (hAPP int bool _let_0 K))) )) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti X_c _let_0)) )) 1.01/1.25 ( int, int, (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))), m ) 1.01/1.25 ( int, int, (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.01/1.25 ( int, int, (minus_minus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))), (number_number_of int min) ) 1.01/1.25 ( int, int, (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))), (one_one int) ) 1.01/1.25 ( int, int, (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 1.01/1.25 ( int, int, (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), t ) 1.01/1.25 ( int, int, (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), skv_3 ) 1.01/1.25 ( int, nat, (power_power int s), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ( int, nat, (power_power int s1), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ( int, nat, (power_power int skv_2), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ( bool, int, zprime, (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.25 ( bool, int, zprime, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int (bit1 (bit1 pls))) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_1 ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), min ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), pls ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 1.01/1.25 ( bool, int, (zcong (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (zero_zero int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (one_one int) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (quadRes (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (number_number_of int min) ) 1.01/1.25 ( bool, int, (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (zcong (hAPP nat int (power_power int s) _let_0) (hAPP nat int (power_power int s1) _let_0))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, twoSqu658283162sum2sq, (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int))), (zero_zero int) ) 1.01/1.25 ( bool, int, (zcong (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (zcong s1 s), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_1), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (zcong s1 skv_1), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (zcong (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (zcong s1 skv_4), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.25 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 1.01/1.25 ( (fun int bool), int, (ord_less int), min ) 1.01/1.25 ( (fun int bool), int, (ord_less int), t ) 1.01/1.25 ( (fun int bool), int, (ord_less int), s ) 1.01/1.25 ( (fun int bool), int, (ord_less int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.01/1.25 ( (fun int bool), int, (ord_less int), skv_1 ) 1.01/1.25 ( (fun int bool), int, (ord_less int), skv_4 ) 1.01/1.25 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 1.01/1.25 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 1.01/1.25 ( (fun int bool), int, (ord_less_eq int), min ) 1.01/1.25 ( (fun int bool), int, (dvd_dvd int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.25 ( nat, nat, (plus_plus nat (one_one nat)), (one_one nat) ) 1.01/1.25 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K)) (bit1 L)))) ))) 1.01/1.25 ( min, min ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (= (zero_zero nat) (hAPP nat nat (minus_minus nat N_1) (hAPP nat nat (plus_plus nat N_1) M))) ) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))) ))) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ) 1.01/1.25 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (= M (hAPP nat nat (minus_minus nat (hAPP nat nat (plus_plus nat N_1) M)) N_1)) ) 1.01/1.25 ( (one_one nat), (one_one nat) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit1 W_1)) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) _let_2))) )))) 1.01/1.25 ( min ) 1.01/1.25 ( pls ) 1.01/1.25 ( (bit1 pls) ) 1.01/1.25 ) 1.01/1.25 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (bit0 K)) (bit1 L)))) )) 1.01/1.25 ( (zero_zero int), (zero_zero int) ) 1.01/1.25 ( (zero_zero int), (one_one int) ) 1.01/1.25 ( (zero_zero int), min ) 1.01/1.25 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.26 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.01/1.26 ( (zero_zero int), s ) 1.01/1.26 ( (zero_zero int), skv_1 ) 1.01/1.26 ( (zero_zero int), skv_4 ) 1.01/1.26 ( (one_one int), t ) 1.01/1.26 ( min, min ) 1.01/1.26 ( min, pls ) 1.01/1.26 ( pls, min ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (bit1 K)))) )) 1.01/1.26 ( min ) 1.01/1.26 ( pls ) 1.01/1.26 ( (bit1 pls) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun int bool))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) pls) K)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) pls) (bit1 K)))) )) 1.01/1.26 ( (zero_zero int) ) 1.01/1.26 ( (one_one int) ) 1.01/1.26 ( min ) 1.01/1.26 ( pls ) 1.01/1.26 ( (bit1 pls) ) 1.01/1.26 ( (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.26 ( (number_number_of int (bit1 (bit1 pls))) ) 1.01/1.26 ( s ) 1.01/1.26 ( skv_1 ) 1.01/1.26 ( skv_4 ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (legendre B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti int _let_0)) )) 1.01/1.26 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (bit0 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))) ))) 1.01/1.26 ( pls ) 1.01/1.26 ( (bit1 pls) ) 1.01/1.26 ( (bit0 (bit1 pls)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (hBOOL (hAPP int bool (zcong A_1 B) (one_one int))) ) 1.01/1.26 ( s1, s ) 1.01/1.26 ( s1, skv_1 ) 1.01/1.26 ( s1, skv_4 ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.01/1.26 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((J_1 $$unsorted) (I_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (plus_plus nat J_1) I_1)) I_1))) ) 1.01/1.26 ( (one_one nat), (one_one nat) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun int bool))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) Z_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP int int (plus_plus int Z_2) (one_one int))))) )) 1.01/1.26 ( (zero_zero int), (zero_zero int) ) 1.01/1.26 ( (zero_zero int), (one_one int) ) 1.01/1.26 ( (zero_zero int), min ) 1.01/1.26 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.01/1.26 ( (zero_zero int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.01/1.26 ( (zero_zero int), s ) 1.01/1.26 ( (zero_zero int), skv_1 ) 1.01/1.26 ( (zero_zero int), skv_4 ) 1.01/1.26 ( (one_one int), t ) 1.01/1.26 ( min, min ) 1.01/1.26 ( min, pls ) 1.01/1.26 ( t, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( s, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( skv_1, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( skv_4, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun nat bool))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (or (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N)) (= Ma N)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N))) )) 1.01/1.26 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (zcong B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti (fun int bool) _let_0)) )) 1.01/1.26 ( s1, s ) 1.01/1.26 ( s1, skv_1 ) 1.01/1.26 ( s1, skv_4 ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.01/1.26 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((K $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (minus_minus int K) L)) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))) ))) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18352 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (plus_plus X_a (zero_zero X_a)) BOUND_VARIABLE_18352) (ti X_a BOUND_VARIABLE_18352))) ) 1.01/1.26 ( int, min ) 1.01/1.26 ( int, pls ) 1.01/1.26 ( int, t ) 1.01/1.26 ( int, m ) 1.01/1.26 ( int, s1 ) 1.01/1.26 ( int, s ) 1.01/1.26 ( (fun int bool), zprime ) 1.01/1.26 ( (fun int bool), twoSqu658283162sum2sq ) 1.01/1.26 ( (fun bool (fun bool bool)), fconj ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18390 $$unsorted) (BOUND_VARIABLE_18391 $$unsorted)) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (= (= (number_number_of X_a BOUND_VARIABLE_18390) (number_number_of X_a BOUND_VARIABLE_18391)) (= (ti int BOUND_VARIABLE_18391) (ti int BOUND_VARIABLE_18390)))) ) 1.01/1.26 ( int, min, (bit1 (bit1 pls)) ) 1.01/1.26 ( int, pls, (bit1 pls) ) 1.01/1.26 ( int, pls, (bit0 (bit1 pls)) ) 1.01/1.26 ( int, (bit1 pls), pls ) 1.01/1.26 ( int, (bit1 pls), (bit1 pls) ) 1.01/1.26 ( int, (bit0 (bit1 pls)), (bit1 pls) ) 1.01/1.26 ( int, (bit0 (bit0 (bit1 pls))), min ) 1.01/1.26 ( int, (bit0 (bit0 (bit1 pls))), (bit1 (bit1 pls)) ) 1.01/1.26 ( int, (bit1 (bit1 pls)), (bit0 (bit0 (bit1 pls))) ) 1.01/1.26 ( int, (bit1 (bit1 pls)), (bit1 (bit1 pls)) ) 1.01/1.26 ( nat, pls, (bit0 (bit1 pls)) ) 1.01/1.26 ( nat, (bit1 pls), pls ) 1.01/1.26 ( nat, (bit1 pls), (bit0 (bit1 pls)) ) 1.01/1.26 ( nat, (bit0 (bit1 pls)), (bit1 pls) ) 1.01/1.26 ( nat, (bit0 (bit1 pls)), (bit0 (bit1 pls)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.01/1.26 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.01/1.26 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_18469))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_18469 $$unsorted) (BOUND_VARIABLE_18470 $$unsorted) (BOUND_VARIABLE_18471 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_18470)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_18471)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_18469))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_18470) BOUND_VARIABLE_18471))) )))) 1.01/1.26 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18533 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_18533) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_18533))) ) 1.01/1.26 ( int, min ) 1.01/1.26 ( int, pls ) 1.01/1.26 ( int, t ) 1.01/1.26 ( int, m ) 1.01/1.26 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( int, s1 ) 1.01/1.26 ( int, s ) 1.01/1.26 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.01/1.26 ( (fun int bool), zprime ) 1.01/1.26 ( (fun int bool), twoSqu658283162sum2sq ) 1.01/1.26 ( nat, (one_one nat) ) 1.01/1.26 ( (fun bool (fun bool bool)), fconj ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((N_1 $$unsorted)) (or (= _let_0 N_1) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N_1))) )) 1.01/1.26 ( (number_number_of nat (bit0 (bit1 pls))) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N))) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 K_2))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) I) K_2))) (not (hBOOL (hAPP nat bool P_1 I)))) )) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) K_2) N)))) ))) )) 1.01/1.26 ( (number_number_of nat (bit0 (bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (quadRes B_1_1))) (forall ((B_1_1 $$unsorted)) (= _let_0 (ti (fun int bool) _let_0)) )) 1.01/1.26 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (plus_plus X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (monoid_add X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.01/1.26 ( (one_one nat), nat ) 1.01/1.26 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), int ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), int ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((D_2 $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (zcong A_1 B) M))) (not (= (ti int B) (ti int C))) (not (hBOOL (hAPP int bool (zcong C D_2) M))) (hBOOL (hAPP int bool (zcong A_1 D_2) M))) ) 1.01/1.26 ( s, s1, s1, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( (number_number_of int min), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( (number_number_of int min), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( skv_1, s1, s1, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( skv_4, s1, s1, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (power_power X_a _let_0) (number_number_of nat (bit0 (bit1 pls)))))) )) 1.01/1.26 ( int ) 1.01/1.26 ( nat ) 1.01/1.26 ( real ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18694 $$unsorted) (BOUND_VARIABLE_18695 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_18694) BOUND_VARIABLE_18695)) BOUND_VARIABLE_18695) (ti X_a BOUND_VARIABLE_18694))) ) 1.01/1.26 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (plus_plus X_a BOUND_VARIABLE_18716))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_18716 $$unsorted) (BOUND_VARIABLE_18717 $$unsorted) (BOUND_VARIABLE_18718 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_18717) (ti X_a BOUND_VARIABLE_18718)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_18717) (hAPP X_a X_a _let_0 BOUND_VARIABLE_18718)))) )) 1.01/1.26 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), s, t ) 1.01/1.26 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), s, s ) 1.01/1.26 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), t, s ) 1.01/1.26 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), s, s ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_18741 $$unsorted) (BOUND_VARIABLE_18742 $$unsorted) (BOUND_VARIABLE_18743 $$unsorted) (BOUND_VARIABLE_18744 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_18743) BOUND_VARIABLE_18744) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_18741) BOUND_VARIABLE_18742))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_18743) BOUND_VARIABLE_18744)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_18741) BOUND_VARIABLE_18742)))) ))) 1.01/1.26 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18775 $$unsorted) (BOUND_VARIABLE_18776 $$unsorted)) (or (not (semiring_div X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (div_mod X_a BOUND_VARIABLE_18776) BOUND_VARIABLE_18775)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_18775) BOUND_VARIABLE_18776)))) ) 1.01/1.26 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18804 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) BOUND_VARIABLE_18804)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (number_number_of X_a BOUND_VARIABLE_18804))))) ) 1.01/1.26 ( int, min ) 1.01/1.26 ( int, pls ) 1.01/1.26 ( int, (bit1 pls) ) 1.01/1.26 ( int, (bit0 (bit1 pls)) ) 1.01/1.26 ( int, (bit0 (bit0 (bit1 pls))) ) 1.01/1.26 ( int, (bit1 (bit1 pls)) ) 1.01/1.26 ( nat, pls ) 1.01/1.26 ( nat, (bit1 pls) ) 1.01/1.26 ( nat, (bit0 (bit1 pls)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (number_number_of X_a (bit1 pls)) (one_one X_a))) ) 1.01/1.26 ( int ) 1.01/1.26 ( nat ) 1.01/1.26 ( real ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (plus_plus int Z_1) (zero_zero int))) ) 1.01/1.26 ( min ) 1.01/1.26 ( pls ) 1.01/1.26 ( t ) 1.01/1.26 ( m ) 1.01/1.26 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.26 ( s1 ) 1.01/1.26 ( s ) 1.01/1.26 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (plus_plus X_a _let_0) _let_0) (number_number_of X_a (bit0 (bit1 pls))))) )) 1.01/1.26 ( int ) 1.01/1.26 ( nat ) 1.01/1.26 ( real ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (times_times int X_1) Y)))) )) 1.01/1.26 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.01/1.26 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.26 ) 1.01/1.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_18983 $$unsorted)) (or (not (number_ring X_a)) (= (number_number_of X_a (hAPP int int (plus_plus int (bit1 pls)) BOUND_VARIABLE_18983)) (hAPP X_a X_a (plus_plus X_a (one_one X_a)) (number_number_of X_a BOUND_VARIABLE_18983)))) ) 1.01/1.26 ( nat, (bit1 pls) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (ab_semigroup_mult X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.01/1.26 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.01/1.26 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19083 $$unsorted) (BOUND_VARIABLE_19084 $$unsorted)) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_19084))) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_19083))) (= (number_number_of X_a (hAPP int int (plus_plus int BOUND_VARIABLE_19084) BOUND_VARIABLE_19083)) (hAPP X_a X_a (plus_plus X_a (number_number_of X_a BOUND_VARIABLE_19084)) (number_number_of X_a BOUND_VARIABLE_19083)))) )) 1.01/1.26 ( nat, (bit1 pls), (bit1 pls) ) 1.01/1.26 ) 1.01/1.26 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19120 $$unsorted)) (or (not (mult_zero X_a)) (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19120) _let_0))) )) 1.01/1.27 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.01/1.27 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ) 1.01/1.27 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Ma))) (= (= (hAPP int int (div_mod int B_2) Ma) (hAPP int int (div_mod int A_3) Ma)) (hBOOL (hAPP int bool (zcong A_3 B_2) Ma)))) ) 1.01/1.27 ( s1, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( s1, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( s1, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ) 1.01/1.27 (instantiation (let ((_let_0 (plus_plus X_a BOUND_VARIABLE_19199))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19199 $$unsorted) (BOUND_VARIABLE_19200 $$unsorted) (BOUND_VARIABLE_19201 $$unsorted)) (or (not (cancel146912293up_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_19200) (hAPP X_a X_a _let_0 BOUND_VARIABLE_19201))) (= (ti X_a BOUND_VARIABLE_19200) (ti X_a BOUND_VARIABLE_19201))) )) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (one_one int) ) 1.01/1.27 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int), (one_one int) ) 1.01/1.27 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 1.01/1.27 ) 1.01/1.27 (instantiation (let ((_let_0 (plus_plus X_a BOUND_VARIABLE_19270))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19270 $$unsorted) (BOUND_VARIABLE_19271 $$unsorted) (BOUND_VARIABLE_19272 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_19272) (hAPP X_a X_a _let_0 BOUND_VARIABLE_19271))) (= (ti X_a BOUND_VARIABLE_19272) (ti X_a BOUND_VARIABLE_19271))) )) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (one_one int) ) 1.01/1.27 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int), (one_one int) ) 1.01/1.27 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 1.01/1.27 ) 1.01/1.27 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19306 $$unsorted) (BOUND_VARIABLE_19307 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_19307) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_19306))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19307) BOUND_VARIABLE_19306)) _let_2))) )))) 1.01/1.27 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.01/1.27 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.01/1.27 ) 1.01/1.27 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_19364))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19364 $$unsorted) (BOUND_VARIABLE_19365 $$unsorted) (BOUND_VARIABLE_19366 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_19366))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_19365))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_19366) BOUND_VARIABLE_19365)))) )) 1.01/1.27 ( int, (zero_zero int), (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( int, t, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( int, s, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( int, skv_1, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( int, skv_4, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 1.01/1.27 ) 1.01/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_19418 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_19418) BOUND_VARIABLE_19418) (hAPP X_a X_a (times_times X_a (number_number_of X_a (bit0 (bit1 pls)))) BOUND_VARIABLE_19418))) ) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.01/1.27 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.01/1.27 ( nat, (one_one nat) ) 1.01/1.27 ) 1.01/1.27 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (= (hAPP nat nat (plus_plus nat N_1) M) (hAPP nat nat (plus_plus nat M) N_1)) ) 1.01/1.27 ( (one_one nat), (one_one nat) ) 1.01/1.27 ) 1.01/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_19446 $$unsorted) (BOUND_VARIABLE_19447 $$unsorted) (BOUND_VARIABLE_19448 $$unsorted)) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19446) BOUND_VARIABLE_19448)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19447) BOUND_VARIABLE_19448)) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_19446) BOUND_VARIABLE_19447)) BOUND_VARIABLE_19448))) ) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (zero_zero int) ) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), t ) 1.01/1.27 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), skv_3 ) 1.01/1.27 ) 1.01/1.27 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) K))) (forall ((P_1 $$unsorted) (K $$unsorted) (I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 I_2))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 I))) (not (hBOOL (hAPP int bool P_1 I))) (hBOOL (hAPP int bool P_1 (hAPP int int (plus_plus int I) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I_2))) )) 1.01/1.27 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int), min ) 1.01/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), (one_one int) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int), t ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) min), (zero_zero int), (zero_zero int) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) min), min, min ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) min), (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min, pls ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) t), (zero_zero int), s ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int))), (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (= (member X_a B_1_1) (member X_a (ti X_a B_1_1))) ) 1.06/1.27 ( int, min ) 1.06/1.27 ( int, pls ) 1.06/1.27 ( int, t ) 1.06/1.27 ( int, m ) 1.06/1.27 ( int, s1 ) 1.06/1.27 ( int, s ) 1.06/1.27 ( (fun int bool), zprime ) 1.06/1.27 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.27 ( (fun bool (fun bool bool)), fconj ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1))) (= M N_1) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1))) )) 1.06/1.27 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (number X_a)) (= (number_number_of X_a B_1_1) (number_number_of X_a (ti int B_1_1)))) ) 1.06/1.27 ( min, int ) 1.06/1.27 ( pls, int ) 1.06/1.27 ( pls, nat ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((K_1 $$unsorted)) (= (bit0 K_1) (hAPP int int (plus_plus int K_1) K_1)) ) 1.06/1.27 ( pls ) 1.06/1.27 ( (bit1 pls) ) 1.06/1.27 ( (bit0 (bit1 pls)) ) 1.06/1.27 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.27 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_19634))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19634 $$unsorted) (BOUND_VARIABLE_19635 $$unsorted) (BOUND_VARIABLE_19636 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_19635) BOUND_VARIABLE_19636))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_19634))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_19635)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_19636)))) )))) 1.06/1.27 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1)) (= M (hAPP nat nat (plus_plus nat N_1) (hAPP nat nat (minus_minus nat M) N_1)))) ) 1.06/1.27 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_19702 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_19702) (hAPP X_a X_a (times_times X_a (one_one X_a)) BOUND_VARIABLE_19702))) ) 1.06/1.27 ( int, min ) 1.06/1.27 ( int, pls ) 1.06/1.27 ( int, t ) 1.06/1.27 ( int, m ) 1.06/1.27 ( int, s1 ) 1.06/1.27 ( int, s ) 1.06/1.27 ( (fun int bool), zprime ) 1.06/1.27 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.27 ( (fun bool (fun bool bool)), fconj ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (zcong B_1_1 B_2_1) (zcong B_1_1 (ti int B_2_1))) ) 1.06/1.27 ( s1, s ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19760 $$unsorted) (BOUND_VARIABLE_19761 $$unsorted)) (or (not (linord581940658strict X_a)) (= (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19760) BOUND_VARIABLE_19761))) (or (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_19760)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_19761))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_19761) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_19760) _let_2)))))) ))))) 1.06/1.27 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.27 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.27 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.27 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (ord_less_eq int))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) C))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) C))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) B)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) A_1))) )))) 1.06/1.27 ( (zero_zero int), (zero_zero int), (one_one int) ) 1.06/1.27 ( min, (zero_zero int), (zero_zero int) ) 1.06/1.27 ( t, t, (one_one int) ) 1.06/1.27 ( s, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.27 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), min, pls ) 1.06/1.27 ( skv_1, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.27 ( skv_4, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_19836 $$unsorted) (BOUND_VARIABLE_19837 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_19837))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_19836))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_19837) BOUND_VARIABLE_19836)))) )) 1.06/1.27 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.27 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.27 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.27 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_19870 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_19870) (hAPP X_a X_a (times_times X_a (number_number_of X_a (bit1 pls))) BOUND_VARIABLE_19870))) ) 1.06/1.27 ( int, min ) 1.06/1.27 ( int, pls ) 1.06/1.27 ( int, t ) 1.06/1.27 ( int, m ) 1.06/1.27 ( int, s1 ) 1.06/1.27 ( int, s ) 1.06/1.27 ( (fun int bool), zprime ) 1.06/1.27 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.27 ( (fun bool (fun bool bool)), fconj ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((P_1 $$unsorted) (I_2 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_2) K))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I) K))) (not (hBOOL (hAPP int bool P_1 I))) (hBOOL (hAPP int bool P_1 (hAPP int int (minus_minus int I) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I_2))) ))) 1.06/1.27 ( zprime, (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), (one_one int), t ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int), (zero_zero int) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), s ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_1 ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_4 ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int), (one_one int) ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less int) min), min, min ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) min), min, pls ) 1.06/1.27 ( (hAPP int (fun int bool) (ord_less_eq int) pls), (zero_zero int), min ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_19984 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP nat X_a (power_power X_a BOUND_VARIABLE_19984) (one_one nat)) (ti X_a BOUND_VARIABLE_19984))) ) 1.06/1.27 ( int, min ) 1.06/1.27 ( int, pls ) 1.06/1.27 ( int, t ) 1.06/1.27 ( int, m ) 1.06/1.27 ( int, s1 ) 1.06/1.27 ( int, s ) 1.06/1.27 ( int, skv_2 ) 1.06/1.27 ( (fun int bool), zprime ) 1.06/1.27 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.27 ( (fun bool (fun bool bool)), fconj ) 1.06/1.27 ) 1.06/1.27 (instantiation (let ((_let_0 (ord_less nat))) (let ((_let_1 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 N) Ma)))) (let ((_let_2 (not _let_1))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (and (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_0 Ma) N)) _let_2) (and (= Ma N) _let_2) (and (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_0 N) Ma)) _let_2) _let_1)) )))) 1.06/1.27 ( (ord_less nat), (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_20024 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_20024) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_20024))) ) 1.06/1.27 ( int, min ) 1.06/1.27 ( int, pls ) 1.06/1.27 ( int, t ) 1.06/1.27 ( int, m ) 1.06/1.27 ( int, s1 ) 1.06/1.27 ( int, s ) 1.06/1.27 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.27 ( (fun int bool), zprime ) 1.06/1.27 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.27 ( (fun bool (fun bool bool)), fconj ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (= (hAPP int int (minus_minus int A_1) B) (ti int C))) (= (ti int A_1) (hAPP int int (plus_plus int C) B))) ) 1.06/1.27 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), s ) 1.06/1.27 ) 1.06/1.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_20127 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_20127) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20127) (one_one X_a)))) ) 1.06/1.28 ( int, min ) 1.06/1.28 ( int, pls ) 1.06/1.28 ( int, t ) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( int, m ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, s1 ) 1.06/1.28 ( int, s ) 1.06/1.28 ( (fun int bool), zprime ) 1.06/1.28 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.28 ( (fun bool (fun bool bool)), fconj ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP int int (plus_plus int Z_1) W) (hAPP int int (plus_plus int W) Z_1)) ) 1.06/1.28 ( (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.28 ( (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.28 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.06/1.28 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (mult_zero X_a)) (= (times_times X_a B_1_1) (times_times X_a (ti X_a B_1_1)))) ) 1.06/1.28 ( min, int ) 1.06/1.28 ( pls, int ) 1.06/1.28 ( zprime, (fun int bool) ) 1.06/1.28 ( t, int ) 1.06/1.28 ( m, int ) 1.06/1.28 ( s1, int ) 1.06/1.28 ( s, int ) 1.06/1.28 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.28 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun nat bool))) (forall ((N $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N))) (not (forall ((K_2 $$unsorted)) (or (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) I) K_2))) (not (hBOOL (hAPP nat bool P_1 I)))) )) (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat (plus_plus nat K_2) (one_one nat))))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) K_2) N)))) ))) )) 1.06/1.28 ( (number_number_of nat (bit0 (bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 A_1))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (times_times int A_1) B)))) (hBOOL (hAPP int bool _let_0 B))) )) 1.06/1.28 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (power_power X_a BOUND_VARIABLE_20282))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20282 $$unsorted) (BOUND_VARIABLE_20283 $$unsorted) (BOUND_VARIABLE_20284 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (plus_plus nat BOUND_VARIABLE_20283) BOUND_VARIABLE_20284)) (hAPP X_a X_a (times_times X_a (hAPP nat X_a _let_0 BOUND_VARIABLE_20283)) (hAPP nat X_a _let_0 BOUND_VARIABLE_20284)))) )) 1.06/1.28 ( int, s1, (one_one nat), (one_one nat) ) 1.06/1.28 ( int, s, (one_one nat), (one_one nat) ) 1.06/1.28 ( int, skv_2, (one_one nat), (one_one nat) ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((Y $$unsorted) (X_1 $$unsorted) (P_3 $$unsorted)) (or (hBOOL (hAPP int bool (zcong X_1 (zero_zero int)) P_3)) (not (hBOOL (hAPP int bool (zcong (hAPP nat int (power_power int Y) (number_number_of nat (bit0 (bit1 pls)))) X_1) P_3))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) P_3) Y)))) ) 1.06/1.28 ( s1, (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( s, (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( s, (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( skv_2, (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20311 $$unsorted) (BOUND_VARIABLE_20312 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_20312))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_20311))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20312) BOUND_VARIABLE_20311)))) )) 1.06/1.28 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (bit1 L) (bit1 K)) (= (ti int K) (ti int L))) ) 1.06/1.28 ( min, (bit1 pls) ) 1.06/1.28 ( pls, min ) 1.06/1.28 ( pls, pls ) 1.06/1.28 ( pls, (bit1 pls) ) 1.06/1.28 ( (bit1 pls), pls ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20539 $$unsorted) (BOUND_VARIABLE_20540 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_20540))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_20539))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20539) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20539) BOUND_VARIABLE_20540)) BOUND_VARIABLE_20540))) )))) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_20569 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_20569) (number_number_of X_a pls)) (ti X_a BOUND_VARIABLE_20569))) ) 1.06/1.28 ( int, min ) 1.06/1.28 ( int, pls ) 1.06/1.28 ( int, t ) 1.06/1.28 ( int, m ) 1.06/1.28 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.28 ( int, s1 ) 1.06/1.28 ( int, s ) 1.06/1.28 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.28 ( (fun int bool), zprime ) 1.06/1.28 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.28 ( nat, (one_one nat) ) 1.06/1.28 ( (fun bool (fun bool bool)), fconj ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((L $$unsorted)) (= (= pls (ti int L)) (= pls (bit0 L))) ) 1.06/1.28 ( min ) 1.06/1.28 ( pls ) 1.06/1.28 ( (bit1 pls) ) 1.06/1.28 ( (bit0 (bit1 pls)) ) 1.06/1.28 ( t ) 1.06/1.28 ( m ) 1.06/1.28 ( s1 ) 1.06/1.28 ( s ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20596 $$unsorted) (BOUND_VARIABLE_20597 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20596) BOUND_VARIABLE_20597)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_20596))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_20597))) )) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (dvd_dvd X_a))) (forall ((X_a $$unsorted)) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 1.06/1.28 ( int ) 1.06/1.28 ( bool ) 1.06/1.28 ( nat ) 1.06/1.28 ( real ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP int int (times_times int (hAPP int int (plus_plus int A_1) B)) (hAPP int int (minus_minus int A_1) B)) (hAPP int int (minus_minus int (hAPP nat int (power_power int A_1) _let_0)) (hAPP nat int (power_power int B) _let_0))) )) 1.06/1.28 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.06/1.28 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20657 $$unsorted) (BOUND_VARIABLE_20658 $$unsorted)) (or (not (no_zero_divisors X_a)) (not (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20657) BOUND_VARIABLE_20658))) (= _let_0 (ti X_a BOUND_VARIABLE_20658)) (= _let_0 (ti X_a BOUND_VARIABLE_20657))) )) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20676 $$unsorted)) (or (not (real_normed_algebra X_a)) (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20676) _let_0))) )) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20690 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_20690) _let_0))) )) 1.06/1.28 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (bit1 pls))) (let ((_let_1 (power_power int A_1))) (forall ((A_1 $$unsorted)) (= (hAPP int int (times_times int A_1) (hAPP nat int _let_1 (number_number_of nat (bit0 _let_0)))) (hAPP nat int _let_1 (number_number_of nat (bit1 _let_0)))) ))) 1.06/1.28 ( (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.28 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( s1 ) 1.06/1.28 ( s ) 1.06/1.28 ( skv_2 ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((B_1_1 $$unsorted)) (= (bit0 B_1_1) (bit0 (ti int B_1_1))) ) 1.06/1.28 ( min ) 1.06/1.28 ( pls ) 1.06/1.28 ( t ) 1.06/1.28 ( m ) 1.06/1.28 ( s1 ) 1.06/1.28 ( s ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20780 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (= _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_20780) BOUND_VARIABLE_20780)) (= _let_0 (ti X_a BOUND_VARIABLE_20780)))) )) 1.06/1.28 ( int, min ) 1.06/1.28 ( int, pls ) 1.06/1.28 ( int, t ) 1.06/1.28 ( int, m ) 1.06/1.28 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.28 ( int, s1 ) 1.06/1.28 ( int, s ) 1.06/1.28 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.28 ( (fun int bool), zprime ) 1.06/1.28 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.28 ( nat, (one_one nat) ) 1.06/1.28 ( (fun bool (fun bool bool)), fconj ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((X_a $$unsorted)) (or (not (zero_neq_one X_a)) (not (= (zero_zero X_a) (one_one X_a)))) ) 1.06/1.28 ( int ) 1.06/1.28 ( nat ) 1.06/1.28 ( real ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= (plus_plus X_a (ti X_a B_1_1)) (plus_plus X_a B_1_1))) ) 1.06/1.28 ( min, int ) 1.06/1.28 ( pls, int ) 1.06/1.28 ( zprime, (fun int bool) ) 1.06/1.28 ( t, int ) 1.06/1.28 ( m, int ) 1.06/1.28 ( s1, int ) 1.06/1.28 ( s, int ) 1.06/1.28 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.28 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (number_number_of X_a BOUND_VARIABLE_20829))) (let ((_let_2 (number_number_of X_a BOUND_VARIABLE_20830))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20829 $$unsorted) (BOUND_VARIABLE_20830 $$unsorted)) (or (not (linorder X_a)) (not (number X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) _let_2)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) _let_1))))) )))) 1.06/1.28 ( int, pls, pls ) 1.06/1.28 ( int, pls, (bit1 pls) ) 1.06/1.28 ( int, pls, (bit0 (bit1 pls)) ) 1.06/1.28 ( int, pls, (bit1 (bit1 pls)) ) 1.06/1.28 ( int, (bit1 pls), pls ) 1.06/1.28 ( nat, (bit0 (bit1 pls)), pls ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (plus_plus int (one_one int)) Z_1)))) ))) 1.06/1.28 ( (zero_zero int) ) 1.06/1.28 ( (one_one int) ) 1.06/1.28 ( min ) 1.06/1.28 ( (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.28 ( (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.28 ( s ) 1.06/1.28 ( skv_1 ) 1.06/1.28 ( skv_4 ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20932 $$unsorted) (BOUND_VARIABLE_20933 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20933) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20932) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_20933) BOUND_VARIABLE_20932)) _let_2))) )))) 1.06/1.28 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.28 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.28 ( nat, (one_one nat), (one_one nat) ) 1.06/1.28 ) 1.06/1.28 (instantiation (forall ((L $$unsorted)) (= (= min (ti int L)) (= min (bit1 L))) ) 1.06/1.28 ( min ) 1.06/1.28 ( pls ) 1.06/1.28 ( (bit1 pls) ) 1.06/1.28 ( t ) 1.06/1.28 ( m ) 1.06/1.28 ( s1 ) 1.06/1.28 ( s ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of nat _let_0))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20963 $$unsorted) (BOUND_VARIABLE_20964 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP nat X_a (power_power X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_20963) BOUND_VARIABLE_20964)) _let_1) (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (plus_plus X_a (hAPP nat X_a (power_power X_a BOUND_VARIABLE_20963) _let_1)) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_20964) _let_1))) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (times_times X_a (number_number_of X_a _let_0)) BOUND_VARIABLE_20963)) BOUND_VARIABLE_20964)))) ))) 1.06/1.28 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.06/1.28 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.06/1.28 ( nat, (one_one nat), (one_one nat) ) 1.06/1.28 ) 1.06/1.28 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_20996 $$unsorted) (BOUND_VARIABLE_20997 $$unsorted)) (or (not (linordered_idom X_a)) (= (ti X_a BOUND_VARIABLE_20997) (ti X_a BOUND_VARIABLE_20996)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20996) BOUND_VARIABLE_20997)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20997) BOUND_VARIABLE_20996))) ))) 1.06/1.28 ( int, (zero_zero int), (zero_zero int) ) 1.06/1.28 ( int, (zero_zero int), (one_one int) ) 1.06/1.28 ( int, (zero_zero int), min ) 1.06/1.28 ( int, (zero_zero int), t ) 1.06/1.28 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.28 ( int, (one_one int), (zero_zero int) ) 1.06/1.28 ( int, (one_one int), t ) 1.06/1.28 ( int, min, (zero_zero int) ) 1.06/1.28 ( int, min, min ) 1.06/1.28 ( int, min, pls ) 1.06/1.28 ( int, pls, min ) 1.06/1.28 ( int, t, (zero_zero int) ) 1.06/1.28 ( int, t, (one_one int) ) 1.06/1.28 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.06/1.28 ( int, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.28 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.29 ( int, (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.29 ( int, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.29 ( int, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.29 ( nat, (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.29 ( nat, (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21090 $$unsorted) (BOUND_VARIABLE_21091 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_21091))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_21090) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21090) BOUND_VARIABLE_21091)) _let_2))) )))) 1.06/1.29 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (forall ((B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (plus_plus int (hAPP int int (times_times int B_3) Q_4)) R_3)) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_2) R_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_3))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Q_4) _let_2))) ))))) 1.06/1.29 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_21155) BOUND_VARIABLE_21156))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21155 $$unsorted) (BOUND_VARIABLE_21156 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21155) _let_0) (hAPP X_a X_a (times_times X_a _let_0) BOUND_VARIABLE_21155))) )) 1.06/1.29 ( int, s1, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.29 ( int, s, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.29 ( int, skv_2, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21210 $$unsorted) (BOUND_VARIABLE_21211 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_21211))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_21211) BOUND_VARIABLE_21210)))) )) 1.06/1.29 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.06/1.29 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.29 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (hBOOL P_4))) (let ((_let_1 (hBOOL P_1))) (let ((_let_2 (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (X $$unsorted)) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X)) (= (not _let_0) _let_1)) (= (or _let_2 _let_1) (or _let_2 _let_0))) )))) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (number_number_of int (bit1 (bit1 pls)))), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (number_number_of int (bit1 (bit1 pls)))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), min ) 1.06/1.29 ( (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 1.06/1.29 ( (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (one_one int)), (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (one_one int) ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (let ((_let_0 (bit0 (bit1 pls)))) (hAPP int bool (zcong (hAPP nat int (power_power int s) (number_number_of nat _let_0)) (number_number_of int min)) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_0))) m)) (one_one int)))), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.29 ( (let ((_let_0 (bit0 (bit1 pls)))) (hAPP int bool (zcong (hAPP nat int (power_power int s) (number_number_of nat _let_0)) (number_number_of int min)) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_0))) m)) (one_one