0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : do_CVC4 %s %d 0.13/0.34 % Computer : n014.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Thu Jul 2 08:30:10 EDT 2020 0.13/0.35 % CPUTime : 0.48/0.63 %----Proving TF0_NAR, FOF, or CNF 0.49/0.64 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.49/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 20.54/20.78 --- Run --no-e-matching --full-saturate-quant at 20... 40.58/40.85 --- Run --finite-model-find --uf-ss=no-minimal at 15... 55.67/55.89 --- Run --multi-trigger-when-single --full-saturate-quant at 5... 57.54/57.75 % SZS status Theorem for theBenchmark 57.54/57.75 % SZS output start Proof for theBenchmark 57.54/57.75 (skolem (forall ((Pa $$unsorted)) (hBOOL Pa) ) 57.54/57.75 ( skv_1 ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) C_1) (bot_bot _let_0))))) ) 57.54/57.75 ( pname, pn ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc N))) ) 57.54/57.75 ( (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K_1 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) K_1)) (zero_zero int)))) ) 57.54/57.75 ( (one_one nat) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_0 X_1)) (hAPP nat int _let_0 Y_2))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) X_1) Y_2)))) ) 57.54/57.75 ( (one_one nat), (one_one nat) ) 57.54/57.75 ( (one_one nat), (zero_zero nat) ) 57.54/57.75 ( (zero_zero nat), (one_one nat) ) 57.54/57.75 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.75 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) B_1)))) ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (image X_b X_c))) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_b bool) (fun X_c bool))) _let_0))) ) 57.54/57.75 ( bool, bool ) 57.54/57.75 ( nat, nat ) 57.54/57.75 ( nat, int ) 57.54/57.75 ( com, com ) 57.54/57.75 ( pname, int ) 57.54/57.75 ( pname, x_a ) 57.54/57.75 ( (fun pname bool), (fun pname bool) ) 57.54/57.75 ( int, x_a ) 57.54/57.75 ( x_a, pname ) 57.54/57.75 ( x_a, x_a ) 57.54/57.75 ( x_a, (fun x_a bool) ) 57.54/57.75 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M)) Na)))) ) 57.54/57.75 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N) M_1))))) ) 57.54/57.75 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit1 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))))) ) 57.54/57.75 ( (zero_zero int), (zero_zero int) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W) W)) ) 57.54/57.75 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) (hAPP nat nat suc Na))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) Na)))) ) 57.54/57.75 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) N)) (hAPP nat nat suc M_1))) ) 57.54/57.75 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) N)) ) 57.54/57.75 ( (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (finite_fold_image X_b X_c))) (= _let_0 (ti (fun (fun X_b (fun X_b X_b)) (fun (fun X_c X_b) (fun X_b (fun (fun X_c bool) X_b)))) _let_0))) ) 57.54/57.75 ( bool, pname ) 57.54/57.75 ( bool, x_a ) 57.54/57.75 ( bool, (fun x_a bool) ) 57.54/57.75 ( nat, pname ) 57.54/57.75 ( int, x_a ) 57.54/57.75 ( (fun x_a bool), pname ) 57.54/57.75 ( (fun x_a bool), int ) 57.54/57.75 ( (fun x_a bool), x_a ) 57.54/57.75 ( (fun int bool), nat ) 57.54/57.75 ( (fun (fun x_a bool) bool), x_a ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (collect X_b))) (= _let_1 (ti (fun _let_0 _let_0) _let_1)))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( com ) 57.54/57.75 ( pname ) 57.54/57.75 ( (fun pname bool) ) 57.54/57.75 ( int ) 57.54/57.75 ( x_a ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) A_3))) ) 57.54/57.75 ( x_a, g ) 57.54/57.75 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N)) N))) ) 57.54/57.75 ( (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_2) (one_one int)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) Z_2)))) ) 57.54/57.75 ( (zero_zero int), (one_one int) ) 57.54/57.75 ( (zero_zero int), (zero_zero int) ) 57.54/57.75 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K_1 $$unsorted)) (= K_1 (hAPP int int (number_number_of int) K_1)) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.75 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B_1) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) B_1)))) ) 57.54/57.75 ( x_a, g, (hAPP pname x_a mgt_call pn) ) 57.54/57.75 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (hAPP pname x_a mgt_call pn) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (semiring_1_of_nat int))) (let ((_let_2 (fun int bool))) (= (hBOOL (hAPP _let_2 bool (hAPP int (fun _let_2 bool) (member int) (hAPP nat int _let_1 X_1)) (hAPP _let_0 _let_2 (hAPP (fun nat int) (fun _let_0 _let_2) (image nat int) _let_1) A_3))) (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X_1) A_3)))))) ) 57.54/57.75 ( (one_one nat), (bot_bot (fun nat bool)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_finite X_b))) (= (hBOOL (hAPP _let_0 bool _let_1 A_3)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_3)))))) ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) (hAPP nat nat suc Na))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) Na))))) ) 57.54/57.75 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na, na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (hBOOL (hAPP (fun X_b (fun _let_0 _let_0)) bool (finite_comp_fun_idem X_b _let_0) (insert X_b)))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( com ) 57.54/57.75 ( pname ) 57.54/57.75 ( (fun pname bool) ) 57.54/57.75 ( int ) 57.54/57.75 ( x_a ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (if X_a))) (= _let_0 (ti (fun bool (fun X_a (fun X_a X_a))) _let_0))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( int ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc Na)) (hAPP nat nat suc M))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Na) M))))) ) 57.54/57.75 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na, na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (bot_bot _let_0))) (= (hBOOL (hAPP X_b bool _let_1 X_2)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) _let_1))))) ) 57.54/57.75 ( pname, pn ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) (hAPP int int (hAPP int (fun int int) (minus_minus int) Z_2) (one_one int)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z_2)))) ) 57.54/57.75 ( (zero_zero int), (one_one int) ) 57.54/57.75 ( (zero_zero int), (zero_zero int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Z_2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (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)))) ) 57.54/57.75 ( (one_one int) ) 57.54/57.75 ( (zero_zero int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted)) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) M_1)) ) 57.54/57.75 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int _let_0 M)) (hAPP nat int _let_0 Na))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) Na)))) ) 57.54/57.75 ( (one_one nat), (one_one nat) ) 57.54/57.75 ( (zero_zero nat), (one_one nat) ) 57.54/57.75 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (= (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) Na))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc Na)) M))))) ) 57.54/57.75 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 57.54/57.75 ( (hAPP nat nat suc na), (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Na $$unsorted)) (= (= (zero_zero nat) Na) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int (semiring_1_of_nat int) Na)) (zero_zero int)))) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hBOOL (hAPP X_b bool A_3 X_1)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3)))) ) 57.54/57.75 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 57.54/57.75 ( pname, pn, u ) 57.54/57.75 ( (fun pname bool), u, (finite_finite pname) ) 57.54/57.75 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 57.54/57.75 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 57.54/57.75 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 57.54/57.75 ( int, (one_one int), nat_neg ) 57.54/57.75 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 57.54/57.75 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 57.54/57.75 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ( int, (hAPP int int (number_number_of int) (zero_zero int)), nat_neg ) 57.54/57.75 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.75 ( (fun x_a bool), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 57.54/57.75 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 57.54/57.75 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (hBOOL (hAPP _let_0 bool (finite_finite X_b) (bot_bot _let_0)))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( com ) 57.54/57.75 ( pname ) 57.54/57.75 ( (fun pname bool) ) 57.54/57.75 ( int ) 57.54/57.75 ( x_a ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (finite_comp_fun_idem X_b X_c))) (= _let_0 (ti (fun (fun X_b (fun X_c X_c)) bool) _let_0))) ) 57.54/57.75 ( bool, bool ) 57.54/57.75 ( int, int ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit1 K2)))))) ) 57.54/57.75 ( (zero_zero int), (zero_zero int) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) Na))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) ) 57.54/57.75 ( (one_one nat) ) 57.54/57.75 ( (zero_zero nat) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M_1) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M_1) M_1))) ) 57.54/57.75 ( (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (combs X_a X_b X_c))) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun (fun X_a X_b) (fun X_a X_c))) _let_0))) ) 57.54/57.75 ( x_a, bool, bool ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (times_times nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M_1) (hAPP nat nat _let_2 (hAPP nat nat _let_2 M_1))))))) ) 57.54/57.75 ( (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (the X_b))) (= _let_0 (ti (fun (fun X_b bool) X_b) _let_0))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( com ) 57.54/57.75 ( pname ) 57.54/57.75 ( (fun pname bool) ) 57.54/57.75 ( int ) 57.54/57.75 ( x_a ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (= (hBOOL (hAPP _let_0 bool (finite_finite nat) A_3)) (hBOOL (hAPP _let_1 bool (finite_finite int) (hAPP _let_0 _let_1 (hAPP (fun nat int) (fun _let_0 _let_1) (image nat int) (semiring_1_of_nat int)) A_3)))))) ) 57.54/57.75 ( (bot_bot (fun nat bool)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (number_number_of int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)))))) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.75 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (fun X_b _let_1))) (let ((_let_3 (fun X_b _let_0))) (let ((_let_4 (fun _let_0 _let_1))) (hBOOL (hAPP _let_2 bool (finite_comp_fun_idem X_b _let_0) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (combb _let_0 _let_1 X_b) (hAPP _let_4 _let_4 (combc _let_0 _let_0 _let_0) (minus_minus _let_0))) (hAPP _let_0 _let_3 (hAPP _let_2 (fun _let_0 _let_3) (combc X_b _let_0 _let_0) (insert X_b)) (bot_bot _let_0)))))))))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( com ) 57.54/57.75 ( pname ) 57.54/57.75 ( (fun pname bool) ) 57.54/57.75 ( int ) 57.54/57.75 ( x_a ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) Na)) (hBOOL (hAPP nat bool (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (nat_case bool) fFalse) (hAPP nat _let_0 _let_1 M)) Na))))) ) 57.54/57.75 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (= (and (not (= Z_2 W_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_2) W_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Z_2) W_1)))) ) 57.54/57.75 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((W_1 $$unsorted)) (let ((_let_0 (number_number_of int))) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit1 W_1)))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 W_1))))) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Z_1 $$unsorted)) (= (hBOOL (hAPP int bool nat_neg Z_1)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Z_1) (zero_zero int)))) ) 57.54/57.75 ( (one_one int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP int bool nat_neg (hAPP nat int (semiring_1_of_nat int) N)))) ) 57.54/57.75 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (semiring_1_of_nat int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (fun nat int))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (image nat int))) (let ((_let_6 (hAPP _let_3 _let_4 _let_5 _let_1))) (= (hBOOL (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_0 _let_2 _let_6 A_3)) (hAPP _let_0 _let_2 _let_6 B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1)))))))))) ) 57.54/57.75 ( (bot_bot (fun nat bool)), (bot_bot (fun nat bool)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun nat X_b))) (let ((_let_1 (nat_case X_b))) (= _let_1 (ti (fun X_b (fun _let_0 _let_0)) _let_1)))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( int ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) N)) M_1)) ) 57.54/57.75 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_0 (combb X_b X_c X_a))) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_a X_b) (fun X_a X_c))) _let_0))) ) 57.54/57.75 ( bool, bool, x_a ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (= (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_3) B_1)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (member X_b) X_1) B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) A_3)) B_1)))))) ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn), g, g ) 57.54/57.75 ( x_a, (hAPP pname x_a mgt_call pn), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (not (= N (hAPP nat nat suc N))) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) M)))))) ) 57.54/57.75 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z) W)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z))))) ) 57.54/57.75 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (one_one int))) Z_2)))) ) 57.54/57.75 ( (zero_zero int), (one_one int) ) 57.54/57.75 ( (zero_zero int), (zero_zero int) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (semiring_1_of_nat int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (fun nat int))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (image nat int))) (let ((_let_6 (hAPP _let_3 _let_4 _let_5 _let_1))) (= (hBOOL (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less _let_2) (hAPP _let_0 _let_2 _let_6 A_3)) (hAPP _let_0 _let_2 _let_6 B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less _let_0) A_3) B_1)))))))))) ) 57.54/57.75 ( (bot_bot (fun nat bool)), (bot_bot (fun nat bool)) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (finite_folding_one X_b))) (= _let_0 (ti (fun (fun X_b (fun X_b X_b)) (fun (fun (fun X_b bool) X_b) bool)) _let_0))) ) 57.54/57.75 ( bool ) 57.54/57.75 ( nat ) 57.54/57.75 ( int ) 57.54/57.75 ( (fun x_a bool) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1)) (not (hBOOL (hAPP int bool nat_neg X_1)))) ) 57.54/57.75 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat suc N))) ) 57.54/57.75 ( (zero_zero nat) ) 57.54/57.75 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.75 ( na ) 57.54/57.75 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((B_1_1 $$unsorted)) (= (hBOOL (ti bool B_1_1)) (hBOOL B_1_1)) ) 57.54/57.75 ( fTrue ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (number_number_of int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))))))) ) 57.54/57.75 ( (hAPP int int bit1 (zero_zero int)), (zero_zero int) ) 57.54/57.75 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_20969 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (fun X_b _let_0))) (or (not (semiring_1 X_b)) (= (hAPP X_b X_b (hAPP nat _let_0 (hAPP _let_0 (fun nat _let_0) (semiri532925092at_aux X_b) (hAPP X_b _let_0 (hAPP _let_1 _let_1 (combc X_b X_b X_b) (plus_plus X_b)) (one_one X_b))) BOUND_VARIABLE_20969) (zero_zero X_b)) (hAPP nat X_b (semiring_1_of_nat X_b) BOUND_VARIABLE_20969))))) ) 57.54/57.75 ( int, (one_one nat) ) 57.54/57.75 ( int, (zero_zero nat) ) 57.54/57.75 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.75 ) 57.54/57.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_20987 $$unsorted) (BOUND_VARIABLE_20988 $$unsorted) (BOUND_VARIABLE_20989 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_20987))) (or (not (linord893533164strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_20988) BOUND_VARIABLE_20989))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_20987))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_20988)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_20989))))))))) ) 57.54/57.75 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.54/57.75 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21016 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_21016) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_21016) (zero_zero X_a)))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (ab_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((Pn $$unsorted)) (let ((_let_0 (option com))) (let ((_let_1 (fun pname bool))) (or (not (hBOOL (hAPP _let_1 bool (hAPP pname (fun _let_1 bool) (member pname) Pn) u))) (hBOOL (hAPP com bool wt (hAPP _let_0 com (the_1 com) (hAPP pname _let_0 body Pn))))))) ) 57.54/57.76 ( pn ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_21043 $$unsorted) (BOUND_VARIABLE_21044 $$unsorted) (BOUND_VARIABLE_21045 $$unsorted)) (or (not (order X_b)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (hAPP nat X_b BOUND_VARIABLE_21045 N_1)) (hAPP nat X_b BOUND_VARIABLE_21045 (hAPP nat nat suc N_1)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_21043) BOUND_VARIABLE_21044))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (hAPP nat X_b BOUND_VARIABLE_21045 BOUND_VARIABLE_21043)) (hAPP nat X_b BOUND_VARIABLE_21045 