int)))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), s ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), skv_1 ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) (zero_zero int)), skv_1 ) 1.06/1.29 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) (zero_zero int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), skv_4 ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (power X_a)) (= (power_power X_a (ti X_a B_1_1)) (power_power X_a B_1_1))) ) 1.06/1.29 ( min, int ) 1.06/1.29 ( pls, int ) 1.06/1.29 ( zprime, (fun int bool) ) 1.06/1.29 ( t, int ) 1.06/1.29 ( m, int ) 1.06/1.29 ( s1, int ) 1.06/1.29 ( s, int ) 1.06/1.29 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.29 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c B_1_1 (ti X_a B_2_1)) (hAPP X_a X_c B_1_1 B_2_1)) ) 1.06/1.29 ( int, int, (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))), m ) 1.06/1.29 ( int, int, (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), pls ) 1.06/1.29 ( int, int, (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), t ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), min ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), pls ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), pls ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) min), min ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) min), pls ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) t), pls ) 1.06/1.29 ( int, bool, (hAPP int (fun int bool) (ord_less int) (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int))), pls ) 1.06/1.29 ( int, (fun int bool), (ord_less int), min ) 1.06/1.29 ( int, (fun int bool), (ord_less int), pls ) 1.06/1.29 ( int, (fun int bool), (ord_less int), t ) 1.06/1.29 ( int, (fun int bool), (ord_less int), s ) 1.06/1.29 ( int, (fun int bool), (ord_less_eq int), min ) 1.06/1.29 ( int, (fun int bool), (ord_less_eq int), pls ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21273 $$unsorted) (BOUND_VARIABLE_21274 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21273) BOUND_VARIABLE_21274)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_21274))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_21273))) )) 1.06/1.29 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((K_1 $$unsorted)) (= (hAPP int int (plus_plus int pls) K_1) (ti int K_1)) ) 1.06/1.29 ( min ) 1.06/1.29 ( pls ) 1.06/1.29 ( t ) 1.06/1.29 ( m ) 1.06/1.29 ( s1 ) 1.06/1.29 ( s ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21333 $$unsorted) (BOUND_VARIABLE_21334 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_21334) _let_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_21333) _let_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_21334) BOUND_VARIABLE_21333)) _let_1))) )))) 1.06/1.29 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.29 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ( nat, (one_one nat), (one_one nat) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) M))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (dvd_dvd nat) N_1) M)))) ))) 1.06/1.29 ( (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21424 $$unsorted) (BOUND_VARIABLE_21425 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a (number_number_of X_a BOUND_VARIABLE_21424)) (number_number_of X_a BOUND_VARIABLE_21425)) (number_number_of X_a (hAPP int int (plus_plus int BOUND_VARIABLE_21424) BOUND_VARIABLE_21425)))) ) 1.06/1.29 ( nat, (bit1 pls), (bit1 pls) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) M))) (not (hBOOL (hAPP int bool _let_2 B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) M))) (not (hBOOL (hAPP int bool (zcong A_1 B) M))) (= (ti int B) (ti int A_1))) )))) 1.06/1.29 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.06/1.29 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.06/1.29 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21490 $$unsorted) (BOUND_VARIABLE_21491 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (hAPP X_a X_a (div_mod X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21490) BOUND_VARIABLE_21491)) BOUND_VARIABLE_21491))) ) 1.06/1.29 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP nat nat (times_times nat Z_1) (number_number_of nat (bit0 (bit1 pls)))) (hAPP nat nat (plus_plus nat Z_1) Z_1)) ) 1.06/1.29 ( (one_one nat) ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((T_3 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) T_3) T_3))) ) 1.06/1.29 ( (zero_zero nat) ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (hBOOL (hAPP int bool (zcong (zfact (hAPP int int (minus_minus int P_3) (one_one int))) (number_number_of int min)) P_3))) ) 1.06/1.29 ( (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.29 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.29 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (ti int M))) (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (= _let_0 (hAPP int int (times_times int M) N_1))) (= _let_0 _let_1) (= (number_number_of int min) _let_1)) ))) 1.06/1.29 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.29 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.29 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((Y $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (plus_plus int X_1) Y)))) )) 1.06/1.29 ( (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.29 ( (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.29 ) 1.06/1.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21542 $$unsorted) (BOUND_VARIABLE_21543 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_21542) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21542) BOUND_VARIABLE_21543)))) ) 1.06/1.29 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.29 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.29 ) 1.06/1.29 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_21559 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a _let_0) _let_0)) BOUND_VARIABLE_21559) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_21559) BOUND_VARIABLE_21559))) )) 1.06/1.29 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.29 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.30 ( nat, (one_one nat) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21606 $$unsorted) (BOUND_VARIABLE_21607 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (number_number_of X_a BOUND_VARIABLE_21606)) (number_number_of X_a BOUND_VARIABLE_21607))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_21606) BOUND_VARIABLE_21607)))) ) 1.06/1.30 ( int, pls, pls ) 1.06/1.30 ( int, pls, (bit1 pls) ) 1.06/1.30 ( nat, pls, (bit0 (bit1 pls)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (bit1 B_1_1))) (forall ((B_1_1 $$unsorted)) (= _let_0 (ti int _let_0)) )) 1.06/1.30 ( min ) 1.06/1.30 ( pls ) 1.06/1.30 ( (bit1 pls) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21625 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_21625) (number_number_of nat (bit0 (bit1 pls))))) (zero_zero X_a))))) ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( int, skv_2 ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21668 $$unsorted) (BOUND_VARIABLE_21669 $$unsorted)) (or (not (group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_21668) BOUND_VARIABLE_21669)) (= (ti X_a BOUND_VARIABLE_21669) (ti X_a BOUND_VARIABLE_21668)))) ) 1.06/1.30 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21687 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21687) BOUND_VARIABLE_21687) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_21687) (number_number_of nat (bit0 (bit1 pls)))))) ) 1.06/1.30 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( int, skv_2 ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21703 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a (power_power X_a BOUND_VARIABLE_21703) (number_number_of nat (bit0 (bit1 pls)))) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21703) BOUND_VARIABLE_21703))) ) 1.06/1.30 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( int, skv_2 ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21745 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_21745) pls)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (number_number_of X_a BOUND_VARIABLE_21745)) (zero_zero X_a))))) ) 1.06/1.30 ( int, min ) 1.06/1.30 ( int, pls ) 1.06/1.30 ( int, (bit1 pls) ) 1.06/1.30 ( int, (bit0 (bit1 pls)) ) 1.06/1.30 ( int, (bit0 (bit0 (bit1 pls))) ) 1.06/1.30 ( int, (bit1 (bit1 pls)) ) 1.06/1.30 ( nat, pls ) 1.06/1.30 ( nat, (bit1 pls) ) 1.06/1.30 ( nat, (bit0 (bit1 pls)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21812 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_21812) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_21812))) ) 1.06/1.30 ( int, min ) 1.06/1.30 ( int, pls ) 1.06/1.30 ( int, t ) 1.06/1.30 ( int, m ) 1.06/1.30 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.30 ( (fun int bool), zprime ) 1.06/1.30 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.30 ( nat, (one_one nat) ) 1.06/1.30 ( (fun bool (fun bool bool)), fconj ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (semiring X_a)) (= (times_times X_a (ti X_a B_1_1)) (times_times X_a B_1_1))) ) 1.06/1.30 ( min, int ) 1.06/1.30 ( pls, int ) 1.06/1.30 ( zprime, (fun int bool) ) 1.06/1.30 ( t, int ) 1.06/1.30 ( m, int ) 1.06/1.30 ( s1, int ) 1.06/1.30 ( s, int ) 1.06/1.30 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.30 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int _let_0 _let_1 I_1))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 J_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 J_1) K_1))) (hBOOL (hAPP int bool _let_2 K_1))) )))) 1.06/1.30 ( min, (zero_zero int), (zero_zero int) ) 1.06/1.30 ( min, min, min ) 1.06/1.30 ( pls, (zero_zero int), min ) 1.06/1.30 ( t, (zero_zero int), (one_one int) ) 1.06/1.30 ( (number_number_of int (bit1 (bit1 pls))), min, pls ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21930 $$unsorted) (BOUND_VARIABLE_21931 $$unsorted)) (or (not (dvd X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_21930) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_21930) BOUND_VARIABLE_21931)))) ) 1.06/1.30 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (forall ((M $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) M))) (not (hBOOL (hAPP int bool (zcong A_1 _let_1) M))) (= _let_1 (ti int A_1))) ))) 1.06/1.30 ( (zero_zero int), (zero_zero int) ) 1.06/1.30 ( (zero_zero int), t ) 1.06/1.30 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.30 ( (one_one int), (zero_zero int) ) 1.06/1.30 ( (one_one int), t ) 1.06/1.30 ( min, (zero_zero int) ) 1.06/1.30 ( min, min ) 1.06/1.30 ( pls, min ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.06/1.30 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (number_number_of X_b BOUND_VARIABLE_22023))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_22021 $$unsorted) (BOUND_VARIABLE_22022 $$unsorted) (BOUND_VARIABLE_22023 $$unsorted)) (or (not (semiring X_b)) (not (number X_b)) (= (hAPP X_b X_b (plus_plus X_b (hAPP X_b X_b (times_times X_b BOUND_VARIABLE_22021) _let_0)) (hAPP X_b X_b (times_times X_b BOUND_VARIABLE_22022) _let_0)) (hAPP X_b X_b (times_times X_b (hAPP X_b X_b (plus_plus X_b BOUND_VARIABLE_22021) BOUND_VARIABLE_22022)) _let_0))) )) 1.06/1.30 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), pls ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1))) (= (ti int Z_1) (ti int W))) ))) 1.06/1.30 ( (zero_zero int), (zero_zero int) ) 1.06/1.30 ( (zero_zero int), (one_one int) ) 1.06/1.30 ( (zero_zero int), min ) 1.06/1.30 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.30 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.30 ( (zero_zero int), s ) 1.06/1.30 ( (zero_zero int), skv_1 ) 1.06/1.30 ( (zero_zero int), skv_4 ) 1.06/1.30 ( (one_one int), (zero_zero int) ) 1.06/1.30 ( (one_one int), t ) 1.06/1.30 ( min, (zero_zero int) ) 1.06/1.30 ( min, min ) 1.06/1.30 ( min, pls ) 1.06/1.30 ( pls, min ) 1.06/1.30 ( (number_number_of int (bit0 (bit1 pls))), (zero_zero int) ) 1.06/1.30 ( t, (one_one int) ) 1.06/1.30 ( (number_number_of int (bit1 (bit1 pls))), (zero_zero int) ) 1.06/1.30 ( s, (zero_zero int) ) 1.06/1.30 ( skv_1, (zero_zero int) ) 1.06/1.30 ( skv_4, (zero_zero int) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22072 $$unsorted) (BOUND_VARIABLE_22073 $$unsorted)) (or (not (no_zero_divisors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_22073)) (= _let_0 (ti X_a BOUND_VARIABLE_22072)) (not (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_22073) BOUND_VARIABLE_22072)))) )) 1.06/1.30 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.30 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22098 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_22098) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_22098) (one_one nat)))) ) 1.06/1.30 ( int, min ) 1.06/1.30 ( int, pls ) 1.06/1.30 ( int, t ) 1.06/1.30 ( int, m ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( int, skv_2 ) 1.06/1.30 ( (fun int bool), zprime ) 1.06/1.30 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.30 ( (fun bool (fun bool bool)), fconj ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22160 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_22160) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_22160) (number_number_of X_a (bit1 pls))))) ) 1.06/1.30 ( int, min ) 1.06/1.30 ( int, pls ) 1.06/1.30 ( int, t ) 1.06/1.30 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.30 ( int, m ) 1.06/1.30 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ( int, s1 ) 1.06/1.30 ( int, s ) 1.06/1.30 ( (fun int bool), zprime ) 1.06/1.30 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.30 ( (fun bool (fun bool bool)), fconj ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Z_1) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) N_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_1) N_1))) )) 1.06/1.30 ( (zero_zero int), (zero_zero int) ) 1.06/1.30 ( (zero_zero int), (one_one int) ) 1.06/1.30 ( (zero_zero int), min ) 1.06/1.30 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.30 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.30 ( (zero_zero int), s ) 1.06/1.30 ( (zero_zero int), skv_1 ) 1.06/1.30 ( (zero_zero int), skv_4 ) 1.06/1.30 ( (one_one int), t ) 1.06/1.30 ( min, min ) 1.06/1.30 ( min, pls ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (no_zero_divisors X_a)) (= (times_times X_a B_1_1) (times_times X_a (ti X_a B_1_1)))) ) 1.06/1.30 ( min, int ) 1.06/1.30 ( pls, int ) 1.06/1.30 ( zprime, (fun int bool) ) 1.06/1.30 ( t, int ) 1.06/1.30 ( m, int ) 1.06/1.30 ( s1, int ) 1.06/1.30 ( s, int ) 1.06/1.30 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.30 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22186 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_22186) BOUND_VARIABLE_22186) (hAPP X_a X_a (times_times X_a (number_number_of X_a (bit0 (bit1 pls)))) BOUND_VARIABLE_22186))) ) 1.06/1.30 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.30 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.30 ( nat, (one_one nat) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22242 $$unsorted) (BOUND_VARIABLE_22243 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (minus_minus X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_22242) BOUND_VARIABLE_22243)) BOUND_VARIABLE_22243) (ti X_a BOUND_VARIABLE_22242))) ) 1.06/1.30 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.06/1.30 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.06/1.30 ( nat, (one_one nat), (one_one nat) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (number_number_of int min))) (let ((_let_2 (ti int Ma))) (let ((_let_3 (ti int N))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (or (and (= _let_0 _let_2) (= _let_0 _let_3)) (and (= _let_1 _let_3) (= _let_1 _let_2))) (= _let_0 (hAPP int int (times_times int Ma) N))) ))))) 1.06/1.30 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (bit0 (bit1 pls)))) (let ((_let_1 (number_number_of nat _let_0))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22265 $$unsorted) (BOUND_VARIABLE_22266 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (minus_minus X_a (hAPP X_a X_a (plus_plus X_a (hAPP nat X_a (power_power X_a BOUND_VARIABLE_22265) _let_1)) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_22266) _let_1))) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (times_times X_a (number_number_of X_a _let_0)) BOUND_VARIABLE_22265)) BOUND_VARIABLE_22266)) (hAPP nat X_a (power_power X_a (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_22265) BOUND_VARIABLE_22266)) _let_1))) ))) 1.06/1.30 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((Ma $$unsorted) (X $$unsorted)) (= (not (forall ((Y_2 $$unsorted)) (not (hBOOL (hAPP int bool (zcong (hAPP nat int (power_power int Y_2) (number_number_of nat (bit0 (bit1 pls)))) X) Ma))) )) (hBOOL (hAPP int bool (quadRes Ma) X))) ) 1.06/1.30 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_1)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Q_3 $$unsorted) (Y $$unsorted)) (or (not (= (ti int A_2) (hAPP int int (plus_plus int (hAPP int int (times_times int B_1) Q_3)) Y))) (and (not _let_4) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Y) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) Y))))) (and _let_4 (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) B_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_2) Y))))) (= _let_2 (ti int B_1)) (= (ti int Y) (hAPP int int (div_mod int A_2) B_1))) )))))) 1.06/1.30 ( s, (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22351 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a (number_number_of X_a BOUND_VARIABLE_22351)) (one_one X_a)) (number_number_of X_a (hAPP int int (plus_plus int BOUND_VARIABLE_22351) (bit1 pls))))) ) 1.06/1.30 ( nat, (bit1 pls) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (zcong A_1 B) M))) (not (hBOOL (hAPP int bool (zcong B C) M))) (hBOOL (hAPP int bool (zcong A_1 C) M))) ) 1.06/1.30 ( (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.30 ) 1.06/1.30 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) _let_0))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22393 $$unsorted) (BOUND_VARIABLE_22394 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_22394))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_22393))) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_22393)) (= _let_0 (ti X_a BOUND_VARIABLE_22394))) (= _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_22394) BOUND_VARIABLE_22393)))) ))) 1.06/1.30 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.30 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.30 ( nat, (one_one nat), (one_one nat) ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (number_number_of X_a (bit1 pls)) (one_one X_a))) ) 1.06/1.30 ( int ) 1.06/1.30 ( nat ) 1.06/1.30 ( real ) 1.06/1.30 ) 1.06/1.30 (instantiation (forall ((X_1 $$unsorted) (M $$unsorted) (Y $$unsorted)) (or (not (= (hAPP int int (div_mod int Y) M) (hAPP int int (div_mod int X_1) M))) (hBOOL (hAPP int bool (zcong X_1 Y) M))) ) 1.06/1.30 ( s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.06/1.31 ( s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.06/1.31 ( s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min) ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.31 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min) ) 1.06/1.31 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22459 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) _let_0) BOUND_VARIABLE_22459))) (= _let_0 (ti X_a BOUND_VARIABLE_22459))) )) 1.06/1.31 ( int, min ) 1.06/1.31 ( int, pls ) 1.06/1.31 ( int, t ) 1.06/1.31 ( int, m ) 1.06/1.31 ( int, s1 ) 1.06/1.31 ( int, s ) 1.06/1.31 ( (fun int bool), zprime ) 1.06/1.31 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.31 ( (fun bool (fun bool bool)), fconj ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (zero_zero X_a))))) ) 1.06/1.31 ( int ) 1.06/1.31 ( bool ) 1.06/1.31 ( nat ) 1.06/1.31 ( real ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (times_times X_a BOUND_VARIABLE_22477))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22477 $$unsorted) (BOUND_VARIABLE_22478 $$unsorted) (BOUND_VARIABLE_22479 $$unsorted)) (or (not (linord581940658strict X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_22478)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_22479))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_22477)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22478) BOUND_VARIABLE_22479))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22477) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22479) BOUND_VARIABLE_22478)))))) ))))) 1.06/1.31 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22541 $$unsorted) (BOUND_VARIABLE_22542 $$unsorted) (BOUND_VARIABLE_22543 $$unsorted)) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (power_power X_a BOUND_VARIABLE_22543) BOUND_VARIABLE_22542) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_22541) BOUND_VARIABLE_22542))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_22541))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_22543))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_22542))) (= (ti X_a BOUND_VARIABLE_22541) (ti X_a BOUND_VARIABLE_22543))) )) 1.06/1.31 ( int, s1, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.31 ( int, s, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.06/1.31 ( int, s, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.31 ( int, skv_2, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_22622 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_22622) _let_0)) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_22622) _let_0)) (hAPP X_a X_a (minus_minus X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_22622) BOUND_VARIABLE_22622)) _let_0))) )) 1.06/1.31 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.31 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.31 ( nat, (one_one nat) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22640 $$unsorted) (BOUND_VARIABLE_22641 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_22640) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_22641) BOUND_VARIABLE_22640)))) ) 1.06/1.31 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.31 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 V_3) V_2)))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (= (and (or (not _let_2) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 pls) V_2))) _let_2) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (number_number_of nat V_3)) (number_number_of nat V_2)))) )))) 1.06/1.31 ( (zero_zero int), (zero_zero int) ) 1.06/1.31 ( (zero_zero int), (one_one int) ) 1.06/1.31 ( (zero_zero int), min ) 1.06/1.31 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( min, min ) 1.06/1.31 ( min, pls ) 1.06/1.31 ( pls, (bit0 (bit1 pls)) ) 1.06/1.31 ( t, (zero_zero int) ) 1.06/1.31 ( t, (one_one int) ) 1.06/1.31 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.31 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (not (= (bit1 K_1) (bit0 L_1))) ) 1.06/1.31 ( min, pls ) 1.06/1.31 ( pls, (bit1 pls) ) 1.06/1.31 ( (bit1 pls), (bit0 (bit1 pls)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (number_number_of int (bit0 (bit1 pls)))) P_3))) (not (hBOOL (hAPP int bool (zcong X_1 (number_number_of int min)) P_3))) (not (hBOOL (hAPP int bool (zcong X_1 (one_one int)) P_3)))) ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (= (not (forall ((K_2 $$unsorted)) (not (= (ti int B_2) (hAPP int int (plus_plus int A_3) (hAPP int int (times_times int Ma) K_2)))) )) (hBOOL (hAPP int bool (zcong A_3 B_2) Ma))) ) 1.06/1.31 ( s1, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( s1, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( s1, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (one_one X_a)))) ) 1.06/1.31 ( int ) 1.06/1.31 ( bool ) 1.06/1.31 ( nat ) 1.06/1.31 ( real ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_1) (hAPP int int (minus_minus int B) (one_one int))))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B))) )) 1.06/1.31 ( (zero_zero int), (zero_zero int) ) 1.06/1.31 ( (zero_zero int), (one_one int) ) 1.06/1.31 ( (zero_zero int), min ) 1.06/1.31 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( min, min ) 1.06/1.31 ( min, pls ) 1.06/1.31 ( t, (zero_zero int) ) 1.06/1.31 ( t, (one_one int) ) 1.06/1.31 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.31 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a _let_0) _let_0) (number_number_of X_a (bit0 (bit1 pls))))) )) 1.06/1.31 ( int ) 1.06/1.31 ( nat ) 1.06/1.31 ( real ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((B_1_1 $$unsorted)) (= (sr B_1_1) (sr (ti int B_1_1))) ) 1.06/1.31 ( min ) 1.06/1.31 ( pls ) 1.06/1.31 ( t ) 1.06/1.31 ( m ) 1.06/1.31 ( s1 ) 1.06/1.31 ( s ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (power X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.06/1.31 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N_1) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N_1) M))) ))) 1.06/1.31 ( (zero_zero int), (zero_zero int) ) 1.06/1.31 ( (zero_zero int), (one_one int) ) 1.06/1.31 ( (zero_zero int), min ) 1.06/1.31 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.31 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.31 ( (zero_zero int), s ) 1.06/1.31 ( (zero_zero int), skv_1 ) 1.06/1.31 ( (zero_zero int), skv_4 ) 1.06/1.31 ( (one_one int), t ) 1.06/1.31 ( min, min ) 1.06/1.31 ( min, pls ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((K_1 $$unsorted)) (= (hAPP int int (minus_minus int K_1) pls) (ti int K_1)) ) 1.06/1.31 ( min ) 1.06/1.31 ( pls ) 1.06/1.31 ( t ) 1.06/1.31 ( m ) 1.06/1.31 ( s1 ) 1.06/1.31 ( s ) 1.06/1.31 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (dvd_dvd int))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 M))) (not (hBOOL (hAPP int bool _let_2 N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N_1) M))) (= (ti int N_1) (ti int M))) )))) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.31 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23091 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (number_number_of X_a BOUND_VARIABLE_23091)) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_23091) (bit1 pls))))) ) 1.06/1.31 ( int, min ) 1.06/1.31 ( int, pls ) 1.06/1.31 ( int, (bit1 pls) ) 1.06/1.31 ( int, (bit0 (bit1 pls)) ) 1.06/1.31 ( int, (bit0 (bit0 (bit1 pls))) ) 1.06/1.31 ( int, (bit1 (bit1 pls)) ) 1.06/1.31 ( nat, pls ) 1.06/1.31 ( nat, (bit1 pls) ) 1.06/1.31 ( nat, (bit0 (bit1 pls)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23152 $$unsorted) (BOUND_VARIABLE_23153 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23153) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_23152) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_23153) BOUND_VARIABLE_23152)) _let_2))) )))) 1.06/1.31 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.31 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.31 ( nat, (one_one nat), (one_one nat) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23186 $$unsorted) (BOUND_VARIABLE_23187 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23187) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23186) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_23187) BOUND_VARIABLE_23186)) _let_2))) )))) 1.06/1.31 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.31 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.31 ( nat, (one_one nat), (one_one nat) ) 1.06/1.31 ) 1.06/1.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23214 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a (number_number_of X_a pls)) BOUND_VARIABLE_23214) (ti X_a BOUND_VARIABLE_23214))) ) 1.06/1.31 ( int, min ) 1.06/1.31 ( int, pls ) 1.06/1.31 ( int, t ) 1.06/1.31 ( int, m ) 1.06/1.31 ( int, s1 ) 1.06/1.31 ( int, s ) 1.06/1.31 ( (fun int bool), zprime ) 1.06/1.31 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.31 ( (fun bool (fun bool bool)), fconj ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_23230))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23229 $$unsorted) (BOUND_VARIABLE_23230 $$unsorted) (BOUND_VARIABLE_23231 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_23231))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_23231) BOUND_VARIABLE_23229)))) )) 1.06/1.31 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.31 ) 1.06/1.31 (instantiation (let ((_let_0 (minus_minus X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (group_add X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.06/1.32 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), int ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP X_a X_c (combc X_a X_b X_c P Q) R) (hAPP X_b X_c (hAPP X_a (fun X_b X_c) P R) Q)) ) 1.06/1.32 ( int, bool, int, (ord_less int), (zero_zero int), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less int), (zero_zero int), t ) 1.06/1.32 ( int, bool, int, (ord_less int), (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.32 ( int, bool, int, (ord_less int), (one_one int), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less int), (one_one int), t ) 1.06/1.32 ( int, bool, int, (ord_less int), min, (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less int), min, min ) 1.06/1.32 ( int, bool, int, (ord_less int), pls, min ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.06/1.32 ( int, bool, int, (ord_less int), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), (zero_zero int), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), (one_one int), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), min, (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), min, min ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), pls, min ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), (number_number_of int (bit0 (bit1 pls))), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), t, (one_one int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), (number_number_of int (bit1 (bit1 pls))), (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), s, (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), skv_1, (zero_zero int) ) 1.06/1.32 ( int, bool, int, (ord_less_eq int), skv_4, (zero_zero int) ) 1.06/1.32 ( int, bool, int, (dvd_dvd int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( nat, bool, nat, (ord_less nat), (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (plus_plus X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (ab_semigroup_add X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.06/1.32 ( (one_one nat), nat ) 1.06/1.32 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), int ) 1.06/1.32 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), int ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (ord_less X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 1.06/1.32 ( int ) 1.06/1.32 ( bool ) 1.06/1.32 ( nat ) 1.06/1.32 ( real ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 (number_number_of int N_1)))) (and (hBOOL (hAPP int bool _let_0 (number_number_of int (bit0 N_1)))) (hBOOL (hAPP int bool _let_0 (number_number_of int (bit1 N_1)))))) )) 1.06/1.32 ( min ) 1.06/1.32 ( pls ) 1.06/1.32 ( (bit1 pls) ) 1.06/1.32 ( (bit0 (bit1 pls)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_23377))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23377 $$unsorted) (BOUND_VARIABLE_23378 $$unsorted) (BOUND_VARIABLE_23379 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_23379))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_23378))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_23379) BOUND_VARIABLE_23378)))) )) 1.06/1.32 ( int, (zero_zero int), (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, t, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, s, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, skv_1, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, skv_4, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X $$unsorted) (N $$unsorted) (Y_1 $$unsorted)) (= (= (hAPP int int (div_mod int X) N) (hAPP int int (div_mod int Y_1) N)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) N) (hAPP int int (minus_minus int X) Y_1)))) ) 1.06/1.32 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23412 $$unsorted) (BOUND_VARIABLE_23413 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23413) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23412) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_23413) BOUND_VARIABLE_23412)))) )))) 1.06/1.32 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.32 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_3))) (forall ((M $$unsorted) (N_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (times_times int M) N_1)))) (hBOOL (hAPP int bool _let_0 N_1)) (hBOOL (hAPP int bool _let_0 M))) )) 1.06/1.32 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23481 $$unsorted) (BOUND_VARIABLE_23482 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_23482))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_23481))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_23482) BOUND_VARIABLE_23481)))) )) 1.06/1.32 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.32 ( nat, (one_one nat), (one_one nat) ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted)) (= (collect X_a P_1) (ti (fun X_a bool) P_1)) ) 1.06/1.32 ( int, zprime ) 1.06/1.32 ( int, twoSqu658283162sum2sq ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (one_one int))) (forall ((N $$unsorted) (Ma $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Ma))) (= (and (= _let_0 (ti int N)) (= _let_0 (ti int Ma))) (= _let_0 (hAPP int int (times_times int Ma) N)))) )) 1.06/1.32 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.32 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23662 $$unsorted) (BOUND_VARIABLE_23663 $$unsorted)) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_23663))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23662) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_23663) BOUND_VARIABLE_23662)) _let_2))) )))) 1.06/1.32 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.32 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (number_number_of X_a BOUND_VARIABLE_23726))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23726 $$unsorted)) (or (not (number_ring X_a)) (= (number_number_of X_a (bit1 BOUND_VARIABLE_23726)) (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (plus_plus X_a (one_one X_a)) _let_0)) _let_0))) )) 1.06/1.32 ( int, min ) 1.06/1.32 ( int, pls ) 1.06/1.32 ( int, (bit1 pls) ) 1.06/1.32 ( nat, pls ) 1.06/1.32 ( nat, (bit1 pls) ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (number_number_of X_a pls) (zero_zero X_a))) ) 1.06/1.32 ( int ) 1.06/1.32 ( nat ) 1.06/1.32 ( real ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (zero_zero nat))) (let ((_let_1 (power_power X_a (zero_zero X_a)))) (let ((_let_2 (number_number_of nat BOUND_VARIABLE_23802))) (let ((_let_3 (number_number_of nat BOUND_VARIABLE_23808))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23802 $$unsorted) (BOUND_VARIABLE_23808 $$unsorted)) (or (not (power X_a)) (not (semiring_0 X_a)) (and (or (= _let_0 _let_2) (= (zero_zero X_a) (hAPP nat X_a _let_1 _let_2))) (or (not (= _let_0 _let_3)) (= (one_one X_a) (hAPP nat X_a _let_1 _let_3))))) ))))) 1.06/1.32 ( int, (bit1 pls), (bit1 pls) ) 1.06/1.32 ( nat, (bit0 (bit1 pls)), (bit0 (bit1 pls)) ) 1.06/1.32 ( real, pls, pls ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1)) (= (hAPP nat nat (div_mod nat (hAPP nat nat (minus_minus nat M) N_1)) N_1) (hAPP nat nat (div_mod nat M) N_1))) ) 1.06/1.32 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_23935 $$unsorted) (BOUND_VARIABLE_23936 $$unsorted)) (or (not (ring_n68954251visors X_a)) (= (or (= _let_0 (ti X_a BOUND_VARIABLE_23935)) (= _let_0 (ti X_a BOUND_VARIABLE_23936))) (= _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_23935) BOUND_VARIABLE_23936)))) )) 1.06/1.32 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (ab_semigroup_mult X_a)) (= (times_times X_a B_1_1) (times_times X_a (ti X_a B_1_1)))) ) 1.06/1.32 ( min, int ) 1.06/1.32 ( pls, int ) 1.06/1.32 ( zprime, (fun int bool) ) 1.06/1.32 ( t, int ) 1.06/1.32 ( m, int ) 1.06/1.32 ( s1, int ) 1.06/1.32 ( s, int ) 1.06/1.32 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.32 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24033 $$unsorted) (BOUND_VARIABLE_24034 $$unsorted) (BOUND_VARIABLE_24035 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24033) BOUND_VARIABLE_24034) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24035) BOUND_VARIABLE_24034))) (= (ti X_a BOUND_VARIABLE_24033) (ti X_a BOUND_VARIABLE_24035))) ) 1.06/1.32 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.32 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.32 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP int int (minus_minus int P_2) (number_number_of int (bit0 (bit1 pls)))))) (forall ((P_2 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_2))) (= (d22set _let_0) (wset _let_0 P_2))) )) 1.06/1.32 ( (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.32 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24060 $$unsorted) (BOUND_VARIABLE_24061 $$unsorted)) (or (not (linord581940658strict X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24060) BOUND_VARIABLE_24061)) _let_2)) (or (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_24060)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24061) _let_2))) (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_24061)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24060) _let_2)))))) ))))) 1.06/1.32 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.32 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (product_Pair int int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti (product_prod int int) _let_0)) )) 1.06/1.32 ( s, (one_one int) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (plus_plus nat K))) (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (= (= Ma N) (= (hAPP nat nat _let_0 Ma) (hAPP nat nat _let_0 N))) )) 1.06/1.32 ( (one_one nat), (one_one nat), (one_one nat) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24148 $$unsorted) (BOUND_VARIABLE_24149 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_24149))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_24148))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24148) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24149) BOUND_VARIABLE_24148)) BOUND_VARIABLE_24149))) )))) 1.06/1.32 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.32 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.32 ) 1.06/1.32 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) K_1))) (forall ((K_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int (minus_minus int M) N_1)))) (not (hBOOL (hAPP int bool _let_0 N_1))) (hBOOL (hAPP int bool _let_0 M))) )) 1.06/1.32 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.32 ) 1.06/1.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24188 $$unsorted) (BOUND_VARIABLE_24189 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24188) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24189) BOUND_VARIABLE_24188)) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24189) (one_one X_a))) BOUND_VARIABLE_24188))) ) 1.06/1.32 ( int, (zero_zero int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.33 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, t, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.33 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.33 ( int, skv_3, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.33 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24210 $$unsorted) (BOUND_VARIABLE_24211 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_24210) BOUND_VARIABLE_24211)) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24210) BOUND_VARIABLE_24211)))) ))) 1.06/1.33 ( int, (zero_zero int), (zero_zero int) ) 1.06/1.33 ( int, (zero_zero int), (one_one int) ) 1.06/1.33 ( int, (zero_zero int), min ) 1.06/1.33 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, min, min ) 1.06/1.33 ( int, min, pls ) 1.06/1.33 ( int, t, (zero_zero int) ) 1.06/1.33 ( int, t, (one_one int) ) 1.06/1.33 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.33 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.33 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.33 ( int, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( nat, (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24250 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24250) (number_number_of nat (bit0 (bit1 pls)))))) (not (= _let_0 (ti X_a BOUND_VARIABLE_24250))))) )) 1.06/1.33 ( int, min ) 1.06/1.33 ( int, pls ) 1.06/1.33 ( int, t ) 1.06/1.33 ( int, m ) 1.06/1.33 ( int, s1 ) 1.06/1.33 ( int, s ) 1.06/1.33 ( int, skv_2 ) 1.06/1.33 ( (fun int bool), zprime ) 1.06/1.33 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.33 ( (fun bool (fun bool bool)), fconj ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((V_1 $$unsorted) (V $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (= (hAPP nat nat (times_times nat (number_number_of nat V)) (number_number_of nat V_1)) (number_number_of nat (hAPP int int (times_times int V) V_1)))) ) 1.06/1.33 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.33 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (one_one int))) (forall ((X $$unsorted) (P_1 $$unsorted)) (or (not (forall ((A_5 $$unsorted)) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) A_5)) (not (hBOOL (hAPP int bool P_1 (hAPP int int (minus_minus int A_5) _let_0))))) (hBOOL (hAPP int bool P_1 A_5))) )) (hBOOL (hAPP int bool P_1 X))) )) 1.06/1.33 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) pls) ) 1.06/1.33 ( (zero_zero int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) t) ) 1.06/1.33 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int))) ) 1.06/1.33 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 1.06/1.33 ( (one_one int), (hAPP int (fun int bool) (ord_less int) t) ) 1.06/1.33 ( min, (hAPP int (fun int bool) (ord_less int) pls) ) 1.06/1.33 ( min, (hAPP int (fun int bool) (ord_less int) min) ) 1.06/1.33 ( min, (hAPP int (fun int bool) (ord_less_eq int) min) ) 1.06/1.33 ( min, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 1.06/1.33 ( pls, (hAPP int (fun int bool) (ord_less int) min) ) 1.06/1.33 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min) ) 1.06/1.33 ( (number_number_of int (bit0 (bit1 pls))), zprime ) 1.06/1.33 ( (number_number_of int (bit0 (bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), zprime ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) t) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (zcong (hAPP nat int (power_power int s) _let_0) (hAPP nat int (power_power int s1) _let_0))) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) s) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 s) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) skv_1) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 skv_1) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zcong s1 skv_4) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int (fun int bool) (ord_less int) skv_4) ) 1.06/1.33 ( (number_number_of int (bit1 (bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( (number_number_of int min), (quadRes (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) ) 1.06/1.33 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t), twoSqu658283162sum2sq ) 1.06/1.33 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int (fun int bool) (ord_less int) (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t)) ) 1.06/1.33 ( skv_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hBOOL (hAPP int bool (zcong A_3 B_2) (zero_zero int))) (= (ti int B_2) (ti int A_3))) ) 1.06/1.33 ( s1, s ) 1.06/1.33 ( s1, skv_1 ) 1.06/1.33 ( s1, skv_4 ) 1.06/1.33 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.33 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.33 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.33 ( (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (ab_semigroup_add X_a)) (= (plus_plus X_a (ti X_a B_1_1)) (plus_plus X_a B_1_1))) ) 1.06/1.33 ( min, int ) 1.06/1.33 ( pls, int ) 1.06/1.33 ( zprime, (fun int bool) ) 1.06/1.33 ( t, int ) 1.06/1.33 ( m, int ) 1.06/1.33 ( s1, int ) 1.06/1.33 ( s, int ) 1.06/1.33 ( fconj, (fun bool (fun bool bool)) ) 1.06/1.33 ( twoSqu658283162sum2sq, (fun int bool) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c B_1_1 B_2_1) (hAPP X_a X_c (ti (fun X_a X_c) B_1_1) B_2_1)) ) 1.06/1.33 ( int, bool, zprime, (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.33 ( int, bool, zprime, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ( int, bool, twoSqu658283162sum2sq, (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((B_1_1 $$unsorted)) (= (quadRes (ti int B_1_1)) (quadRes B_1_1)) ) 1.06/1.33 ( min ) 1.06/1.33 ( pls ) 1.06/1.33 ( t ) 1.06/1.33 ( m ) 1.06/1.33 ( s1 ) 1.06/1.33 ( s ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24476 $$unsorted)) (or (not (linordered_ring X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24476) BOUND_VARIABLE_24476)))) ) 1.06/1.33 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.33 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24525 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (number_number_of X_a BOUND_VARIABLE_24525)) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_24525) (bit1 pls))))) ) 1.06/1.33 ( int, min ) 1.06/1.33 ( int, pls ) 1.06/1.33 ( int, (bit1 pls) ) 1.06/1.33 ( int, (bit0 (bit1 pls)) ) 1.06/1.33 ( int, (bit0 (bit0 (bit1 pls))) ) 1.06/1.33 ( int, (bit1 (bit1 pls)) ) 1.06/1.33 ( nat, pls ) 1.06/1.33 ( nat, (bit1 pls) ) 1.06/1.33 ( nat, (bit0 (bit1 pls)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (plus_plus X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.06/1.33 ( (one_one nat), nat ) 1.06/1.33 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), int ) 1.06/1.33 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), int ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ti int X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) X_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X_1) (number_number_of int (bit0 (bit1 pls)))))) (= (one_one int) _let_2) (= _let_1 _let_2)) )))) 1.06/1.33 ( (zero_zero int) ) 1.06/1.33 ( (one_one int) ) 1.06/1.33 ( min ) 1.06/1.33 ( pls ) 1.06/1.33 ( (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.33 ( t ) 1.06/1.33 ( m ) 1.06/1.33 ( s1 ) 1.06/1.33 ( (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.33 ( s ) 1.06/1.33 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.33 ( skv_1 ) 1.06/1.33 ( skv_4 ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((B_1_1 $$unsorted)) (= (bit1 B_1_1) (bit1 (ti int B_1_1))) ) 1.06/1.33 ( min ) 1.06/1.33 ( pls ) 1.06/1.33 ( t ) 1.06/1.33 ( m ) 1.06/1.33 ( s1 ) 1.06/1.33 ( s ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24606 $$unsorted) (BOUND_VARIABLE_24607 $$unsorted) (BOUND_VARIABLE_24608 $$unsorted) (BOUND_VARIABLE_24609 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_24608) BOUND_VARIABLE_24609))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24606) BOUND_VARIABLE_24607))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_24608))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_2) BOUND_VARIABLE_24606))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24608) BOUND_VARIABLE_24606)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24609) BOUND_VARIABLE_24607)))) ))))) 1.06/1.33 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (zero_zero nat))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (= _let_0 (hAPP nat nat (plus_plus nat Ma) N)) (and (= _let_0 Ma) (= _let_0 N))) )) 1.06/1.33 ( (one_one nat), (one_one nat) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24652 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24652) BOUND_VARIABLE_24652)) BOUND_VARIABLE_24652) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24652) (number_number_of nat (bit1 (bit1 pls)))))) ) 1.06/1.33 ( int, s1 ) 1.06/1.33 ( int, s ) 1.06/1.33 ( int, skv_2 ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (one_one X_a)))) ) 1.06/1.33 ( int ) 1.06/1.33 ( bool ) 1.06/1.33 ( nat ) 1.06/1.33 ( real ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24669 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_24669) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24669) (one_one X_a))))) ) 1.06/1.33 ( int, (zero_zero int) ) 1.06/1.33 ( int, min ) 1.06/1.33 ( int, t ) 1.06/1.33 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.33 ( int, s ) 1.06/1.33 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.33 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.33 ( int, skv_1 ) 1.06/1.33 ( int, skv_4 ) 1.06/1.33 ( nat, (zero_zero nat) ) 1.06/1.33 ( nat, (one_one nat) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (plus_plus int (zero_zero int)) Z_1) (ti int Z_1)) ) 1.06/1.33 ( min ) 1.06/1.33 ( pls ) 1.06/1.33 ( t ) 1.06/1.33 ( m ) 1.06/1.33 ( s1 ) 1.06/1.33 ( s ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24731 $$unsorted) (BOUND_VARIABLE_24732 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_24732))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_24731))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24732) BOUND_VARIABLE_24731)))) )) 1.06/1.33 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.06/1.33 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.33 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) I_1))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 J_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (plus_plus nat J_1) M)))) )) 1.06/1.33 ( (one_one nat), (zero_zero nat), (one_one nat) ) 1.06/1.33 ) 1.06/1.33 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (number_number_of X_a pls) (zero_zero X_a))) ) 1.06/1.33 ( int ) 1.06/1.33 ( nat ) 1.06/1.33 ( real ) 1.06/1.33 ) 1.06/1.33 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24784 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_24784) BOUND_VARIABLE_24784)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24784) _let_2)))) )))) 1.06/1.33 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.34 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( nat, (one_one nat) ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (forall ((M $$unsorted) (Y $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 X_1))) (not (hBOOL (hAPP int bool _let_2 Y))) (not (hBOOL (hAPP int bool _let_2 M))) (not (hBOOL (hAPP int bool (zcong X_1 Y) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) M))) (= (ti int X_1) (ti int Y))) )))) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s, s1 ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (number_number_of int min), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1, s1 ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4, s1 ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((L_1 $$unsorted)) (not (= min (bit0 L_1))) ) 1.06/1.34 ( pls ) 1.06/1.34 ( (bit1 pls) ) 1.06/1.34 ( (bit0 (bit1 pls)) ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24869 $$unsorted) (BOUND_VARIABLE_24870 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24869) _let_0)) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24870) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (zero_zero X_a)) BOUND_VARIABLE_24870))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_24869) BOUND_VARIABLE_24870))) )))) 1.06/1.34 ( int, (zero_zero int), (zero_zero int) ) 1.06/1.34 ( int, (zero_zero int), (one_one int) ) 1.06/1.34 ( int, (zero_zero int), min ) 1.06/1.34 ( int, (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.34 ( int, (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.34 ( int, (zero_zero int), s ) 1.06/1.34 ( int, (zero_zero int), skv_1 ) 1.06/1.34 ( int, (zero_zero int), skv_4 ) 1.06/1.34 ( int, (one_one int), t ) 1.06/1.34 ( int, min, min ) 1.06/1.34 ( int, min, pls ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (mult_zero X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.06/1.34 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (power_power X_a _let_0) (number_number_of nat (bit0 (bit1 pls)))))) )) 1.06/1.34 ( int ) 1.06/1.34 ( nat ) 1.06/1.34 ( real ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP X_b X_c P (hAPP X_a X_b Q R)) (hAPP X_a X_c (combb X_b X_c X_a P Q) R)) ) 1.06/1.34 ( int, bool, int, zprime, (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) t), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (zcong (hAPP nat int (power_power int s) _let_0) (hAPP nat int (power_power int s1) _let_0))), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, twoSqu658283162sum2sq, (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t)), (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) s), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong s1 s), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_1), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong s1 skv_1), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) (number_number_of int min)), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (zcong s1 skv_4), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( int, (fun int bool), int, (ord_less int), (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))), (one_one int) ) 1.06/1.34 ( int, (fun int bool), int, (dvd_dvd int), (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)), (one_one int) ) 1.06/1.34 ( nat, int, nat, (power_power int s), (plus_plus nat (one_one nat)), (one_one nat) ) 1.06/1.34 ( nat, int, nat, (power_power int s1), (plus_plus nat (one_one nat)), (one_one nat) ) 1.06/1.34 ( nat, int, nat, (power_power int skv_2), (plus_plus nat (one_one nat)), (one_one nat) ) 1.06/1.34 ( nat, bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (plus_plus nat (one_one nat)), (one_one nat) ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_24922) BOUND_VARIABLE_24921))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_24921 $$unsorted) (BOUND_VARIABLE_24922 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_24922))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24922) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_24922) _let_2)) _let_2))) )))) 1.06/1.34 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.06/1.34 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.34 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (hBOOL P_1))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X)))) (let ((_let_2 (hBOOL P_4))) (forall ((P_4 $$unsorted) (P_1 $$unsorted) (X $$unsorted)) (or (and _let_1 (= (not _let_0) _let_2)) (= (and _let_0 _let_1) (and _let_2 _let_1))) )))) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (number_number_of int (bit1 (bit1 pls)))), min ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (number_number_of int (bit1 (bit1 pls)))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) t), (number_number_of int (bit1 (bit1 pls))) ) 1.06/1.34 ( (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 1.06/1.34 ( (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (one_one int)), (one_one int) ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (one_one int)), (hAPP int bool zprime (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))), (zero_zero int) ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (let ((_let_0 (bit0 (bit1 pls)))) (hAPP int bool (zcong (hAPP nat int (power_power int s) (number_number_of nat _let_0)) (number_number_of int min)) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_0))) m)) (one_one int)))), s ) 1.06/1.34 ( (let ((_let_0 (bit0 (bit1 pls)))) (hAPP int bool (zcong (hAPP nat int (power_power int s) (number_number_of nat _let_0)) (number_number_of int min)) (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 _let_0))) m)) (one_one int)))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) min) pls), (number_number_of int (bit0 (bit1 pls))) ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), skv_1 ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) (zero_zero int)), skv_4 ) 1.06/1.34 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) (zero_zero int)), (hAPP int bool (hAPP int (fun int bool) (ord_less int) t) (one_one int)), skv_1 ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24982 $$unsorted) (BOUND_VARIABLE_24983 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_24982) BOUND_VARIABLE_24983)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (number_number_of X_a BOUND_VARIABLE_24982)) (number_number_of X_a BOUND_VARIABLE_24983))))) ) 1.06/1.34 ( int, pls, pls ) 1.06/1.34 ( int, pls, (bit1 pls) ) 1.06/1.34 ( int, pls, (bit0 (bit1 pls)) ) 1.06/1.34 ( int, pls, (bit1 (bit1 pls)) ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25016 $$unsorted) (BOUND_VARIABLE_25017 $$unsorted) (BOUND_VARIABLE_25018 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_25016) BOUND_VARIABLE_25018)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_25017) BOUND_VARIABLE_25018)) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_25016) BOUND_VARIABLE_25017)) BOUND_VARIABLE_25018))) ) 1.06/1.34 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (zero_zero int) ) 1.06/1.34 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), t ) 1.06/1.34 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), skv_3 ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (times_times int K_1))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_1) J_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) K_1))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 I_1)) (hAPP int int _let_2 J_1)))) )))) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25073 $$unsorted)) (or (not (ring_11004092258visors X_a)) (= (= _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_25073) (number_number_of nat (bit0 (bit1 pls))))) (= _let_0 (ti X_a BOUND_VARIABLE_25073)))) )) 1.06/1.34 ( int, min ) 1.06/1.34 ( int, pls ) 1.06/1.34 ( int, t ) 1.06/1.34 ( int, m ) 1.06/1.34 ( int, s1 ) 1.06/1.34 ( int, s ) 1.06/1.34 ( int, skv_2 ) 1.06/1.34 ( (fun int bool), zprime ) 1.06/1.34 ( (fun int bool), twoSqu658283162sum2sq ) 1.06/1.34 ( (fun bool (fun bool bool)), fconj ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a _let_0 (ord_less X_a) _let_1))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25095 $$unsorted) (BOUND_VARIABLE_25096 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_25096))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_25095))) (hBOOL (hAPP X_a bool _let_2 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_25096) BOUND_VARIABLE_25095)))) )))) 1.06/1.34 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.06/1.34 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.06/1.34 ( nat, (one_one nat), (one_one nat) ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (fun int bool))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_1) (zero_zero int)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) B) A_1))) (= (ti int A_1) (hAPP int int (div_mod int A_1) B))) )) 1.06/1.34 ( (zero_zero int), (zero_zero int) ) 1.06/1.34 ( (zero_zero int), (one_one int) ) 1.06/1.34 ( (zero_zero int), min ) 1.06/1.34 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.34 ( min, min ) 1.06/1.34 ( min, pls ) 1.06/1.34 ( t, (zero_zero int) ) 1.06/1.34 ( t, (one_one int) ) 1.06/1.34 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.34 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.34 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.34 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.34 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((X_a $$unsorted) (B_1_1 $$unsorted)) (= (collect X_a B_1_1) (collect X_a (ti (fun X_a bool) B_1_1))) ) 1.06/1.34 ( int, zprime ) 1.06/1.34 ( int, twoSqu658283162sum2sq ) 1.06/1.34 ) 1.06/1.34 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25139 $$unsorted) (BOUND_VARIABLE_25140 $$unsorted)) (or (not (power X_a)) (not (zero_neq_one X_a)) (not (no_zero_divisors X_a)) (not (mult_zero X_a)) (= (= _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_25139) BOUND_VARIABLE_25140)) (and (= _let_0 (ti X_a BOUND_VARIABLE_25139)) (not (= (zero_zero nat) BOUND_VARIABLE_25140))))) )) 1.06/1.34 ( int, s1, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.34 ( int, s, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.34 ( int, skv_2, (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.34 ) 1.06/1.34 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (= M (hAPP nat nat (plus_plus nat M) N_1))) (= (zero_zero nat) N_1)) ) 1.06/1.35 ( (one_one nat), (one_one nat) ) 1.06/1.35 ) 1.06/1.35 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N_1 $$unsorted)) (or (and (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1))) (not (= M N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1))) )) 1.06/1.35 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.06/1.35 ) 1.06/1.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25263 $$unsorted) (BOUND_VARIABLE_25264 $$unsorted) (BOUND_VARIABLE_25265 $$unsorted) (BOUND_VARIABLE_25266 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_25265) BOUND_VARIABLE_25266) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_25263) BOUND_VARIABLE_25264))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25265) BOUND_VARIABLE_25266)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25263) BOUND_VARIABLE_25264)))) ))) 1.06/1.35 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.06/1.35 ) 1.06/1.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25303 $$unsorted) (BOUND_VARIABLE_25304 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_25303) BOUND_VARIABLE_25304) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_25304) BOUND_VARIABLE_25303))) ) 1.06/1.35 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.06/1.35 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.06/1.35 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.35 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.35 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.06/1.35 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ) 1.06/1.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25358 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_25358) (zero_zero nat)))) ) 1.06/1.35 ( int, s1 ) 1.06/1.35 ( int, s ) 1.06/1.35 ( int, skv_2 ) 1.06/1.35 ) 1.06/1.35 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) Y)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) X_1)) (= (ti int X_1) (ti int Y))) ))) 1.06/1.35 ( (zero_zero int), (zero_zero int) ) 1.06/1.35 ( (zero_zero int), (one_one int) ) 1.06/1.35 ( (zero_zero int), min ) 1.06/1.35 ( (zero_zero int), t ) 1.06/1.35 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.35 ( (one_one int), (zero_zero int) ) 1.06/1.35 ( (one_one int), t ) 1.06/1.35 ( min, (zero_zero int) ) 1.06/1.35 ( min, min ) 1.06/1.35 ( min, pls ) 1.06/1.35 ( pls, min ) 1.06/1.35 ( t, (zero_zero int) ) 1.06/1.35 ( t, (one_one int) ) 1.06/1.35 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.06/1.35 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.06/1.35 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.06/1.35 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.06/1.35 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.06/1.35 ) 1.06/1.