BOUND_VARIABLE_21044)))) ) 57.54/57.76 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M_1) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_1) (hAPP nat nat suc N))))) ) 57.54/57.76 ( (hAPP nat nat suc na), (zero_zero nat) ) 57.54/57.76 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (= (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) Z_2) (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) A_3))) (not (forall ((X_2 $$unsorted)) (or (not (= (hAPP X_c X_b F X_2) (ti X_b Z_2))) (not (hBOOL (hAPP _let_1 bool (hAPP X_c (fun _let_1 bool) (member X_c) X_2) A_3)))) ))))) ) 57.54/57.76 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, u ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted) (BOUND_VARIABLE_21198 $$unsorted)) (or (hBOOL (hAPP X_b bool Pa (hAPP (fun X_b bool) X_b (the X_b) Pa))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool Pa Y_1))) (= (ti X_b Y_1) (ti X_b BOUND_VARIABLE_21198))) )) (not (hBOOL (hAPP X_b bool Pa BOUND_VARIABLE_21198)))) ) 57.54/57.76 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( (fun pname bool), (finite_finite pname), u ) 57.54/57.76 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.54/57.76 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.54/57.76 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.54/57.76 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.54/57.76 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (forall ((X_2 $$unsorted)) (let ((_let_1 (member X_b))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (hAPP X_b _let_2 _let_1 X_2))) (or (not (hBOOL (hAPP _let_0 bool _let_3 A_3))) (hBOOL (hAPP _let_0 bool _let_3 B_1)))))) )) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1)))) ) 57.54/57.76 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (sum_sum X_b X_c))) (let ((_let_3 (fun _let_2 bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (finite_finite X_c) B_1))) (= (hAPP _let_3 nat (finite_card _let_2) (hAPP _let_0 _let_3 (hAPP _let_1 (fun _let_0 _let_3) (sum_Plus X_b X_c) A_3) B_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP _let_1 nat (finite_card X_b) A_3)) (hAPP _let_0 nat (finite_card X_c) B_1)))))))) ) 57.54/57.76 ( pname, pname, u, u ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (= X_1 Y_2) (= (hAPP nat int _let_0 Y_2) (hAPP nat int _let_0 X_1)))) ) 57.54/57.76 ( (one_one nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (one_one nat) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M_1) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) (hAPP nat nat suc N))))) ) 57.54/57.76 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.76 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.76 ( na, na ) 57.54/57.76 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun X_b _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun X_b _let_0))) (= (hAPP _let_0 _let_0 (hAPP X_b _let_3 (insert X_b) A_2) B_1) (hAPP _let_0 _let_0 (collect X_b) (hAPP _let_0 _let_0 (hAPP _let_2 _let_3 (combs X_b bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 X_b) fdisj) (hAPP X_b _let_0 (hAPP _let_4 _let_4 (combc X_b X_b bool) (fequal X_b)) A_2))) (hAPP _let_0 _let_0 (hAPP (fun X_b (fun _let_0 bool)) _let_3 (combc X_b _let_0 bool) (member X_b)) B_1))))))))) ) 57.54/57.76 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21465 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_21465))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_21465) (ti X_a BOUND_VARIABLE_21465))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (one_one int) ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a X_c))) (= (hAPP X_a X_c (hAPP X_b _let_1 (hAPP (fun X_a _let_0) (fun X_b _let_1) (combc X_a X_b X_c) P) Q) R) (hAPP X_b X_c (hAPP X_a _let_0 P R) Q)))) ) 57.54/57.76 ( nat, bool, nat, (ord_less_eq nat), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.76 ( nat, nat, nat, (minus_minus nat), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( pname, bool, (fun pname bool), (member pname), u, pn ) 57.54/57.76 ( int, bool, int, (ord_less_eq int), (one_one int), (zero_zero int) ) 57.54/57.76 ( int, bool, int, (ord_less_eq int), (zero_zero int), (zero_zero int) ) 57.54/57.76 ( int, bool, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.76 ( int, bool, int, (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.76 ( int, bool, int, (ord_less int), (one_one int), (zero_zero int) ) 57.54/57.76 ( int, bool, int, (ord_less int), (zero_zero int), (zero_zero int) ) 57.54/57.76 ( x_a, bool, (fun x_a bool), (member x_a), g, (hAPP pname x_a mgt_call pn) ) 57.54/57.76 ( x_a, (fun x_a bool), (fun x_a bool), (insert x_a), g, (hAPP pname x_a mgt_call pn) ) 57.54/57.76 ( (fun x_a bool), bool, (fun x_a bool), (ord_less_eq (fun x_a bool)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.76 ( (fun x_a bool), bool, (fun x_a bool), (ord_less_eq (fun x_a bool)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ( (fun nat int), (fun int bool), (fun nat bool), (image nat int), (bot_bot (fun nat bool)), (semiring_1_of_nat int) ) 57.54/57.76 ( (fun pname x_a), (fun x_a bool), (fun pname bool), (image pname x_a), u, mgt_call ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (let ((_let_4 (hAPP nat _let_2 _let_3 L_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat _let_4 N)) (hAPP nat nat _let_4 M_1))))))))) ) 57.54/57.76 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_21491 $$unsorted)) (let ((_let_0 (bot_bot X_b))) (or (not (bot X_b)) (= (= _let_0 (ti X_b BOUND_VARIABLE_21491)) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_21491) _let_0))))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( nat, (hAPP nat nat suc na) ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (K $$unsorted)) (or (not (= (hAPP (fun X_b bool) nat (finite_card X_b) A_3) (hAPP nat nat suc K))) (not (forall ((B_5 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (= (ti _let_0 A_3) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_5) B_4))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) B_5) B_4)) (and (= (zero_zero nat) K) (not (= (ti _let_0 B_4) (bot_bot _let_0)))) (not (= K (hAPP _let_0 nat (finite_card X_b) B_4))))) ))) ) 57.54/57.76 ( x_a, g, na ) 57.54/57.76 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (zero_zero nat) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21565 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_21565) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_21565))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21650 $$unsorted) (BOUND_VARIABLE_21651 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_21650) BOUND_VARIABLE_21651))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_21651) BOUND_VARIABLE_21650)))))) ) 57.54/57.76 ( int, (one_one int), (zero_zero int) ) 57.54/57.76 ( int, (zero_zero int), (one_one int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (monoid_mult X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (not (= (ti _let_0 A_3) (bot_bot _let_0))) (not (forall ((X_2 $$unsorted) (B_4 $$unsorted)) (or (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) B_4)) (not (= (ti _let_0 A_3) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) B_4)))) )))) ) 57.54/57.76 ( bool, fNot ) 57.54/57.76 ( com, wt ) 57.54/57.76 ( pname, u ) 57.54/57.76 ( int, nat_neg ) 57.54/57.76 ( x_a, g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_b _let_0))) (= (hAPP _let_0 X_b (the X_b) (hAPP X_b _let_0 (hAPP _let_1 _let_1 (combc X_b X_b bool) (fequal X_b)) A_2)) (ti X_b A_2)))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21744 $$unsorted) (BOUND_VARIABLE_21745 $$unsorted) (BOUND_VARIABLE_21746 $$unsorted) (BOUND_VARIABLE_21747 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_21746) BOUND_VARIABLE_21747))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_21744) BOUND_VARIABLE_21745))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_1) BOUND_VARIABLE_21747))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_21744))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_21746) BOUND_VARIABLE_21744)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_21747) BOUND_VARIABLE_21745))))))))) ) 57.54/57.76 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (collect X_b) (hAPP bool _let_0 (combk bool X_b) fFalse)) (bot_bot _let_0))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( com ) 57.54/57.76 ( pname ) 57.54/57.76 ( (fun pname bool) ) 57.54/57.76 ( int ) 57.54/57.76 ( x_a ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21843 $$unsorted) (BOUND_VARIABLE_21844 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_21843)) BOUND_VARIABLE_21844))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_21843) BOUND_VARIABLE_21844))))) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (no_zero_divisors X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((Nat_1 $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat suc Nat_1))) ) 57.54/57.76 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.76 ( na ) 57.54/57.76 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_21914 $$unsorted) (BOUND_VARIABLE_21915 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (linorder X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_21914) BOUND_VARIABLE_21915))) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_21914) BOUND_VARIABLE_21915))) (= (ti X_b BOUND_VARIABLE_21914) (ti X_b BOUND_VARIABLE_21915))))) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), na ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( int, (zero_zero int), (one_one int) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (hAPP int int bit1 K) (hAPP int int bit1 L)) (= K L)) ) 57.54/57.76 ( (zero_zero int), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.76 ( (hAPP int int bit1 (zero_zero int)), (zero_zero int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) F_1))) (not (hBOOL (hAPP _let_0 bool Pa (bot_bot _let_0)))) (not (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) F_3))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) F_3)) (not (hBOOL (hAPP _let_0 bool Pa F_3))) (hBOOL (hAPP _let_0 bool Pa (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) F_3)))) )) (hBOOL (hAPP _let_0 bool Pa F_1)))) ) 57.54/57.76 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( x_a, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21958 $$unsorted)) (or (not (preorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_21958) BOUND_VARIABLE_21958))) ) 57.54/57.76 ( nat, (hAPP nat nat suc na) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_21968 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (ordere142940540dd_abs X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) _let_0) (hAPP X_b X_b (abs_abs X_b) BOUND_VARIABLE_21968))) (not (= _let_0 (ti X_b BOUND_VARIABLE_21968)))))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((W $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W) Z))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) W) (one_one int))) Z)))) ) 57.54/57.76 ( (zero_zero int), (one_one int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) A_3))) (= (ti _let_0 A_3) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_3)))) ) 57.54/57.76 ( pname, pn, u ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((BOUND_VARIABLE_22074 $$unsorted) (BOUND_VARIABLE_22075 $$unsorted) (BOUND_VARIABLE_22076 $$unsorted)) (let ((_let_0 (fun BOUND_VARIABLE_22074 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_22075) (hAPP _let_0 _let_0 (hAPP BOUND_VARIABLE_22074 (fun _let_0 _let_0) (insert BOUND_VARIABLE_22074) BOUND_VARIABLE_22076) (bot_bot _let_0))))) (= (ti BOUND_VARIABLE_22074 BOUND_VARIABLE_22076) (hAPP _let_0 BOUND_VARIABLE_22074 (hAPP BOUND_VARIABLE_22074 (fun _let_0 BOUND_VARIABLE_22074) (partial_flat_lub BOUND_VARIABLE_22074) BOUND_VARIABLE_22076) BOUND_VARIABLE_22075)))) ) 57.54/57.76 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (hAPP pname x_a mgt_call pn) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((BOUND_VARIABLE_22098 $$unsorted) (BOUND_VARIABLE_22099 $$unsorted) (BOUND_VARIABLE_22100 $$unsorted)) (let ((_let_0 (fun BOUND_VARIABLE_22098 bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (insert BOUND_VARIABLE_22098))) (let ((_let_4 (hAPP BOUND_VARIABLE_22098 _let_2 _let_3 BOUND_VARIABLE_22100))) (let ((_let_5 (bot_bot _let_0))) (let ((_let_6 (hAPP _let_0 _let_0 _let_4 _let_5))) (or (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) BOUND_VARIABLE_22099) _let_6)) (= (hAPP _let_0 BOUND_VARIABLE_22098 (hAPP BOUND_VARIABLE_22098 (fun _let_0 BOUND_VARIABLE_22098) (partial_flat_lub BOUND_VARIABLE_22098) BOUND_VARIABLE_22100) BOUND_VARIABLE_22099) (hAPP _let_0 BOUND_VARIABLE_22098 (the BOUND_VARIABLE_22098) (hAPP _let_0 _let_0 (hAPP (fun BOUND_VARIABLE_22098 _let_1) _let_2 (combc BOUND_VARIABLE_22098 _let_0 bool) (member BOUND_VARIABLE_22098)) (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) BOUND_VARIABLE_22099) _let_6)))))))))))) ) 57.54/57.76 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (hAPP pname x_a mgt_call pn) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)) (hAPP nat nat suc N)) ) 57.54/57.76 ( (zero_zero nat) ) 57.54/57.76 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.76 ( na ) 57.54/57.76 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22255 $$unsorted) (BOUND_VARIABLE_22256 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_22256))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22255) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_22256) BOUND_VARIABLE_22255)) _let_2)))))) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_less X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( com ) 57.54/57.76 ( pname ) 57.54/57.76 ( (fun pname bool) ) 57.54/57.76 ( int ) 57.54/57.76 ( x_a ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_22281 $$unsorted) (BOUND_VARIABLE_22282 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (or (not (ordered_ab_group_add X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_22281) BOUND_VARIABLE_22282)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) BOUND_VARIABLE_22281) BOUND_VARIABLE_22282)) (zero_zero X_b))))))) ) 57.54/57.76 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( int, (zero_zero int), (one_one int) ) 57.54/57.76 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.76 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (not (= (ti _let_0 A_3) (bot_bot _let_0))) (not (forall ((X_2 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_3))) )))) ) 57.54/57.76 ( bool, fNot ) 57.54/57.76 ( com, wt ) 57.54/57.76 ( pname, u ) 57.54/57.76 ( int, nat_neg ) 57.54/57.76 ( x_a, g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22366 $$unsorted) (BOUND_VARIABLE_22367 $$unsorted) (BOUND_VARIABLE_22368 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_22366))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22367) BOUND_VARIABLE_22368))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_22366))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_22367)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_22368))))))))) ) 57.54/57.76 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.54/57.76 ( int, (zero_zero int), (zero_zero int), (zero_zero int) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22402 $$unsorted) (BOUND_VARIABLE_22403 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22402) BOUND_VARIABLE_22403))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22403) BOUND_VARIABLE_22402))) (= (ti X_a BOUND_VARIABLE_22402) (ti X_a BOUND_VARIABLE_22403))))) ) 57.54/57.76 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.76 ( (fun x_a bool), g, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_3) B_1))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP _let_0 nat _let_2 A_3)) (hAPP _let_0 nat _let_2 B_1)))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less _let_0) A_3) B_1)))))) ) 57.54/57.76 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22449 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_22449) (one_one X_a)) (ti X_a BOUND_VARIABLE_22449))) ) 57.54/57.76 ( bool, fFalse ) 57.54/57.76 ( bool, fTrue ) 57.54/57.76 ( nat, na ) 57.54/57.76 ( (fun (option com) com), (the_1 com) ) 57.54/57.76 ( pname, pn ) 57.54/57.76 ( (fun pname bool), u ) 57.54/57.76 ( int, (zero_zero int) ) 57.54/57.76 ( (fun int int), bit1 ) 57.54/57.76 ( (fun int int), succ ) 57.54/57.76 ( (fun nat nat), suc ) 57.54/57.76 ( (fun x_a bool), g ) 57.54/57.76 ( (fun int bool), nat_neg ) 57.54/57.76 ( (fun bool bool), fNot ) 57.54/57.76 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.76 ( (fun com x_a), mgt ) 57.54/57.76 ( (fun pname x_a), mgt_call ) 57.54/57.76 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.76 ( (fun pname (option com)), body ) 57.54/57.76 ( (fun com bool), wt ) 57.54/57.76 ( (fun int (fun int int)), nat_tsub ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_22470 $$unsorted) (BOUND_VARIABLE_22471 $$unsorted) (BOUND_VARIABLE_22472 $$unsorted)) (or (not (order X_b)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP nat X_b BOUND_VARIABLE_22472 N_1)) (hAPP nat X_b BOUND_VARIABLE_22472 (hAPP nat nat suc N_1)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_22470) BOUND_VARIABLE_22471))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP nat X_b BOUND_VARIABLE_22472 BOUND_VARIABLE_22470)) (hAPP nat X_b BOUND_VARIABLE_22472 BOUND_VARIABLE_22471)))) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))) ) 57.54/57.76 ( int, (one_one nat), (zero_zero nat), (semiring_1_of_nat int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22507 $$unsorted) (BOUND_VARIABLE_22508 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_22507) BOUND_VARIABLE_22508))) (= (ti X_a BOUND_VARIABLE_22508) (ti X_a BOUND_VARIABLE_22507)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_22507) BOUND_VARIABLE_22508)))) ) 