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_25423) BOUND_VARIABLE_25422))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25422 $$unsorted) (BOUND_VARIABLE_25423 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_25423))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_25423) _let_2)))) )))) 1.06/1.35 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.06/1.35 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.06/1.35 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.06/1.35 ) 1.06/1.35 (instantiation (let ((_let_0 (times_times X_a BOUND_VARIABLE_25468))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25464 $$unsorted) (BOUND_VARIABLE_25465 $$unsorted) (BOUND_VARIABLE_25466 $$unsorted) (BOUND_VARIABLE_25467 $$unsorted) (BOUND_VARIABLE_25468 $$unsorted)) (or (not (semiri456707255roduct X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_25468)) (= (ti X_a BOUND_VARIABLE_25465) (ti X_a BOUND_VARIABLE_25464)) (not (= (ti X_a BOUND_VARIABLE_25467) (ti X_a BOUND_VARIABLE_25466))) (not (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_25466) (hAPP X_a X_a _let_0 BOUND_VARIABLE_25464)) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_25467) (hAPP X_a X_a _let_0 BOUND_VARIABLE_25465))))) )) 1.06/1.35 ( int, min, min, min, min, min ) 1.06/1.35 ( int, min, min, min, m, min ) 1.06/1.35 ( int, min, min, m, min, min ) 1.06/1.35 ( int, min, min, m, m, min ) 1.06/1.35 ( int, min, m, m, m, m ) 1.06/1.35 ( int, pls, s1, s1, s1, s1 ) 1.06/1.35 ( int, t, s, s, s, s ) 1.06/1.35 ( int, m, min, min, min, min ) 1.06/1.35 ( int, s1, pls, pls, pls, pls ) 1.06/1.35 ( int, s1, s1, min, min, s1 ) 1.06/1.35 ( int, s1, s1, min, pls, s1 ) 1.06/1.35 ( int, s1, s1, min, m, s1 ) 1.06/1.35 ( int, s1, s1, min, s1, s1 ) 1.06/1.35 ( int, s1, s1, pls, min, s1 ) 1.06/1.35 ( int, s1, s1, pls, pls, s1 ) 1.06/1.35 ( int, s1, s1, pls, m, s1 ) 1.06/1.35 ( int, s1, s1, pls, s1, s1 ) 1.06/1.35 ( int, s1, s1, m, min, s1 ) 1.06/1.35 ( int, s1, s1, m, pls, s1 ) 1.06/1.35 ( int, s1, s1, m, m, s1 ) 1.06/1.35 ( int, s1, s1, m, s1, s1 ) 1.06/1.35 ( int, s1, s1, s1, min, s1 ) 1.06/1.35 ( int, s1, s1, s1, pls, s1 ) 1.06/1.35 ( int, s1, s1, s1, m, s1 ) 1.06/1.35 ( int, s1, s1, s1, s1, s1 ) 1.06/1.35 ( int, s, t, t, t, t ) 1.06/1.35 ( int, s, s, min, min, s ) 1.06/1.35 ( int, s, s, min, pls, s ) 1.06/1.35 ( int, s, s, min, t, s ) 1.06/1.35 ( int, s, s, min, m, s ) 1.06/1.35 ( int, s, s, min, s1, s ) 1.06/1.35 ( int, s, s, min, s, s ) 1.06/1.35 ( int, s, s, pls, min, s ) 1.06/1.35 ( int, s, s, pls, pls, s ) 1.06/1.35 ( int, s, s, pls, t, s ) 1.06/1.35 ( int, s, s, pls, m, s ) 1.06/1.35 ( int, s, s, pls, s1, s ) 1.06/1.35 ( int, s, s, pls, s, s ) 1.06/1.35 ( int, s, s, t, min, s ) 1.06/1.35 ( int, s, s, t, pls, s ) 1.06/1.35 ( int, s, s, t, t, s ) 1.14/1.35 ( int, s, s, t, m, s ) 1.14/1.35 ( int, s, s, t, s1, s ) 1.14/1.35 ( int, s, s, t, s, s ) 1.14/1.35 ( int, s, s, m, min, s ) 1.14/1.35 ( int, s, s, m, pls, s ) 1.14/1.35 ( int, s, s, m, t, s ) 1.14/1.35 ( int, s, s, m, m, s ) 1.14/1.35 ( int, s, s, m, s1, s ) 1.14/1.35 ( int, s, s, m, s, s ) 1.14/1.35 ( int, s, s, s1, min, s ) 1.14/1.35 ( int, s, s, s1, pls, s ) 1.14/1.35 ( int, s, s, s1, t, s ) 1.14/1.35 ( int, s, s, s1, m, s ) 1.14/1.35 ( int, s, s, s1, s1, s ) 1.14/1.35 ( int, s, s, s1, s, s ) 1.14/1.35 ( int, s, s, s, min, s ) 1.14/1.35 ( int, s, s, s, pls, s ) 1.14/1.35 ( int, s, s, s, t, s ) 1.14/1.35 ( int, s, s, s, m, s ) 1.14/1.35 ( int, s, s, s, s1, s ) 1.14/1.35 ( int, s, s, s, s, s ) 1.14/1.35 ( (fun int bool), zprime, zprime, zprime, zprime, zprime ) 1.14/1.35 ( (fun int bool), zprime, zprime, zprime, twoSqu658283162sum2sq, zprime ) 1.14/1.35 ( (fun int bool), zprime, zprime, twoSqu658283162sum2sq, zprime, zprime ) 1.14/1.35 ( (fun int bool), zprime, zprime, twoSqu658283162sum2sq, twoSqu658283162sum2sq, zprime ) 1.14/1.35 ( (fun int bool), zprime, twoSqu658283162sum2sq, twoSqu658283162sum2sq, twoSqu658283162sum2sq, twoSqu658283162sum2sq ) 1.14/1.35 ( (fun int bool), twoSqu658283162sum2sq, zprime, zprime, zprime, zprime ) 1.14/1.35 ( (fun bool (fun bool bool)), fconj, fconj, fconj, fconj, fconj ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP int int (times_times int W) Z_1) (hAPP int int (times_times int Z_1) W)) ) 1.14/1.35 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.35 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.14/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.14/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.14/1.35 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (fun int bool))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (member int B_2) (d22set A_3)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) A_3))) )) 1.14/1.35 ( (zero_zero int), (zero_zero int) ) 1.14/1.35 ( (zero_zero int), (one_one int) ) 1.14/1.35 ( (zero_zero int), min ) 1.14/1.35 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.35 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.14/1.35 ( (zero_zero int), s ) 1.14/1.35 ( (zero_zero int), skv_1 ) 1.14/1.35 ( (zero_zero int), skv_4 ) 1.14/1.35 ( (one_one int), t ) 1.14/1.35 ( min, min ) 1.14/1.35 ( min, pls ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (dvd X_a)) (= (times_times X_a B_1_1) (times_times X_a (ti X_a B_1_1)))) ) 1.14/1.35 ( min, int ) 1.14/1.35 ( pls, int ) 1.14/1.35 ( zprime, (fun int bool) ) 1.14/1.35 ( t, int ) 1.14/1.35 ( m, int ) 1.14/1.35 ( s1, int ) 1.14/1.35 ( s, int ) 1.14/1.35 ( fconj, (fun bool (fun bool bool)) ) 1.14/1.35 ( twoSqu658283162sum2sq, (fun int bool) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_1 $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) (zero_zero int))) (= (zfact N_1) (hAPP int int (times_times int N_1) (zfact (hAPP int int (minus_minus int N_1) (one_one int)))))) ) 1.14/1.35 ( (zero_zero int) ) 1.14/1.35 ( (one_one int) ) 1.14/1.35 ( min ) 1.14/1.35 ( (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) (zero_zero int)))) (= (one_one int) (zfact N_1))) ) 1.14/1.35 ( (zero_zero int) ) 1.14/1.35 ( (one_one int) ) 1.14/1.35 ( min ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (one X_a)) (= _let_0 (ti X_a _let_0))) )) 1.14/1.35 ( int ) 1.14/1.35 ( nat ) 1.14/1.35 ( real ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (= (hAPP nat nat (times_times nat (hAPP nat nat (plus_plus nat X_1) Y)) (hAPP nat nat (minus_minus nat X_1) Y)) (hAPP nat nat (minus_minus nat (hAPP nat nat (power_power nat X_1) _let_0)) (hAPP nat nat (power_power nat Y) _let_0))) )) 1.14/1.35 ( (one_one nat), (one_one nat) ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25651 $$unsorted) (BOUND_VARIABLE_25652 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_25652))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_25651))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_25652) BOUND_VARIABLE_25651)))) )) 1.14/1.35 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.35 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.35 ( nat, (one_one nat), (one_one nat) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25709 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_25709) BOUND_VARIABLE_25709))) ) 1.14/1.35 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((B $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (= (hAPP int int (minus_minus int B) (one_one int)) (hAPP int int (div_mod int (number_number_of int min)) B))) ) 1.14/1.35 ( (zero_zero int) ) 1.14/1.35 ( (one_one int) ) 1.14/1.35 ( min ) 1.14/1.35 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25802 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_25802) (hAPP X_a X_a (plus_plus X_a (zero_zero X_a)) BOUND_VARIABLE_25802))) ) 1.14/1.35 ( int, min ) 1.14/1.35 ( int, pls ) 1.14/1.35 ( int, t ) 1.14/1.35 ( int, m ) 1.14/1.35 ( int, s1 ) 1.14/1.35 ( int, s ) 1.14/1.35 ( (fun int bool), zprime ) 1.14/1.35 ( (fun int bool), twoSqu658283162sum2sq ) 1.14/1.35 ( (fun bool (fun bool bool)), fconj ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (hAPP int int (times_times int (hAPP int int (plus_plus int Z1) Z2)) W) (hAPP int int (plus_plus int (hAPP int int (times_times int Z1) W)) (hAPP int int (times_times int Z2) W))) ) 1.14/1.35 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (zero_zero int) ) 1.14/1.35 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), t ) 1.14/1.35 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), skv_3 ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_25948 $$unsorted) (BOUND_VARIABLE_25949 $$unsorted)) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25948) BOUND_VARIABLE_25949)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_25948) BOUND_VARIABLE_25949)) (zero_zero X_a))))) ))) 1.14/1.35 ( int, (zero_zero int), (zero_zero int) ) 1.14/1.35 ( int, (zero_zero int), (one_one int) ) 1.14/1.35 ( int, (zero_zero int), min ) 1.14/1.35 ( int, (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.35 ( int, (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.14/1.35 ( int, (zero_zero int), s ) 1.14/1.35 ( int, (zero_zero int), skv_1 ) 1.14/1.35 ( int, (zero_zero int), skv_4 ) 1.14/1.35 ( int, (one_one int), t ) 1.14/1.35 ( int, min, min ) 1.14/1.35 ( int, min, pls ) 1.14/1.35 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted)) (or (not (zero X_a)) (= _let_0 (ti X_a _let_0))) )) 1.14/1.35 ( int ) 1.14/1.35 ( nat ) 1.14/1.35 ( real ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26004 $$unsorted) (BOUND_VARIABLE_26005 $$unsorted) (BOUND_VARIABLE_26006 $$unsorted) (BOUND_VARIABLE_26007 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26006) BOUND_VARIABLE_26007))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_26004) BOUND_VARIABLE_26005))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) BOUND_VARIABLE_26006))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_26004))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_26006) BOUND_VARIABLE_26004)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_26007) BOUND_VARIABLE_26005)))) ))))) 1.14/1.35 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.35 ) 1.14/1.35 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_26116))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26116 $$unsorted) (BOUND_VARIABLE_26117 $$unsorted) (BOUND_VARIABLE_26118 $$unsorted)) (or (not (linord893533164strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26117) BOUND_VARIABLE_26118))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_26116))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_26117)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_26118)))) )))) 1.14/1.35 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.14/1.35 ) 1.14/1.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26171 $$unsorted) (BOUND_VARIABLE_26172 $$unsorted)) (or (not (ab_group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_26171) BOUND_VARIABLE_26172)) (= (ti X_a BOUND_VARIABLE_26171) (ti X_a BOUND_VARIABLE_26172)))) ) 1.14/1.36 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_26209))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26208 $$unsorted) (BOUND_VARIABLE_26209 $$unsorted) (BOUND_VARIABLE_26210 $$unsorted)) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_26210))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_26208))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_26210) BOUND_VARIABLE_26208)))) )) 1.14/1.36 ( int, (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun int bool))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (plus_plus int W) (one_one int))) Z_1))) )) 1.14/1.36 ( (zero_zero int), (zero_zero int) ) 1.14/1.36 ( (zero_zero int), (one_one int) ) 1.14/1.36 ( (zero_zero int), min ) 1.14/1.36 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( t, (zero_zero int) ) 1.14/1.36 ( t, (one_one int) ) 1.14/1.36 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.36 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_1) J_1))) (not (forall ((K_2 $$unsorted)) (or (not (= J_1 (hAPP nat nat (plus_plus nat I_1) K_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) K_2)))) ))) ))) 1.14/1.36 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26308 $$unsorted) (BOUND_VARIABLE_26309 $$unsorted)) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_26308) BOUND_VARIABLE_26309))) (= (zero_zero X_a) (hAPP X_a X_a (div_mod X_a BOUND_VARIABLE_26309) BOUND_VARIABLE_26308))) ) 1.14/1.36 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26335 $$unsorted) (BOUND_VARIABLE_26336 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_26336))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_26335))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_26336) BOUND_VARIABLE_26335)))) )) 1.14/1.36 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.36 ( nat, (one_one nat), (one_one nat) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (= (= Ma N) (= (hAPP nat nat (plus_plus nat Ma) K) (hAPP nat nat (plus_plus nat N) K))) ) 1.14/1.36 ( (one_one nat), (one_one nat), (one_one nat) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26421 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_26421)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_26421) BOUND_VARIABLE_26421))))) )) 1.14/1.36 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.36 ( nat, (one_one nat) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_3) B_2))) (not (hBOOL (hAPP _let_0 bool (member int B_2) (d22set A_3))))) )) 1.14/1.36 ( (zero_zero int), (zero_zero int) ) 1.14/1.36 ( (zero_zero int), (one_one int) ) 1.14/1.36 ( (zero_zero int), min ) 1.14/1.36 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( t, (zero_zero int) ) 1.14/1.36 ( t, (one_one int) ) 1.14/1.36 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.36 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_2 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26498 $$unsorted) (BOUND_VARIABLE_26499 $$unsorted) (BOUND_VARIABLE_26500 $$unsorted) (BOUND_VARIABLE_26501 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_26500) BOUND_VARIABLE_26501))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_26498) BOUND_VARIABLE_26499))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_26500))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_26498))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_26500) BOUND_VARIABLE_26498)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_26501) BOUND_VARIABLE_26499)))) )))) 1.14/1.36 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((X_1 $$unsorted) (Y $$unsorted)) (or (= X_1 Y) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 X_1) Y)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Y) X_1))) ))) 1.14/1.36 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.14/1.36 ( (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (one_one int))) (let ((_let_3 (ti int A_1))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) P_3))) (not (hBOOL (hAPP int bool (zcong (hAPP int int (times_times int A_1) A_1) _let_2) P_3))) (= _let_2 _let_3) (= _let_3 (hAPP int int (minus_minus int P_3) _let_2))) ))))) 1.14/1.36 ( (zero_zero int), (zero_zero int) ) 1.14/1.36 ( (zero_zero int), (one_one int) ) 1.14/1.36 ( (zero_zero int), min ) 1.14/1.36 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( min, min ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( t, (zero_zero int) ) 1.14/1.36 ( t, (one_one int) ) 1.14/1.36 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.36 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26610 $$unsorted) (BOUND_VARIABLE_26611 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_26610) BOUND_VARIABLE_26611))) (= (ti X_a BOUND_VARIABLE_26611) (ti X_a BOUND_VARIABLE_26610)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_26610) BOUND_VARIABLE_26611))) )) 1.14/1.36 ( int, (zero_zero int), (zero_zero int) ) 1.14/1.36 ( int, (zero_zero int), (one_one int) ) 1.14/1.36 ( int, (zero_zero int), min ) 1.14/1.36 ( int, (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.36 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( int, (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.14/1.36 ( int, (zero_zero int), s ) 1.14/1.36 ( int, (zero_zero int), skv_1 ) 1.14/1.36 ( int, (zero_zero int), skv_4 ) 1.14/1.36 ( int, (one_one int), t ) 1.14/1.36 ( int, min, min ) 1.14/1.36 ( int, min, pls ) 1.14/1.36 ( int, t, (zero_zero int) ) 1.14/1.36 ( int, t, (one_one int) ) 1.14/1.36 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( int, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.36 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.36 ( int, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( int, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( nat, (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (zero_zero X_a))))) ) 1.14/1.36 ( int ) 1.14/1.36 ( bool ) 1.14/1.36 ( nat ) 1.14/1.36 ( real ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_1_1 $$unsorted)) (= (zfact B_1_1) (zfact (ti int B_1_1))) ) 1.14/1.36 ( min ) 1.14/1.36 ( pls ) 1.14/1.36 ( t ) 1.14/1.36 ( m ) 1.14/1.36 ( s1 ) 1.14/1.36 ( s ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (number_number_of X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (number X_a)) (= _let_0 (ti X_a _let_0))) )) 1.14/1.36 ( min, int ) 1.14/1.36 ( pls, int ) 1.14/1.36 ( pls, nat ) 1.14/1.36 ( (bit1 pls), int ) 1.14/1.36 ( (bit1 pls), nat ) 1.14/1.36 ( (bit0 (bit1 pls)), int ) 1.14/1.36 ( (bit0 (bit1 pls)), nat ) 1.14/1.36 ( (bit0 (bit0 (bit1 pls))), int ) 1.14/1.36 ( (bit1 (bit1 pls)), int ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (product_Pair int int (ti int B_1_1) B_2_1) (product_Pair int int B_1_1 B_2_1)) ) 1.14/1.36 ( s, (one_one int) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26660 $$unsorted)) (or (not (monoid_add X_a)) (= (hAPP X_a X_a (plus_plus X_a (zero_zero X_a)) BOUND_VARIABLE_26660) (ti X_a BOUND_VARIABLE_26660))) ) 1.14/1.36 ( int, min ) 1.14/1.36 ( int, pls ) 1.14/1.36 ( int, t ) 1.14/1.36 ( int, m ) 1.14/1.36 ( int, s1 ) 1.14/1.36 ( int, s ) 1.14/1.36 ( (fun int bool), zprime ) 1.14/1.36 ( (fun int bool), twoSqu658283162sum2sq ) 1.14/1.36 ( (fun bool (fun bool bool)), fconj ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26674 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_26674) (one_one X_a)) (ti X_a BOUND_VARIABLE_26674))) ) 1.14/1.36 ( int, min ) 1.14/1.36 ( int, pls ) 1.14/1.36 ( int, t ) 1.14/1.36 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.36 ( int, m ) 1.14/1.36 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ( int, s1 ) 1.14/1.36 ( int, s ) 1.14/1.36 ( (fun int bool), zprime ) 1.14/1.36 ( (fun int bool), twoSqu658283162sum2sq ) 1.14/1.36 ( (fun bool (fun bool bool)), fconj ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (plus_plus X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (dvd X_a)) (not (linorder X_a)) (not (plus X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.14/1.36 ( (one_one nat), nat ) 1.14/1.36 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), int ) 1.14/1.36 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), int ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_26833))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26831 $$unsorted) (BOUND_VARIABLE_26832 $$unsorted) (BOUND_VARIABLE_26833 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_26833))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26831) BOUND_VARIABLE_26832)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_26831)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_26832))))) )))) 1.14/1.36 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (number_number_of nat BOUND_VARIABLE_26869))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26868 $$unsorted) (BOUND_VARIABLE_26869 $$unsorted)) (or (not (zero_neq_one X_a)) (not (no_zero_divisors X_a)) (not (mult_zero X_a)) (not (power X_a)) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_26868)) (not (= (zero_zero nat) _let_1))) (= _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_26868) _let_1)))) ))) 1.14/1.36 ( int, s1, (bit0 (bit1 pls)) ) 1.14/1.36 ( int, s, (bit0 (bit1 pls)) ) 1.14/1.36 ( int, skv_2, (bit0 (bit1 pls)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (number_number_of X_b BOUND_VARIABLE_26898))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_26898 $$unsorted)) (or (not (monoid_mult X_b)) (not (number X_b)) (= (hAPP X_b X_b (times_times X_b _let_0) _let_0) (hAPP nat X_b (power_power X_b _let_0) (number_number_of nat (bit0 (bit1 pls)))))) )) 1.14/1.36 ( int, min ) 1.14/1.36 ( int, pls ) 1.14/1.36 ( int, (bit1 pls) ) 1.14/1.36 ( int, (bit0 (bit1 pls)) ) 1.14/1.36 ( int, (bit0 (bit0 (bit1 pls))) ) 1.14/1.36 ( int, (bit1 (bit1 pls)) ) 1.14/1.36 ( nat, pls ) 1.14/1.36 ( nat, (bit1 pls) ) 1.14/1.36 ( nat, (bit0 (bit1 pls)) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (semiring X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.14/1.36 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.14/1.36 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (minus_minus int min))) (forall ((L_1 $$unsorted)) (= (hAPP int int _let_0 (bit1 L_1)) (bit0 (hAPP int int _let_0 L_1))) )) 1.14/1.36 ( min ) 1.14/1.36 ( pls ) 1.14/1.36 ( (bit1 pls) ) 1.14/1.36 ) 1.14/1.36 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_26942 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26942) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_26942) BOUND_VARIABLE_26942)) _let_2)))) )))) 1.14/1.36 ( int, (zero_zero int) ) 1.14/1.36 ( int, min ) 1.14/1.36 ( int, t ) 1.14/1.36 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.36 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.36 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.14/1.36 ( nat, (one_one nat) ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (ti int L) (ti int K)) (= (bit0 K) (bit0 L))) ) 1.14/1.36 ( min, pls ) 1.14/1.36 ( pls, min ) 1.14/1.36 ( pls, pls ) 1.14/1.36 ( pls, m ) 1.14/1.36 ( t, s ) 1.14/1.36 ( m, min ) 1.14/1.36 ( s1, t ) 1.14/1.36 ( s, t ) 1.14/1.36 ( s, s1 ) 1.14/1.36 ( s, s ) 1.14/1.36 ) 1.14/1.36 (instantiation (forall ((K_1 $$unsorted)) (= (ti int K_1) (hAPP int int (plus_plus int K_1) pls)) ) 1.14/1.37 ( min ) 1.14/1.37 ( pls ) 1.14/1.37 ( t ) 1.14/1.37 ( m ) 1.14/1.37 ( (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.14/1.37 ( s1 ) 1.14/1.37 ( s ) 1.14/1.37 ( (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (hBOOL (hAPP int bool _let_0 (hAPP nat int (power_power int X_1) N_1)))) )) 1.14/1.37 ( (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.14/1.37 ( (number_number_of nat (bit0 (bit1 pls))), s ) 1.14/1.37 ( (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27035 $$unsorted)) (or (not (power X_a)) (= (one_one X_a) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_27035) (zero_zero nat)))) ) 1.14/1.37 ( int, s1 ) 1.14/1.37 ( int, s ) 1.14/1.37 ( int, skv_2 ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27051 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (bit1 pls)) BOUND_VARIABLE_27051)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (number_number_of X_a BOUND_VARIABLE_27051))))) ) 1.14/1.37 ( int, min ) 1.14/1.37 ( int, pls ) 1.14/1.37 ( int, (bit1 pls) ) 1.14/1.37 ( int, (bit0 (bit1 pls)) ) 1.14/1.37 ( int, (bit0 (bit0 (bit1 pls))) ) 1.14/1.37 ( int, (bit1 (bit1 pls)) ) 1.14/1.37 ( nat, pls ) 1.14/1.37 ( nat, (bit1 pls) ) 1.14/1.37 ( nat, (bit0 (bit1 pls)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (one_one int))) (let ((_let_2 (ti int M_2))) (forall ((P_2 $$unsorted)) (= (and (forall ((M_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) M_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) M_2) P_2))) (= (ti int P_2) _let_2) (= _let_1 _let_2)) ) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) P_2))) (hBOOL (hAPP int bool zprime P_2))) )))) 1.14/1.37 ( (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.37 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27146 $$unsorted) (BOUND_VARIABLE_27147 $$unsorted) (BOUND_VARIABLE_27148 $$unsorted) (BOUND_VARIABLE_27149 $$unsorted)) (or (not (ab_group_add X_a)) (not (= (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_27146) BOUND_VARIABLE_27147) (hAPP X_a X_a (minus_minus X_a BOUND_VARIABLE_27148) BOUND_VARIABLE_27149))) (= (= (ti X_a BOUND_VARIABLE_27149) (ti X_a BOUND_VARIABLE_27148)) (= (ti X_a BOUND_VARIABLE_27147) (ti X_a BOUND_VARIABLE_27146)))) ) 1.14/1.37 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (number_number_of