57.54/57.76 ( nat, (hAPP nat nat suc na), na ) 57.54/57.76 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I) Na))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (abs_abs int) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int F (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I) (one_one nat)))) (hAPP nat int F I)))) (one_one int)))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP nat int F (zero_zero nat))) K))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) (hAPP nat int F Na)))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I) Na))) (not (= K (hAPP nat int F I)))) ))))) ) 57.54/57.76 ( (one_one int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (zero_zero int), (semiring_1_of_nat int), (one_one nat) ) 57.54/57.76 ( (zero_zero int), (semiring_1_of_nat int), (zero_zero nat) ) 57.54/57.76 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (semiring_1_of_nat int), (one_one nat) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (semiring X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun int bool))) (= (hAPP _let_0 nat (finite_card nat) A_3) (hAPP _let_1 nat (finite_card int) (hAPP _let_0 _let_1 (hAPP (fun nat int) (fun _let_0 _let_1) (image nat int) (semiring_1_of_nat int)) A_3))))) ) 57.54/57.76 ( (bot_bot (fun nat bool)) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_22670 $$unsorted) (BOUND_VARIABLE_22671 $$unsorted) (BOUND_VARIABLE_22672 $$unsorted)) (let ((_let_0 (fun X_b X_c))) (or (not (ord X_c)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_22671) BOUND_VARIABLE_22672))) (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) (hAPP X_b X_c BOUND_VARIABLE_22671 BOUND_VARIABLE_22670)) (hAPP X_b X_c BOUND_VARIABLE_22672 BOUND_VARIABLE_22670))))) ) 57.54/57.76 ( int, int, (zero_zero int), succ, (number_number_of int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (insert X_b))) (let ((_let_3 (bot_bot _let_0))) (or (not (= (hAPP _let_0 _let_0 (hAPP X_b _let_1 _let_2 A_2) _let_3) (hAPP _let_0 _let_0 (hAPP X_b _let_1 _let_2 B_3) _let_3))) (= (ti X_b B_3) (ti X_b A_2))))))) ) 57.54/57.76 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_c $$unsorted)) (let ((_let_0 (finite_card X_c))) (= _let_0 (ti (fun (fun X_c bool) nat) _let_0))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( com ) 57.54/57.76 ( pname ) 57.54/57.76 ( (fun pname bool) ) 57.54/57.76 ( int ) 57.54/57.76 ( x_a ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (finite_finite X_b))) (= _let_0 (ti (fun (fun X_b bool) bool) _let_0))) ) 57.54/57.76 ( pname ) 57.54/57.76 ( x_a ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (semiri532925092at_aux X_b))) (or (not (semiring_1 X_b)) (= _let_1 (ti (fun _let_0 (fun nat _let_0)) _let_1))))) ) 57.54/57.76 ( bool ) 57.54/57.76 ( nat ) 57.54/57.76 ( int ) 57.54/57.76 ( (fun x_a bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M_1))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M_1) N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) N))))) ) 57.54/57.76 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22842 $$unsorted) (BOUND_VARIABLE_22843 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_22842)) (hAPP nat X_a _let_0 BOUND_VARIABLE_22843)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_22842) BOUND_VARIABLE_22843)))) ) 57.54/57.76 ( int, (one_one nat), (one_one nat) ) 57.54/57.76 ( int, (zero_zero nat), (one_one nat) ) 57.54/57.76 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_22900 $$unsorted) (BOUND_VARIABLE_22901 $$unsorted)) (let ((_let_0 (fun X_b X_c))) (or (not (ord X_c)) (= (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_22900) BOUND_VARIABLE_22901)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) (hAPP X_b X_c BOUND_VARIABLE_22900 X_2)) (hAPP X_b X_c BOUND_VARIABLE_22901 X_2))) )))) ) 57.54/57.76 ( x_a, bool, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ( x_a, bool, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (bot T_1)) (bot (fun T_2 T_1))) ) 57.54/57.76 ( bool, bool ) 57.54/57.76 ( bool, (fun bool bool) ) 57.54/57.76 ( nat, bool ) 57.54/57.76 ( nat, nat ) 57.54/57.76 ( nat, int ) 57.54/57.76 ( (fun nat bool), (fun int bool) ) 57.54/57.76 ( com, bool ) 57.54/57.76 ( com, x_a ) 57.54/57.76 ( (option com), com ) 57.54/57.76 ( pname, bool ) 57.54/57.76 ( pname, (option com) ) 57.54/57.76 ( pname, x_a ) 57.54/57.76 ( (fun pname bool), bool ) 57.54/57.76 ( (fun pname bool), (fun x_a bool) ) 57.54/57.76 ( int, bool ) 57.54/57.76 ( int, int ) 57.54/57.76 ( int, (fun int int) ) 57.54/57.76 ( x_a, bool ) 57.54/57.76 ( (fun x_a bool), bool ) 57.54/57.76 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.76 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22929 $$unsorted) (BOUND_VARIABLE_22930 $$unsorted) (BOUND_VARIABLE_22931 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22930) BOUND_VARIABLE_22931))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22929) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_22931) BOUND_VARIABLE_22929)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_22930) BOUND_VARIABLE_22929)))))))) ) 57.54/57.76 ( int, (zero_zero int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((Na $$unsorted)) (= (= (zero_zero nat) Na) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) Na))) ) 57.54/57.76 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22968 $$unsorted) (BOUND_VARIABLE_22969 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (ti X_a BOUND_VARIABLE_22968) (ti X_a BOUND_VARIABLE_22969)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22968) BOUND_VARIABLE_22969)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22969) BOUND_VARIABLE_22968))))) ) 57.54/57.76 ( bool, fFalse, fTrue ) 57.54/57.76 ( bool, fTrue, fFalse ) 57.54/57.76 ( (fun int int), bit1, succ ) 57.54/57.76 ( (fun int int), succ, bit1 ) 57.54/57.76 ( (fun bool (fun bool bool)), fconj, fimplies ) 57.54/57.76 ( (fun bool (fun bool bool)), fimplies, fconj ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_22995 $$unsorted) (BOUND_VARIABLE_22996 $$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 (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_22996))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_22995) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_22995) BOUND_VARIABLE_22996)) _let_2)))))) ) 57.54/57.76 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) B_1) (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (image X_b X_c) F) A_3)))) (hBOOL (hAPP _let_1 bool (finite_finite X_c) B_1))))) ) 57.54/57.76 ( x_a, pname, g, mgt_call, u ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (= (bot_bot _let_1) (hAPP _let_0 _let_1 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F) (bot_bot _let_0))))) ) 57.54/57.76 ( pname, x_a, mgt_call ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23120 $$unsorted) (BOUND_VARIABLE_23121 $$unsorted) (BOUND_VARIABLE_23122 $$unsorted) (BOUND_VARIABLE_23123 $$unsorted) (BOUND_VARIABLE_23124 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP X_a _let_0 _let_2 _let_3))) (let ((_let_5 (fun X_a X_a))) (let ((_let_6 (plus_plus X_a))) (let ((_let_7 (times_times X_a))) (or (not (linord626643107strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23123) BOUND_VARIABLE_23124))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23122) BOUND_VARIABLE_23124))) (not (hBOOL (hAPP X_a bool _let_4 BOUND_VARIABLE_23121))) (not (hBOOL (hAPP X_a bool _let_4 BOUND_VARIABLE_23120))) (not (= (one_one X_a) (hAPP X_a X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_23121) BOUND_VARIABLE_23120))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_5 _let_6 (hAPP X_a X_a (hAPP X_a _let_5 _let_7 BOUND_VARIABLE_23121) BOUND_VARIABLE_23123)) (hAPP X_a X_a (hAPP X_a _let_5 _let_7 BOUND_VARIABLE_23120) BOUND_VARIABLE_23122))) BOUND_VARIABLE_23124))))))))))) ) 57.54/57.76 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (zero_zero int), (one_one int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP int int (hAPP int (fun int int) nat_tsub (hAPP nat int _let_0 X)) (hAPP nat int _let_0 Y)) (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) X) Y)))) ) 57.54/57.76 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_23180 $$unsorted) (BOUND_VARIABLE_23181 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (linorder X_b)) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_23180) BOUND_VARIABLE_23181))) (or (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_23181) BOUND_VARIABLE_23180)) (= (ti X_b BOUND_VARIABLE_23181) (ti X_b BOUND_VARIABLE_23180))))))) ) 57.54/57.76 ( int, (one_one int), (zero_zero int) ) 57.54/57.76 ( int, (zero_zero int), (one_one int) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) N) (hAPP nat nat (hAPP nat _let_0 _let_1 M_1) (hAPP nat nat suc N))))) ) 57.54/57.76 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.76 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.76 ( na, na ) 57.54/57.76 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (not (= (bot_bot _let_0) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_3)))) ) 57.54/57.76 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (= (ti _let_0 A_3) (ti _let_0 B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1)))) ) 57.54/57.76 ( bool, fNot, fNot ) 57.54/57.76 ( com, wt, wt ) 57.54/57.76 ( pname, u, u ) 57.54/57.76 ( int, nat_neg, nat_neg ) 57.54/57.76 ( x_a, g, g ) 57.54/57.76 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.76 ) 57.54/57.76 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (= (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B_1) (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) A_3))) (not (forall ((AA $$unsorted)) (or (not (= (ti _let_0 B_1) (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) AA))) (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) AA) A_3)))) ))))) ) 57.54/57.76 ( x_a, pname, g, mgt_call, u ) 57.54/57.77 ( x_a, pname, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), mgt_call, u ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23371 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_23371) BOUND_VARIABLE_23371))) ) 57.54/57.77 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$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)))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( com ) 57.54/57.77 ( pname ) 57.54/57.77 ( (fun pname bool) ) 57.54/57.77 ( x_a ) 57.54/57.77 ( (fun x_a bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((I_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_2) N))) (= I_2 (hAPP nat nat _let_2 (hAPP nat nat _let_2 I_2))))))) ) 57.54/57.77 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun X_b X_c))) (or (not (forall ((X_2 $$unsorted)) (= (hAPP X_b X_c G X_2) (hAPP X_b X_c F X_2)) )) (= (ti _let_0 F) (ti _let_0 G)))) ) 57.54/57.77 ( bool, (fun bool bool), fdisj, fimplies ) 57.54/57.77 ( bool, (fun bool bool), fconj, fdisj ) 57.54/57.77 ( bool, (fun bool bool), fconj, fimplies ) 57.54/57.77 ( bool, (fun bool bool), fimplies, fconj ) 57.54/57.77 ( int, int, bit1, succ ) 57.54/57.77 ( int, int, succ, bit1 ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23517 $$unsorted) (BOUND_VARIABLE_23518 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) BOUND_VARIABLE_23517) BOUND_VARIABLE_23518))) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_23517)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_23518))))))) ) 57.54/57.77 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (finite908156982e_idem X_b X_c))) (= _let_0 (ti (fun (fun X_b (fun X_b X_b)) (fun X_b (fun (fun X_c X_b) (fun (fun (fun X_c bool) X_b) bool)))) _let_0))) ) 57.54/57.77 ( bool, pname ) 57.54/57.77 ( bool, x_a ) 57.54/57.77 ( (fun x_a bool), pname ) 57.54/57.77 ( (fun x_a bool), x_a ) 57.54/57.77 ( (fun int bool), nat ) 57.54/57.77 ( (fun (fun x_a bool) bool), x_a ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3)) (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_b) A_3)))) ) 57.54/57.77 ( x_a, g ) 57.54/57.77 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (sum_sum X_b X_c))) (let ((_let_3 (fun _let_2 bool))) (= (and (= (bot_bot _let_0) (ti _let_0 B_1)) (= (bot_bot _let_1) (ti _let_1 A_3))) (= (bot_bot _let_3) (hAPP _let_0 _let_3 (hAPP _let_1 (fun _let_0 _let_3) (sum_Plus X_b X_c) A_3) B_1))))))) ) 57.54/57.77 ( bool, bool, fNot, fNot ) 57.54/57.77 ( com, com, wt, wt ) 57.54/57.77 ( pname, pname, u, u ) 57.54/57.77 ( int, int, nat_neg, nat_neg ) 57.54/57.77 ( x_a, x_a, g, g ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23563 $$unsorted)) (let ((_let_0 (bot_bot X_a))) (or (not (bot X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_23563) _let_0))) (= _let_0 (ti X_a BOUND_VARIABLE_23563)))) ) 57.54/57.77 ( bool, fFalse ) 57.54/57.77 ( bool, fTrue ) 57.54/57.77 ( nat, na ) 57.54/57.77 ( nat, (hAPP nat nat suc na) ) 57.54/57.77 ( (fun (option com) com), (the_1 com) ) 57.54/57.77 ( pname, pn ) 57.54/57.77 ( (fun pname bool), u ) 57.54/57.77 ( int, (zero_zero int) ) 57.54/57.77 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.77 ( (fun int int), bit1 ) 57.54/57.77 ( (fun int int), succ ) 57.54/57.77 ( (fun nat nat), suc ) 57.54/57.77 ( (fun x_a bool), g ) 57.54/57.77 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.77 ( (fun int bool), nat_neg ) 57.54/57.77 ( (fun bool bool), fNot ) 57.54/57.77 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.77 ( (fun bool (fun bool bool)), fconj ) 57.54/57.77 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.77 ( (fun com x_a), mgt ) 57.54/57.77 ( (fun pname x_a), mgt_call ) 57.54/57.77 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.77 ( (fun pname (option com)), body ) 57.54/57.77 ( (fun com bool), wt ) 57.54/57.77 ( (fun int (fun int int)), nat_tsub ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23583 $$unsorted) (BOUND_VARIABLE_23584 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_23583) BOUND_VARIABLE_23584)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_23584) BOUND_VARIABLE_23583))))))) ) 57.54/57.77 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.77 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (one_one nat))))) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23617 $$unsorted) (BOUND_VARIABLE_23618 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_23617) BOUND_VARIABLE_23618))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_23617)) (hAPP nat X_a _let_0 BOUND_VARIABLE_23618))))) ) 57.54/57.77 ( int, (zero_zero nat), (zero_zero nat) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (Y_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (hAPP (fun X_b X_b) (fun _let_0 _let_0) (image X_b X_b) (combi X_b)) Y_3) (ti _let_0 Y_3))) ) 57.54/57.77 ( bool, fNot ) 57.54/57.77 ( com, wt ) 57.54/57.77 ( pname, u ) 57.54/57.77 ( int, nat_neg ) 57.54/57.77 ( x_a, g ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z) W))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z))) (= Z W)))) ) 57.54/57.77 ( (zero_zero int), (one_one int) ) 57.54/57.77 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.77 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 B_1)) (hAPP _let_0 nat _let_1 A_3)))) (= (ti _let_0 B_1) (ti _let_0 A_3))))) ) 57.54/57.77 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23678 $$unsorted) (BOUND_VARIABLE_23679 $$unsorted) (BOUND_VARIABLE_23680 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (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_23680))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_23678) BOUND_VARIABLE_23679))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_23678) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_23680) BOUND_VARIABLE_23679)))))) ) 57.54/57.77 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (one_one int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) K_1))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (= K_1 (hAPP nat int (semiring_1_of_nat int) N_1)))) ))) ) 57.54/57.77 ( (one_one int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_23780 $$unsorted) (BOUND_VARIABLE_23781 $$unsorted) (BOUND_VARIABLE_23782 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (fun X_b X_b))) (let ((_let_3 (times_times X_b))) (let ((_let_4 (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_23782))) (or (not (linord581940658strict X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (zero_zero X_b)) BOUND_VARIABLE_23782))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_23780) BOUND_VARIABLE_23781)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b _let_4 BOUND_VARIABLE_23780)) (hAPP X_b X_b _let_4 BOUND_VARIABLE_23781)))))))))) ) 57.54/57.77 ( int, (zero_zero int), (one_one int), (one_one int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun nat X_a) _let_0)))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( int ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B_1) (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) A_3)))) (not (forall ((C_3 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_c) C_3))) (not (= (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) C_3) (ti _let_0 B_1))) (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) C_3) A_3)))) ))))) ) 57.54/57.77 ( pname, x_a, mgt_call, u, g ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted)) (or (not (ab_sem1668676832m_mult X_b)) (hBOOL (hAPP (fun X_b (fun X_b X_b)) bool (finite_comp_fun_idem X_b X_b) (times_times X_b)))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( int ) 57.54/57.77 ( (fun x_a bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23853 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (hAPP int X_a _let_0 BOUND_VARIABLE_23853))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (one_one X_a)) _let_3)) _let_3) (hAPP int X_a _let_0 (hAPP int int bit1 BOUND_VARIABLE_23853)))))))) ) 57.54/57.77 ( nat, (zero_zero int) ) 57.54/57.77 ( nat, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.77 ( int, (zero_zero int) ) 57.54/57.77 ( int, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23893 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_23893) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_23893))) ) 57.54/57.77 ( bool, fFalse ) 57.54/57.77 ( bool, fTrue ) 57.54/57.77 ( nat, na ) 57.54/57.77 ( (fun (option com) com), (the_1 com) ) 57.54/57.77 ( pname, pn ) 57.54/57.77 ( (fun pname bool), u ) 57.54/57.77 ( int, (zero_zero int) ) 57.54/57.77 ( (fun int int), bit1 ) 57.54/57.77 ( (fun int int), succ ) 57.54/57.77 ( (fun nat nat), suc ) 57.54/57.77 ( (fun x_a bool), g ) 57.54/57.77 ( (fun int bool), nat_neg ) 57.54/57.77 ( (fun bool bool), fNot ) 57.54/57.77 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.77 ( (fun bool (fun bool bool)), fconj ) 57.54/57.77 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.77 ( (fun com x_a), mgt ) 57.54/57.77 ( (fun pname x_a), mgt_call ) 57.54/57.77 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.77 ( (fun pname (option com)), body ) 57.54/57.77 ( (fun com bool), wt ) 57.54/57.77 ( (fun int (fun int int)), nat_tsub ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_23913 $$unsorted) (BOUND_VARIABLE_23914 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_23913) BOUND_VARIABLE_23914))) (not (= (ti X_a BOUND_VARIABLE_23914) (ti X_a BOUND_VARIABLE_23913)))) ) 57.54/57.77 ( int, (zero_zero int), (one_one int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((Z $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z))) (not (forall ((M_2 $$unsorted)) (not (= Z (hAPP nat int (semiring_1_of_nat int) M_2))) ))) ) 57.54/57.77 ( (one_one int) ) 57.54/57.77 ( (zero_zero int) ) 57.54/57.77 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (insert X_b))) (let ((_let_4 (hAPP X_b _let_2 _let_3 X_1))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 _let_4 A_3)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 _let_4 (bot_bot _let_0)))))))))))) ) 57.54/57.77 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (insert X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 X_1))) (let ((_let_4 (bot_bot _let_0))) (let ((_let_5 (ti _let_0 A_3))) (let ((_let_6 (hAPP _let_0 _let_0 _let_3 _let_4))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) _let_6))) (= _let_5 _let_6) (= _let_4 _let_5))))))))) ) 57.54/57.77 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (hAPP pname x_a mgt_call pn) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24018 $$unsorted) (BOUND_VARIABLE_24019 $$unsorted) (BOUND_VARIABLE_24020 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24019) BOUND_VARIABLE_24020))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_24018))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_24019) BOUND_VARIABLE_24018)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_24020) BOUND_VARIABLE_24018)))))))) ) 57.54/57.77 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.54/57.77 ( int, (zero_zero int), (zero_zero int), (zero_zero int) ) 57.54/57.77 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (one_one X_b))) (or (not (one X_b)) (= _let_0 (ti X_b _let_0)))) ) 57.54/57.77 ( nat ) 57.54/57.77 ( int ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24059 $$unsorted) (BOUND_VARIABLE_24060 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_24059) BOUND_VARIABLE_24060))) (= (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) BOUND_VARIABLE_24060) BOUND_VARIABLE_24059)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_24060)) (hAPP nat X_a _let_0 BOUND_VARIABLE_24059))))) ) 57.54/57.77 ( int, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (let ((_let_4 (hAPP nat _let_0 _let_1 M_1))) (let ((_let_5 (hAPP nat _let_2 _let_3 L_1))) (or (not (hBOOL (hAPP nat bool _let_4 N))) (not (hBOOL (hAPP nat bool _let_4 L_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat _let_5 N)) (hAPP nat nat _let_5 M_1)))))))))) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_less_eq X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( com ) 57.54/57.77 ( pname ) 57.54/57.77 ( (fun pname bool) ) 57.54/57.77 ( int ) 57.54/57.77 ( x_a ) 57.54/57.77 ( (fun x_a bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_0 nat _let_1 A_3)) (one_one nat)) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 (hAPP X_b _let_2 (insert X_b) X_1) (bot_bot _let_0))))))))) ) 57.54/57.77 ( pname, pn, u ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((Na $$unsorted) (Pa $$unsorted)) (or (hBOOL (hAPP nat bool Pa (zero_zero nat))) (not (hBOOL (hAPP nat bool Pa Na))) (not (forall ((K_2 $$unsorted)) (or (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I) K_2))) (not (hBOOL (hAPP nat bool Pa I)))) )) (not (hBOOL (hAPP nat bool Pa (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) K_2) (one_one nat))))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) K_2) Na)))) ))) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) B_3) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) (bot_bot _let_0))))) (= (ti X_b A_2) (ti X_b B_3)))) ) 57.54/57.77 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 A_3)) (hAPP _let_0 nat _let_1 B_1)))))) ) 57.54/57.77 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less _let_0) A_3) B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_3) B_1))))) ) 57.54/57.77 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 K_1) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) (hAPP nat nat (hAPP nat _let_2 (minus_minus nat) (hAPP nat nat (hAPP nat _let_2 (plus_plus nat) N) M_1)) K_1))))))) ) 57.54/57.77 ( (hAPP nat nat suc na), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_2)) (or (= (ti _let_0 A_2) (bot_bot _let_0)) (not (forall ((A_5 $$unsorted) (A_4 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_5))) (not (= (ti _let_0 A_2) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_4) A_5)))) ))))) ) 57.54/57.77 ( bool, fNot ) 57.54/57.77 ( com, wt ) 57.54/57.77 ( pname, u ) 57.54/57.77 ( int, nat_neg ) 57.54/57.77 ( x_a, g ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24219 $$unsorted) (BOUND_VARIABLE_24220 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linordered_idom X_a)) (= (ti X_a BOUND_VARIABLE_24219) (ti X_a BOUND_VARIABLE_24220)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24219) BOUND_VARIABLE_24220)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24220) BOUND_VARIABLE_24219))))) ) 57.54/57.77 ( bool, fFalse, fTrue ) 57.54/57.77 ( bool, fTrue, fFalse ) 57.54/57.77 ( (fun int int), bit1, succ ) 57.54/57.77 ( (fun int int), succ, bit1 ) 57.54/57.77 ( (fun bool (fun bool bool)), fconj, fimplies ) 57.54/57.77 ( (fun bool (fun bool bool)), fimplies, fconj ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (preorder T_1)) (preorder (fun T_2 T_1))) ) 57.54/57.77 ( bool, bool ) 57.54/57.77 ( bool, (fun bool bool) ) 57.54/57.77 ( nat, bool ) 57.54/57.77 ( nat, nat ) 57.54/57.77 ( nat, int ) 57.54/57.77 ( (fun nat bool), (fun int bool) ) 57.54/57.77 ( com, bool ) 57.54/57.77 ( com, x_a ) 57.54/57.77 ( (option com), com ) 57.54/57.77 ( pname, bool ) 57.54/57.77 ( pname, (option com) ) 57.54/57.77 ( pname, x_a ) 57.54/57.77 ( (fun pname bool), bool ) 57.54/57.77 ( (fun pname bool), (fun x_a bool) ) 57.54/57.77 ( int, bool ) 57.54/57.77 ( int, int ) 57.54/57.77 ( int, (fun int int) ) 57.54/57.77 ( x_a, bool ) 57.54/57.77 ( (fun x_a bool), bool ) 57.54/57.77 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.77 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (finite1357897459simple X_b X_c))) (= _let_0 (ti (fun (fun X_b (fun X_b X_b)) (fun X_b (fun (fun X_c X_b) (fun (fun (fun X_c bool) X_b) bool)))) _let_0))) ) 57.54/57.77 ( bool, pname ) 57.54/57.77 ( bool, x_a ) 57.54/57.77 ( (fun x_a bool), pname ) 57.54/57.77 ( (fun x_a bool), x_a ) 57.54/57.77 ( (fun int bool), nat ) 57.54/57.77 ( (fun (fun x_a bool) bool), x_a ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24380 $$unsorted) (BOUND_VARIABLE_24381 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_24380) BOUND_VARIABLE_24381)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_24381) BOUND_VARIABLE_24380)))) ) 57.54/57.77 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fequal X_a))) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( com ) 57.54/57.77 ( pname ) 57.54/57.77 ( (fun pname bool) ) 57.54/57.77 ( int ) 57.54/57.77 ( x_a ) 57.54/57.77 ( (fun x_a bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24463 $$unsorted) (BOUND_VARIABLE_24464 $$unsorted) (BOUND_VARIABLE_24465 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_24463))) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24464) BOUND_VARIABLE_24465))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24463) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_24465)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_24464))))))))) ) 