int min) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (power_power X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (power X_a)) (= _let_0 (ti (fun nat X_a) _let_0))) )) 1.14/1.37 ( s1, int ) 1.14/1.37 ( s, int ) 1.14/1.37 ( skv_2, int ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27199 $$unsorted) (BOUND_VARIABLE_27200 $$unsorted) (BOUND_VARIABLE_27201 $$unsorted) (BOUND_VARIABLE_27202 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27201) BOUND_VARIABLE_27202))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27199) BOUND_VARIABLE_27200))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_27202))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_2) BOUND_VARIABLE_27199))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_27201) BOUND_VARIABLE_27199)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_27202) BOUND_VARIABLE_27200)))) )))) 1.14/1.37 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (number_number_of int (bit1 (bit0 (bit1 pls))))) P_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) P_3))) (= (ti int A_1) (inv P_3 (inv P_3 A_1)))) ))) 1.14/1.37 ( (zero_zero int), (zero_zero int) ) 1.14/1.37 ( (zero_zero int), (one_one int) ) 1.14/1.37 ( (zero_zero int), min ) 1.14/1.37 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( min, min ) 1.14/1.37 ( min, pls ) 1.14/1.37 ( t, (zero_zero int) ) 1.14/1.37 ( t, (one_one int) ) 1.14/1.37 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.37 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.37 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (plus_plus X_a _let_0) _let_0)))) )) 1.14/1.37 ( int ) 1.14/1.37 ( bool ) 1.14/1.37 ( nat ) 1.14/1.37 ( real ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27272 $$unsorted) (BOUND_VARIABLE_27273 $$unsorted)) (or (not (ordere453448008miring X_a)) (and (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27272))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27273) _let_2)))) (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27273))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27272) _let_2))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_27273) BOUND_VARIABLE_27272)) _let_2))) ))))) 1.14/1.37 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.14/1.37 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27310 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_27310)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (number_number_of X_a BOUND_VARIABLE_27310))))) ) 1.14/1.37 ( int, min ) 1.14/1.37 ( int, pls ) 1.14/1.37 ( int, (bit1 pls) ) 1.14/1.37 ( int, (bit0 (bit1 pls)) ) 1.14/1.37 ( int, (bit0 (bit0 (bit1 pls))) ) 1.14/1.37 ( int, (bit1 (bit1 pls)) ) 1.14/1.37 ( nat, pls ) 1.14/1.37 ( nat, (bit1 pls) ) 1.14/1.37 ( nat, (bit0 (bit1 pls)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((K_1 $$unsorted)) (= (bit1 K_1) (hAPP int int (plus_plus int (hAPP int int (plus_plus int (one_one int)) K_1)) K_1)) ) 1.14/1.37 ( min ) 1.14/1.37 ( pls ) 1.14/1.37 ( (bit1 pls) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1))) (= M (hAPP nat nat (div_mod nat M) N_1))) ) 1.14/1.37 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27415 $$unsorted) (BOUND_VARIABLE_27416 $$unsorted)) (or (not (ring_11004092258visors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_27416)) (not (= _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_27416) BOUND_VARIABLE_27415)))) )) 1.14/1.37 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.14/1.37 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.14/1.37 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (number_number_of X_a BOUND_VARIABLE_27496))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27496 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (plus_plus X_a (zero_zero X_a)) _let_0)) _let_0) (number_number_of X_a (bit0 BOUND_VARIABLE_27496)))) )) 1.14/1.37 ( int, pls ) 1.14/1.37 ( int, (bit1 pls) ) 1.14/1.37 ( int, (bit0 (bit1 pls)) ) 1.14/1.37 ( nat, pls ) 1.14/1.37 ( nat, (bit1 pls) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27548 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (number_number_of X_a BOUND_VARIABLE_27548))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (bit1 pls)) BOUND_VARIABLE_27548)))) ) 1.14/1.37 ( int, min ) 1.14/1.37 ( int, pls ) 1.14/1.37 ( int, (bit1 pls) ) 1.14/1.37 ( int, (bit0 (bit1 pls)) ) 1.14/1.37 ( int, (bit0 (bit0 (bit1 pls))) ) 1.14/1.37 ( int, (bit1 (bit1 pls)) ) 1.14/1.37 ( nat, pls ) 1.14/1.37 ( nat, (bit1 pls) ) 1.14/1.37 ( nat, (bit0 (bit1 pls)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27575 $$unsorted) (BOUND_VARIABLE_27576 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_27575) BOUND_VARIABLE_27576)) BOUND_VARIABLE_27576) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_27575) (one_one X_a))) BOUND_VARIABLE_27576))) ) 1.14/1.37 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.14/1.37 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (zero_zero int) ) 1.14/1.37 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), t ) 1.14/1.37 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), skv_3 ) 1.14/1.37 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.14/1.37 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.14/1.37 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_27619))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27618 $$unsorted) (BOUND_VARIABLE_27619 $$unsorted) (BOUND_VARIABLE_27620 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_27620))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_27618) BOUND_VARIABLE_27620)))) )) 1.14/1.37 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (power_power X_a BOUND_VARIABLE_27642))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_27642 $$unsorted) (BOUND_VARIABLE_27643 $$unsorted) (BOUND_VARIABLE_27644 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (plus_plus nat BOUND_VARIABLE_27643) BOUND_VARIABLE_27644)) (hAPP X_a X_a (times_times X_a (hAPP nat X_a _let_0 BOUND_VARIABLE_27643)) (hAPP nat X_a _let_0 BOUND_VARIABLE_27644)))) )) 1.14/1.37 ( int, s1, (one_one nat), (one_one nat) ) 1.14/1.37 ( int, s, (one_one nat), (one_one nat) ) 1.14/1.37 ( int, skv_2, (one_one nat), (one_one nat) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (times_times int (one_one int)) Z_1) (ti int Z_1)) ) 1.14/1.37 ( min ) 1.14/1.37 ( pls ) 1.14/1.37 ( t ) 1.14/1.37 ( m ) 1.14/1.37 ( s1 ) 1.14/1.37 ( s ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (zero_zero int))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool (zcong A_1 _let_0) P_3))) (= _let_0 (legendre A_1 P_3))) )) 1.14/1.37 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (legendre A_1 P_3))) (let ((_let_1 (hBOOL (hAPP int bool (quadRes P_3) A_1)))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (or (hBOOL (hAPP int bool (zcong A_1 (zero_zero int)) P_3)) (and (or _let_1 (= (number_number_of int min) _let_0)) (or (not _let_1) (= (one_one int) _let_0)))) ))) 1.14/1.37 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (forall ((Ma $$unsorted) (N $$unsorted)) (= (not (= Ma N)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) N)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N) Ma)))) ))) 1.14/1.37 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.14/1.37 ( (number_number_of nat (bit0 (bit1 pls))), (zero_zero nat) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun int bool))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (one_one int)) B_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) A_3))) (hBOOL (hAPP _let_0 bool (member int B_2) (d22set A_3)))) )) 1.14/1.37 ( (zero_zero int), (zero_zero int) ) 1.14/1.37 ( (one_one int), (zero_zero int) ) 1.14/1.37 ( min, (zero_zero int) ) 1.14/1.37 ( min, min ) 1.14/1.37 ( pls, min ) 1.14/1.37 ( (number_number_of int (bit0 (bit1 pls))), (zero_zero int) ) 1.14/1.37 ( t, (one_one int) ) 1.14/1.37 ( (number_number_of int (bit1 (bit1 pls))), (zero_zero int) ) 1.14/1.37 ( s, (zero_zero int) ) 1.14/1.37 ( skv_1, (zero_zero int) ) 1.14/1.37 ( skv_4, (zero_zero int) ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27747 $$unsorted)) (or (not (linordered_idom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_27747) (number_number_of nat (bit0 (bit1 pls))))))) ) 1.14/1.37 ( int, s1 ) 1.14/1.37 ( int, s ) 1.14/1.37 ( int, skv_2 ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (order T_1)) (order (fun T_2 T_1))) ) 1.14/1.37 ( int, bool ) 1.14/1.37 ( bool, bool ) 1.14/1.37 ( bool, (fun bool bool) ) 1.14/1.37 ( nat, bool ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (power X_a)) (= (times_times X_a (ti X_a B_1_1)) (times_times X_a B_1_1))) ) 1.14/1.37 ( min, int ) 1.14/1.37 ( pls, int ) 1.14/1.37 ( zprime, (fun int bool) ) 1.14/1.37 ( t, int ) 1.14/1.37 ( m, int ) 1.14/1.37 ( s1, int ) 1.14/1.37 ( s, int ) 1.14/1.37 ( fconj, (fun bool (fun bool bool)) ) 1.14/1.37 ( twoSqu658283162sum2sq, (fun int bool) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) M)) _let_0))) (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool zprime _let_1))) (= _let_0 (legendre (number_number_of int min) _let_1))) ))) 1.14/1.37 ( m ) 1.14/1.37 ) 1.14/1.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27778 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (number_number_of X_a BOUND_VARIABLE_27778)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_27778) pls)))) ) 1.14/1.37 ( int, min ) 1.14/1.37 ( int, pls ) 1.14/1.37 ( int, (bit1 pls) ) 1.14/1.37 ( int, (bit0 (bit1 pls)) ) 1.14/1.37 ( int, (bit0 (bit0 (bit1 pls))) ) 1.14/1.37 ( int, (bit1 (bit1 pls)) ) 1.14/1.37 ( nat, pls ) 1.14/1.37 ( nat, (bit1 pls) ) 1.14/1.37 ( nat, (bit0 (bit1 pls)) ) 1.14/1.37 ) 1.14/1.37 (instantiation (let ((_let_0 (fun int bool))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (= (and (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_2) W_1)) (not (= (ti int W_1) (ti int Z_2)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Z_2) W_1))) )) 1.14/1.37 ( (zero_zero int), (zero_zero int) ) 1.14/1.37 ( (zero_zero int), (one_one int) ) 1.14/1.37 ( (zero_zero int), min ) 1.14/1.37 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.37 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.14/1.37 ( (zero_zero int), s ) 1.14/1.37 ( (zero_zero int), skv_1 ) 1.14/1.37 ( (zero_zero int), skv_4 ) 1.14/1.37 ( (one_one int), t ) 1.14/1.37 ( min, min ) 1.14/1.37 ( min, pls ) 1.14/1.37 ( t, (zero_zero int) ) 1.14/1.37 ( t, (one_one int) ) 1.14/1.37 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.37 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.14/1.37 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.14/1.37 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.38 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.38 ) 1.14/1.38 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (group_add X_a)) (= (minus_minus X_a (ti X_a B_1_1)) (minus_minus X_a B_1_1))) ) 1.14/1.38 ( min, int ) 1.14/1.38 ( pls, int ) 1.14/1.38 ( zprime, (fun int bool) ) 1.14/1.38 ( t, int ) 1.14/1.38 ( m, int ) 1.14/1.38 ( s1, int ) 1.14/1.38 ( s, int ) 1.14/1.38 ( fconj, (fun bool (fun bool bool)) ) 1.14/1.38 ( twoSqu658283162sum2sq, (fun int bool) ) 1.14/1.38 ) 1.14/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27896 $$unsorted)) (or (not (semiring_div X_a)) (= (ti X_a BOUND_VARIABLE_27896) (hAPP X_a X_a (div_mod X_a BOUND_VARIABLE_27896) (zero_zero X_a)))) ) 1.14/1.38 ( int, min ) 1.14/1.38 ( int, pls ) 1.14/1.38 ( int, t ) 1.14/1.38 ( int, m ) 1.14/1.38 ( int, s1 ) 1.14/1.38 ( int, s ) 1.14/1.38 ( (fun int bool), zprime ) 1.14/1.38 ( (fun int bool), twoSqu658283162sum2sq ) 1.14/1.38 ( (fun bool (fun bool bool)), fconj ) 1.14/1.38 ) 1.14/1.38 (instantiation (let ((_let_0 (bit1 pls))) (let ((_let_1 (bit0 _let_0))) (let ((_let_2 (ti int P_3))) (forall ((P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (= (number_number_of int _let_1) _let_2) (= (number_number_of int (bit1 _let_0)) _let_2) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (number_number_of int (bit1 _let_1))) P_3))) )))) 1.14/1.38 ( min ) 1.14/1.38 ( pls ) 1.14/1.38 ( (number_number_of int (bit0 (bit1 pls))) ) 1.14/1.38 ( t ) 1.14/1.38 ( m ) 1.14/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.14/1.38 ( s1 ) 1.14/1.38 ( s ) 1.14/1.38 ) 1.14/1.38 (instantiation (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28066 $$unsorted) (BOUND_VARIABLE_28067 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_28066) _let_0)) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_28067) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_28067))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_28066) BOUND_VARIABLE_28067))) )))) 1.17/1.38 ( int, (zero_zero int), (zero_zero int) ) 1.17/1.38 ( int, (zero_zero int), (one_one int) ) 1.17/1.38 ( int, (zero_zero int), min ) 1.17/1.38 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, min, min ) 1.17/1.38 ( int, min, pls ) 1.17/1.38 ( int, t, (zero_zero int) ) 1.17/1.38 ( int, t, (one_one int) ) 1.17/1.38 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.17/1.38 ( int, skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( nat, (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (ord_less_eq X_a))) (forall ((X_a $$unsorted)) (or (not (order X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 1.17/1.38 ( int ) 1.17/1.38 ( bool ) 1.17/1.38 ( nat ) 1.17/1.38 ( real ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X $$unsorted)) (= (hBOOL (hAPP int bool twoSqu658283162sum2sq X)) (not (forall ((A_5 $$unsorted) (B_4 $$unsorted)) (not (= (twoSqu1929807760sum2sq (product_Pair int int A_5 B_4)) (ti int X))) ))) ) 1.17/1.38 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) t) ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP nat nat (plus_plus nat Z_1) Z_1) (hAPP nat nat (times_times nat (number_number_of nat (bit0 (bit1 pls)))) Z_1)) ) 1.17/1.38 ( (one_one nat) ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28167 $$unsorted)) (or (not (linordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28167) BOUND_VARIABLE_28167)) (zero_zero X_a))))) ) 1.17/1.38 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28264 $$unsorted) (BOUND_VARIABLE_28265 $$unsorted) (BOUND_VARIABLE_28266 $$unsorted)) (or (not (comm_semiring X_a)) (= (hAPP X_a X_a (plus_plus X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28264) BOUND_VARIABLE_28266)) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28265) BOUND_VARIABLE_28266)) (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28264) BOUND_VARIABLE_28265)) BOUND_VARIABLE_28266))) ) 1.17/1.38 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), (zero_zero int) ) 1.17/1.38 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), t ) 1.17/1.38 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), skv_3 ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28299 $$unsorted) (BOUND_VARIABLE_28300 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (hAPP X_a X_a (div_mod X_a (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28299) BOUND_VARIABLE_28300)) BOUND_VARIABLE_28299))) ) 1.17/1.38 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))), m ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.17/1.38 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3 ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28322 $$unsorted) (BOUND_VARIABLE_28323 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_28323))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28322) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28323) BOUND_VARIABLE_28322)) _let_2))) )))) 1.17/1.38 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.38 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_3))) (forall ((N_1 $$unsorted) (P_3 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) M))) (not (hBOOL (hAPP int bool zprime P_3))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (times_times int M) N_1)))) (hBOOL (hAPP int bool _let_0 M)) (hBOOL (hAPP int bool _let_0 N_1))) )) 1.17/1.38 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (hAPP int _let_0 (ord_less_eq int) _let_2))) (forall ((B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_3 (hAPP int int (plus_plus int (hAPP int int (times_times int B_3) Q_4)) R_3)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 R_3) B_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_3))) (hBOOL (hAPP int bool _let_3 Q_4))) ))))) 1.17/1.38 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int) ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (zcong X_1 Y) M))) (hBOOL (hAPP int bool (zcong (hAPP nat int (power_power int X_1) Z_1) (hAPP nat int (power_power int Y) Z_1)) M))) ) 1.17/1.38 ( (number_number_of nat (bit0 (bit1 pls))), s, s1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (fun nat bool))) (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1))) )) 1.17/1.38 ( (zero_zero nat), (number_number_of nat (bit0 (bit1 pls))) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (fun int bool))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B))) (= (hAPP int int (div_mod int A_1) B) (ti int A_1))) )) 1.17/1.38 ( (zero_zero int), (zero_zero int) ) 1.17/1.38 ( (zero_zero int), t ) 1.17/1.38 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.38 ( (one_one int), (zero_zero int) ) 1.17/1.38 ( (one_one int), t ) 1.17/1.38 ( min, (zero_zero int) ) 1.17/1.38 ( min, min ) 1.17/1.38 ( pls, min ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.17/1.38 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) I_1))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 J_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (plus_plus nat M) J_1)))) )) 1.17/1.38 ( (one_one nat), (zero_zero nat), (one_one nat) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) V_3))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (number_number_of nat V_3)) (number_number_of nat V_2))) (or (hBOOL (hAPP int bool _let_0 V_2)) (hBOOL (hAPP int bool _let_0 pls)))) )) 1.17/1.38 ( (zero_zero int), (zero_zero int) ) 1.17/1.38 ( (zero_zero int), (one_one int) ) 1.17/1.38 ( (zero_zero int), min ) 1.17/1.38 ( (zero_zero int), (number_number_of int (bit0 (bit1 pls))) ) 1.17/1.38 ( (zero_zero int), (number_number_of int (bit1 (bit1 pls))) ) 1.17/1.38 ( (zero_zero int), s ) 1.17/1.38 ( (zero_zero int), skv_1 ) 1.17/1.38 ( (zero_zero int), skv_4 ) 1.17/1.38 ( (one_one int), t ) 1.17/1.38 ( min, min ) 1.17/1.38 ( min, pls ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((A_1 $$unsorted) (P_3 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) P_3))) (hBOOL (hAPP int bool (zcong (hAPP int int (times_times int A_1) (inv P_3 A_1)) (one_one int)) P_3))) ))) 1.17/1.38 ( (zero_zero int), (zero_zero int) ) 1.17/1.38 ( (zero_zero int), (one_one int) ) 1.17/1.38 ( (zero_zero int), min ) 1.17/1.38 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( min, min ) 1.17/1.38 ( min, pls ) 1.17/1.38 ( t, (zero_zero int) ) 1.17/1.38 ( t, (one_one int) ) 1.17/1.38 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (zero_zero int) ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)), (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)) ) 1.17/1.38 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28577 $$unsorted) (BOUND_VARIABLE_28578 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ring X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28578) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28577) _let_2)))) (or (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28578))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28577))))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28578) BOUND_VARIABLE_28577))))))) )) 1.17/1.38 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.38 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28614 $$unsorted) (BOUND_VARIABLE_28615 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28615))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_28615) BOUND_VARIABLE_28614)))) )) 1.17/1.38 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.17/1.38 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.17/1.38 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (linorder X_a)) (not (dvd X_a)) (not (plus X_a)) (= (plus_plus X_a (ti X_a B_1_1)) (plus_plus X_a B_1_1))) ) 1.17/1.38 ( min, int ) 1.17/1.38 ( pls, int ) 1.17/1.38 ( zprime, (fun int bool) ) 1.17/1.38 ( t, int ) 1.17/1.38 ( m, int ) 1.17/1.38 ( s1, int ) 1.17/1.38 ( s, int ) 1.17/1.38 ( fconj, (fun bool (fun bool bool)) ) 1.17/1.38 ( twoSqu658283162sum2sq, (fun int bool) ) 1.17/1.38 ) 1.17/1.38 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_28650))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28649 $$unsorted) (BOUND_VARIABLE_28650 $$unsorted) (BOUND_VARIABLE_28651 $$unsorted)) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28651))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28649))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28651) BOUND_VARIABLE_28649)))) )) 1.17/1.38 ( int, (one_one int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (times_times int Z_1) (one_one int))) ) 1.17/1.38 ( min ) 1.17/1.38 ( pls ) 1.17/1.38 ( t ) 1.17/1.38 ( (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.38 ( m ) 1.17/1.38 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.38 ( s1 ) 1.17/1.38 ( s ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (zcong (ti int B_1_1) B_2_1) (zcong B_1_1 B_2_1)) ) 1.17/1.38 ( s1, s ) 1.17/1.38 ( s1, skv_1 ) 1.17/1.38 ( s1, skv_4 ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28761 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a (one_one X_a)) BOUND_VARIABLE_28761) (ti X_a BOUND_VARIABLE_28761))) ) 1.17/1.38 ( int, min ) 1.17/1.38 ( int, pls ) 1.17/1.38 ( int, t ) 1.17/1.38 ( int, m ) 1.17/1.38 ( int, s1 ) 1.17/1.38 ( int, s ) 1.17/1.38 ( (fun int bool), zprime ) 1.17/1.38 ( (fun int bool), twoSqu658283162sum2sq ) 1.17/1.38 ( (fun bool (fun bool bool)), fconj ) 1.17/1.38 ) 1.17/1.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28784 $$unsorted) (BOUND_VARIABLE_28785 $$unsorted) (BOUND_VARIABLE_28786 $$unsorted)) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_28784) (ti X_a BOUND_VARIABLE_28786)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28784) BOUND_VARIABLE_28785) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28786) BOUND_VARIABLE_28785)))) ) 1.17/1.39 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int), s ) 1.17/1.39 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int), t ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28806 $$unsorted) (BOUND_VARIABLE_28807 $$unsorted)) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (div_mod X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28806) BOUND_VARIABLE_28807)) BOUND_VARIABLE_28807) (hAPP X_a X_a (div_mod X_a BOUND_VARIABLE_28806) BOUND_VARIABLE_28807))) ) 1.17/1.39 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.17/1.39 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.17/1.39 ( nat, (one_one nat), (one_one nat) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((B_1_1 $$unsorted)) (= (d22set B_1_1) (d22set (ti int B_1_1))) ) 1.17/1.39 ( min ) 1.17/1.39 ( pls ) 1.17/1.39 ( t ) 1.17/1.39 ( m ) 1.17/1.39 ( s1 ) 1.17/1.39 ( s ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (times_times X_a B_1_1))) (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (no_zero_divisors X_a)) (= _let_0 (ti (fun X_a X_a) _let_0))) )) 1.17/1.39 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), int ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), int ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28856 $$unsorted) (BOUND_VARIABLE_28857 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28857))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (power_power X_a BOUND_VARIABLE_28857) BOUND_VARIABLE_28856)))) )) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28905 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28905) (number_number_of X_a (bit0 (bit1 pls)))) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28905) BOUND_VARIABLE_28905))) ) 1.17/1.39 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.39 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( nat, (one_one nat) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28923 $$unsorted) (BOUND_VARIABLE_28924 $$unsorted)) (or (not (semiri456707255roduct X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_28924)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_28923) BOUND_VARIABLE_28924) (ti X_a BOUND_VARIABLE_28923)))) ) 1.17/1.39 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.17/1.39 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.17/1.39 ( nat, (one_one nat), (one_one nat) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_28952 $$unsorted) (BOUND_VARIABLE_28953 $$unsorted)) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28953))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_28952))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_28953) BOUND_VARIABLE_28952)))) )) 1.17/1.39 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.39 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (forall ((M $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) X_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) M))) (not (hBOOL (hAPP int bool (zcong X_1 _let_2) M)))) )))) 1.17/1.39 ( (zero_zero int), (zero_zero int) ) 1.17/1.39 ( (zero_zero int), t ) 1.17/1.39 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.39 ( (one_one int), (zero_zero int) ) 1.17/1.39 ( (one_one int), t ) 1.17/1.39 ( min, (zero_zero int) ) 1.17/1.39 ( min, min ) 1.17/1.39 ( pls, min ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.17/1.39 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (number_number_of nat V_1))) (forall ((V_1 $$unsorted) (V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_0 (hAPP nat nat (plus_plus nat (number_number_of nat V)) _let_0))) )) 1.17/1.39 ( (bit1 pls), (bit1 pls) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (hAPP nat nat (plus_plus nat (number_number_of nat V)) (number_number_of nat V_1)))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)))) (forall ((V_1 $$unsorted) (V $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (and (or (not _let_1) (= (number_number_of nat V) _let_0)) (or _let_1 (= _let_0 (number_number_of nat (hAPP int int (plus_plus int V) V_1)))))) ))) 1.17/1.39 ( (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( (bit1 pls), (bit1 pls) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (hAPP int int (plus_plus int A_1) B))) (forall ((B $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_2) _let_1))) (= _let_2 (hAPP int int (div_mod int A_1) B))) )))) 1.17/1.39 ( (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (semiring_div X_a)) (= (div_mod X_a B_1_1) (div_mod X_a (ti X_a B_1_1)))) ) 1.17/1.39 ( min, int ) 1.17/1.39 ( pls, int ) 1.17/1.39 ( zprime, (fun int bool) ) 1.17/1.39 ( t, int ) 1.17/1.39 ( m, int ) 1.17/1.39 ( s1, int ) 1.17/1.39 ( s, int ) 1.17/1.39 ( fconj, (fun bool (fun bool bool)) ) 1.17/1.39 ( twoSqu658283162sum2sq, (fun int bool) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29147 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_29147) (one_one X_a)) (ti X_a BOUND_VARIABLE_29147))) ) 1.17/1.39 ( int, min ) 1.17/1.39 ( int, pls ) 1.17/1.39 ( int, t ) 1.17/1.39 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.39 ( int, m ) 1.17/1.39 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ( int, s1 ) 1.17/1.39 ( int, s ) 1.17/1.39 ( (fun int bool), zprime ) 1.17/1.39 ( (fun int bool), twoSqu658283162sum2sq ) 1.17/1.39 ( (fun bool (fun bool bool)), fconj ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool _let_2 A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) M))) (not (hBOOL (hAPP int bool _let_2 B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) A_1))) (not (hBOOL (hAPP int bool (zcong A_1 B) M)))) )))) 1.17/1.39 ( s, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.17/1.39 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( (number_number_of int min), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int skv_2) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( (hAPP nat int (power_power int s1) (number_number_of nat (bit0 (bit1 pls)))), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( skv_1, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.17/1.39 ( skv_4, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s1 ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((B_1_1 $$unsorted) (X_a $$unsorted)) (or (not (monoid_add X_a)) (= (plus_plus X_a B_1_1) (plus_plus X_a (ti X_a B_1_1)))) ) 1.17/1.39 ( min, int ) 1.17/1.39 ( pls, int ) 1.17/1.39 ( zprime, (fun int bool) ) 1.17/1.39 ( t, int ) 1.17/1.39 ( m, int ) 1.17/1.39 ( s1, int ) 1.17/1.39 ( s, int ) 1.17/1.39 ( fconj, (fun bool (fun bool bool)) ) 1.17/1.39 ( twoSqu658283162sum2sq, (fun int bool) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29342 $$unsorted) (BOUND_VARIABLE_29343 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_29342) BOUND_VARIABLE_29343) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_29343) BOUND_VARIABLE_29342))) ) 1.17/1.39 ( int, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( int, (one_one int), (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.39 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.17/1.39 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.17/1.39 ( nat, (one_one nat), (one_one nat) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((K_1 $$unsorted)) (= (number_number_of int K_1) (ti int K_1)) ) 1.17/1.39 ( min ) 1.17/1.39 ( pls ) 1.17/1.39 ( (bit1 pls) ) 1.17/1.39 ( (bit0 (bit1 pls)) ) 1.17/1.39 ( t ) 1.17/1.39 ( (bit0 (bit0 (bit1 pls))) ) 1.17/1.39 ( m ) 1.17/1.39 ( s1 ) 1.17/1.39 ( (bit1 (bit1 pls)) ) 1.17/1.39 ( s ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (power_power X_a BOUND_VARIABLE_29380))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29378 $$unsorted) (BOUND_VARIABLE_29379 $$unsorted) (BOUND_VARIABLE_29380 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_29380))) (= (= (hAPP nat X_a _let_0 BOUND_VARIABLE_29379) (hAPP nat X_a _let_0 BOUND_VARIABLE_29378)) (= BOUND_VARIABLE_29378 BOUND_VARIABLE_29379))) )) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), (number_number_of nat (bit0 (bit1 pls))), s ) 1.17/1.39 ( int, (number_number_of nat (bit0 (bit1 pls))), (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_29414))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29412 $$unsorted) (BOUND_VARIABLE_29413 $$unsorted) (BOUND_VARIABLE_29414 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29414) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29413) BOUND_VARIABLE_29412)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_29412)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_29413))))) )))) 1.17/1.39 ( int, skv_3, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (hAPP int (fun int bool) (ord_less int) W_1))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (or (= (ti int W_1) (ti int Z_2)) (hBOOL (hAPP int bool _let_0 Z_2))) (hBOOL (hAPP int bool _let_0 (hAPP int int (plus_plus int Z_2) (one_one int))))) )) 1.17/1.39 ( (zero_zero int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( t, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( s, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( skv_1, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ( skv_4, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (forall ((N_1 $$unsorted) (M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N_1) M)))) ))) 1.17/1.39 ( (zero_zero int), (zero_zero int) ) 1.17/1.39 ( (zero_zero int), t ) 1.17/1.39 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.39 ( (one_one int), (zero_zero int) ) 1.17/1.39 ( (one_one int), t ) 1.17/1.39 ( min, (zero_zero int) ) 1.17/1.39 ( min, min ) 1.17/1.39 ( pls, min ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int) ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), t ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), s ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_1 ) 1.17/1.39 ( (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_4 ) 1.17/1.39 ( (hAPP int int (times_times int (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int))) (zero_zero int)), (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29505 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_29505) (zero_zero X_a)))) ) 1.17/1.39 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29516 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_29516) BOUND_VARIABLE_29516))) ) 1.17/1.39 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (number_number_of nat (bit0 (bit1 pls))))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29541 $$unsorted) (BOUND_VARIABLE_29542 $$unsorted)) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (power_power X_a BOUND_VARIABLE_29542) _let_0) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_29541) _let_0))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_29541))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_29542))) (= (ti X_a BOUND_VARIABLE_29541) (ti X_a BOUND_VARIABLE_29542))) ))) 1.17/1.39 ( int, s1, s ) 1.17/1.39 ( int, s, s1 ) 1.17/1.39 ( int, s, s ) 1.17/1.39 ( int, skv_2, skv_2 ) 1.17/1.39 ) 1.17/1.39 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (hAPP int int (plus_plus int (hAPP int int (times_times int B_3) Q_4)) R_3))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (or (not (= (hAPP int int (plus_plus int (hAPP int int (times_times int B) Q_1)) R_1) _let_4)) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_4) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 R_1) B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_2) R_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 B_3) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Q_4) Q_1))) )))))) 1.17/1.39 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int), (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29622 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_29622) (number_number_of X_a (bit0 (bit1 pls)))) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_29622) BOUND_VARIABLE_29622))) ) 1.17/1.40 ( int, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.40 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.40 ( nat, (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_29698))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29698 $$unsorted) (BOUND_VARIABLE_29699 $$unsorted) (BOUND_VARIABLE_29700 $$unsorted)) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29699) BOUND_VARIABLE_29700))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29698) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_29700)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_29699)))) )))) 1.17/1.40 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), (zero_zero int), skv_3 ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (minus_minus int min))) (forall ((L_1 $$unsorted)) (= (bit1 (hAPP int int _let_0 L_1)) (hAPP int int _let_0 (bit0 L_1))) )) 1.17/1.40 ( pls ) 1.17/1.40 ( (bit1 pls) ) 1.17/1.40 ( (bit0 (bit1 pls)) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29730 $$unsorted) (BOUND_VARIABLE_29731 $$unsorted)) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (div_mod X_a (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_29730) BOUND_VARIABLE_29731)) BOUND_VARIABLE_29730) (hAPP X_a X_a (div_mod X_a BOUND_VARIABLE_29731) BOUND_VARIABLE_29730))) ) 1.17/1.40 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m), (one_one int) ) 1.17/1.40 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))), (one_one int) ) 1.17/1.40 ( nat, (one_one nat), (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (one_one X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29749 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (times_times X_a (hAPP X_a X_a (plus_plus X_a _let_0) _let_0)) (number_number_of X_a BOUND_VARIABLE_29749)) (number_number_of X_a (bit0 BOUND_VARIABLE_29749)))) )) 1.17/1.40 ( int, pls ) 1.17/1.40 ( int, (bit1 pls) ) 1.17/1.40 ( int, (bit0 (bit1 pls)) ) 1.17/1.40 ( nat, pls ) 1.17/1.40 ( nat, (bit1 pls) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (hAPP int _let_0 _let_3 _let_2))) (let ((_let_5 (hAPP int int (plus_plus int (hAPP int int (times_times int B_3) Q_4)) R_3))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_1 $$unsorted) (B_3 $$unsorted) (Q_4 $$unsorted) (R_3 $$unsorted)) (or (not (= _let_5 (hAPP int int (plus_plus int (hAPP int int (times_times int B) Q_1)) R_1))) (not (hBOOL (hAPP int bool _let_4 _let_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 R_3) B_3))) (not (hBOOL (hAPP int bool _let_4 R_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 B_3) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Q_1) Q_4))) ))))))) 1.17/1.40 ( (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int), (number_number_of int (bit0 (bit0 (bit1 pls)))), m, (one_one int) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29843 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_29843) (hAPP X_a X_a (times_times X_a (one_one X_a)) BOUND_VARIABLE_29843))) ) 1.17/1.40 ( int, min ) 1.17/1.40 ( int, pls ) 1.17/1.40 ( int, t ) 1.17/1.40 ( int, m ) 1.17/1.40 ( int, s1 ) 1.17/1.40 ( int, s ) 1.17/1.40 ( (fun int bool), zprime ) 1.17/1.40 ( (fun int bool), twoSqu658283162sum2sq ) 1.17/1.40 ( (fun bool (fun bool bool)), fconj ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29860 $$unsorted) (BOUND_VARIABLE_29861 $$unsorted)) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29861) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29860) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_29861) BOUND_VARIABLE_29860)))) )))) 1.17/1.40 ( int, (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ( int, t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ( int, m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.40 ( int, skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((M $$unsorted)) (= M (hAPP nat nat (plus_plus nat M) (zero_zero nat))) ) 1.17/1.40 ( (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_29925 $$unsorted) (BOUND_VARIABLE_29926 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_29926))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (times_times X_a BOUND_VARIABLE_29926) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_29926) BOUND_VARIABLE_29925))))) )) 1.17/1.40 ( int, (number_number_of nat (bit0 (bit1 pls))), s1 ) 1.17/1.40 ( int, (number_number_of nat (bit0 (bit1 pls))), s ) 1.17/1.40 ( int, (number_number_of nat (bit0 (bit1 pls))), skv_2 ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_30018 $$unsorted) (BOUND_VARIABLE_30019 $$unsorted) (BOUND_VARIABLE_30020 $$unsorted)) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_30020))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_30018) BOUND_VARIABLE_30019))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30018) (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_30020) BOUND_VARIABLE_30019)))) ))) 1.17/1.40 ( int, (zero_zero int), (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, t, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, s, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, skv_1, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, skv_4, (one_one int), (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_30047 $$unsorted)) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_30047)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_30047) BOUND_VARIABLE_30047))))) )) 1.17/1.40 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.40 ( nat, (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30096 $$unsorted) (BOUND_VARIABLE_30097 $$unsorted)) (or (not (comm_semiring_1 X_a)) (and (not (= (one_one X_a) (ti X_a BOUND_VARIABLE_30096))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_30097)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_30096) (hAPP nat X_a (power_power X_a BOUND_VARIABLE_30096) BOUND_VARIABLE_30097)))) ) 1.17/1.40 ( int, s1, (number_number_of nat (bit0 (bit1 pls))) ) 1.17/1.40 ( int, s, (number_number_of nat (bit0 (bit1 pls))) ) 1.17/1.40 ( int, skv_2, (number_number_of nat (bit0 (bit1 pls))) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (power_power int X_1))) (forall ((X_1 $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (= (hAPP nat int _let_0 (hAPP nat nat (plus_plus nat Y) Z_1)) (hAPP int int (times_times int (hAPP nat int _let_0 Y)) (hAPP nat int _let_0 Z_1))) )) 1.17/1.40 ( s1, (one_one nat), (one_one nat) ) 1.17/1.40 ( s, (one_one nat), (one_one nat) ) 1.17/1.40 ( skv_2, (one_one nat), (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((Y $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool twoSqu658283162sum2sq X_1))) (not (hBOOL (hAPP int bool twoSqu658283162sum2sq Y))) (hBOOL (hAPP int bool twoSqu658283162sum2sq (hAPP int int (times_times int X_1) Y)))) ) 1.17/1.40 ( (zero_zero int), (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ( t, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ( m, (number_number_of int (bit0 (bit0 (bit1 pls)))) ) 1.17/1.40 ( skv_3, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_30133 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_30133) BOUND_VARIABLE_30133)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30133) _let_2)))) )))) 1.17/1.40 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.40 ( nat, (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (times_times X_a BOUND_VARIABLE_30156))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_30156 $$unsorted) (BOUND_VARIABLE_30157 $$unsorted) (BOUND_VARIABLE_30158 $$unsorted)) (or (not (linordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_30157)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_30158)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_30156))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30157) BOUND_VARIABLE_30158))) )))) 1.17/1.40 ( int, (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)), skv_3, (zero_zero int) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (= M (hAPP nat nat (minus_minus nat (hAPP nat nat (plus_plus nat M) N_1)) N_1)) ) 1.17/1.40 ( (one_one nat), (one_one nat) ) 1.17/1.40 ) 1.17/1.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30263 $$unsorted)) (or (not (monoid_add X_a)) (= (hAPP X_a X_a (plus_plus X_a BOUND_VARIABLE_30263) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_30263))) ) 1.17/1.40 ( int, min ) 1.17/1.40 ( int, pls ) 1.17/1.40 ( int, t ) 1.17/1.40 ( int, m ) 1.17/1.40 ( int, (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m) ) 1.17/1.40 ( int, s1 ) 1.17/1.40 ( int, s ) 1.17/1.40 ( int, (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls)))) ) 1.17/1.40 ( (fun int bool), zprime ) 1.17/1.40 ( (fun int bool), twoSqu658283162sum2sq ) 1.17/1.40 ( nat, (one_one nat) ) 1.17/1.40 ( (fun bool (fun bool bool)), fconj ) 1.17/1.40 ) 1.17/1.40 (instantiation (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (plus_plus int (hAPP int int (times_times int (number_number_of int (bit0 (bit0 (bit1 pls))))) m)) (one_one int)))) (forall ((Y_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Y_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Y_2) _let_1))) (not (hBOOL (hAPP int bool (zcong s1 Y_2) _let_1))) (= (ti int Y_2) (ti int skv_4))) ))) 1.17/1.40 ( (zero_zero int) ) 1.17/1.40 ( (one_one int) ) 1.17/1.40 ( min ) 1.17/1.40 ( pls ) 1.17/1.40 ( (number_number_of int (bit0 (bit1 pls))) ) 1.17/1.40 ( t ) 1.17/1.40 ( m ) 1.17/1.40 ( s1 ) 1.17/1.40 ( (number_number_of int (bit1 (bit1 pls))) ) 1.17/1.40 ( s ) 1.17/1.40 ( (hAPP int int (plus_plus int (hAPP nat int (power_power int s) (number_number_of nat (bit0 (bit1 pls))))) (one_one int)) ) 1.17/1.40 ( skv_1 ) 1.17/1.40 ( skv_4 ) 1.17/1.40 ) 1.17/1.40 % SZS output end Proof for theBenchmark 1.17/1.41 EOF