57.54/57.77 ( int, (zero_zero int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (hBOOL (hAPP _let_1 bool (hAPP X_c (fun _let_1 bool) (member X_c) (hAPP X_b X_c F X_1)) (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (image X_b X_c) F) A_3)))))) ) 57.54/57.77 ( x_a, pname, mgt_call, pn, u ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_c $$unsorted)) (let ((_let_0 (minus_minus X_c))) (or (not (minus X_c)) (= _let_0 (ti (fun X_c (fun X_c X_c)) _let_0)))) ) 57.54/57.77 ( bool ) 57.54/57.77 ( nat ) 57.54/57.77 ( int ) 57.54/57.77 ( (fun x_a bool) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (zero_zero nat))) (let ((_let_3 (hAPP nat _let_0 _let_1 _let_2))) (or (not (hBOOL (hAPP nat bool _let_3 N))) (not (hBOOL (hAPP nat bool _let_3 M_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) N)) M_1))))))) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M))) (= (hAPP nat nat _let_2 (hAPP nat nat suc Na)) (hAPP nat nat (hAPP _let_0 _let_0 (hAPP nat (fun _let_0 _let_0) (nat_case nat) (zero_zero nat)) (combi nat)) (hAPP nat nat _let_2 Na)))))) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (zero_zero nat) ) 57.54/57.77 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24606 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_24606) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_24606) (one_one X_a)))) ) 57.54/57.77 ( bool, fFalse ) 57.54/57.77 ( bool, fTrue ) 57.54/57.77 ( nat, na ) 57.54/57.77 ( (fun (option com) com), (the_1 com) ) 57.54/57.77 ( pname, pn ) 57.54/57.77 ( (fun pname bool), u ) 57.54/57.77 ( int, (zero_zero int) ) 57.54/57.77 ( (fun int int), bit1 ) 57.54/57.77 ( (fun int int), succ ) 57.54/57.77 ( (fun nat nat), suc ) 57.54/57.77 ( (fun x_a bool), g ) 57.54/57.77 ( (fun int bool), nat_neg ) 57.54/57.77 ( (fun bool bool), fNot ) 57.54/57.77 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.77 ( (fun bool (fun bool bool)), fconj ) 57.54/57.77 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.77 ( (fun com x_a), mgt ) 57.54/57.77 ( (fun pname x_a), mgt_call ) 57.54/57.77 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.77 ( (fun pname (option com)), body ) 57.54/57.77 ( (fun com bool), wt ) 57.54/57.77 ( (fun int (fun int int)), nat_tsub ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_b _let_0))) (= (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) (bot_bot _let_0)) (hAPP _let_0 _let_0 (collect X_b) (hAPP X_b _let_0 (hAPP _let_1 _let_1 (combc X_b X_b bool) (fequal X_b)) A_2))))) ) 57.54/57.77 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted) (F $$unsorted)) (let ((_let_0 (fun X_c X_c))) (let ((_let_1 (hAPP X_b _let_0 F X_1))) (let ((_let_2 (hAPP X_c X_c _let_1 Z_2))) (or (not (hBOOL (hAPP (fun X_b _let_0) bool (finite_comp_fun_idem X_b X_c) F))) (= _let_2 (hAPP X_c X_c _let_1 _let_2)))))) ) 57.54/57.77 ( nat, nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (minus_minus nat) ) 57.54/57.77 ( x_a, (fun x_a bool), (hAPP pname x_a mgt_call pn), g, (insert x_a) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_24709 $$unsorted)) (let ((_let_0 (bot_bot X_b))) (or (not (bot X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) _let_0) BOUND_VARIABLE_24709)) (not (= _let_0 (ti X_b BOUND_VARIABLE_24709)))))) ) 57.54/57.77 ( bool, fFalse ) 57.54/57.77 ( bool, fTrue ) 57.54/57.77 ( nat, na ) 57.54/57.77 ( (fun (option com) com), (the_1 com) ) 57.54/57.77 ( pname, pn ) 57.54/57.77 ( (fun pname bool), u ) 57.54/57.77 ( int, (zero_zero int) ) 57.54/57.77 ( (fun int int), bit1 ) 57.54/57.77 ( (fun int int), succ ) 57.54/57.77 ( (fun nat nat), suc ) 57.54/57.77 ( (fun x_a bool), g ) 57.54/57.77 ( (fun int bool), nat_neg ) 57.54/57.77 ( (fun bool bool), fNot ) 57.54/57.77 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.77 ( (fun bool (fun bool bool)), fconj ) 57.54/57.77 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.77 ( (fun com x_a), mgt ) 57.54/57.77 ( (fun pname x_a), mgt_call ) 57.54/57.77 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.77 ( (fun pname (option com)), body ) 57.54/57.77 ( (fun com bool), wt ) 57.54/57.77 ( (fun int (fun int int)), nat_tsub ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (combc X_a X_b X_c))) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun X_b (fun X_a X_c))) _let_0))) ) 57.54/57.77 ( bool, bool, bool ) 57.54/57.77 ( int, (fun nat bool), bool ) 57.54/57.77 ( int, int, int ) 57.54/57.77 ( x_a, (fun pname bool), bool ) 57.54/57.77 ( x_a, (fun x_a bool), bool ) 57.54/57.77 ( (fun x_a bool), (fun x_a bool), bool ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 A_1) B))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) C) A_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_2 _let_3 A_1) C)) (hAPP nat nat (hAPP nat _let_2 _let_3 B) C)))))))) ) 57.54/57.77 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_24753 $$unsorted) (BOUND_VARIABLE_24754 $$unsorted) (BOUND_VARIABLE_24755 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (dense_linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_24754) BOUND_VARIABLE_24755))) (not (forall ((W_3 $$unsorted)) (let ((_let_1 (ord_less X_a))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_24754) W_3))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 W_3) BOUND_VARIABLE_24755))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) W_3) BOUND_VARIABLE_24753)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_24755) BOUND_VARIABLE_24753)))) ) 57.54/57.77 ( int, (zero_zero int), (zero_zero int), (one_one int) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((N $$unsorted)) (= N (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat suc N)) (one_one nat))) ) 57.54/57.77 ( (zero_zero nat) ) 57.54/57.77 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.77 ( na ) 57.54/57.77 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_finite X_b))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) B_1))) (not (hBOOL (hAPP _let_0 bool _let_1 B_1))) (hBOOL (hAPP _let_0 bool _let_1 A_3))))) ) 57.54/57.77 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_24828 $$unsorted) (BOUND_VARIABLE_24829 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (number_number_of X_b))) (let ((_let_2 (hAPP int X_b _let_1 BOUND_VARIABLE_24829))) (let ((_let_3 (hAPP int X_b _let_1 BOUND_VARIABLE_24828))) (or (not (number X_b)) (not (linorder X_b)) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) _let_2) _let_3))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) _let_3) _let_2)))))))) ) 57.54/57.77 ( nat, (zero_zero int), (zero_zero int) ) 57.54/57.77 ( nat, (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.77 ( nat, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.77 ( int, (zero_zero int), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.77 ( int, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.77 ( int, (hAPP int int bit1 (zero_zero int)), (zero_zero int) ) 57.54/57.77 ( int, (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.77 ( int, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_a $$unsorted)) (or (not (zero_neq_one X_a)) (not (= (zero_zero X_a) (one_one X_a)))) ) 57.54/57.77 ( nat ) 57.54/57.77 ) 57.54/57.77 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_24927 $$unsorted) (BOUND_VARIABLE_24928 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (or (not (order X_b)) (= (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_24928) BOUND_VARIABLE_24927)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_24927) BOUND_VARIABLE_24928))) (= (ti X_b BOUND_VARIABLE_24927) (ti X_b BOUND_VARIABLE_24928)))))) ) 57.54/57.77 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.77 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.77 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.77 ( int, (one_one int), (zero_zero int) ) 57.54/57.77 ( int, (zero_zero int), (one_one int) ) 57.54/57.77 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.77 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.77 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int _let_2 V_2))) (let ((_let_4 (hBOOL (hAPP int bool nat_neg _let_3)))) (let ((_let_5 (hAPP int int _let_2 V_3))) (let ((_let_6 (hBOOL (hAPP int bool nat_neg _let_5)))) (= (= (hAPP int nat _let_1 V_3) (hAPP int nat _let_1 V_2)) (and (or _let_6 (and (or (not _let_4) (= _let_0 _let_5)) (or _let_4 (= V_3 V_2)))) (or (not _let_6) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_3) _let_0)))))))))))) ) 57.54/57.78 ( (zero_zero int), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.78 ( (hAPP int int bit1 (zero_zero int)), (zero_zero int) ) 57.54/57.78 ( (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_24987 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (linord219039673up_add X_b)) (= (= _let_0 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_24987) BOUND_VARIABLE_24987)) (= _let_0 (ti X_b BOUND_VARIABLE_24987))))) ) 57.54/57.78 ( bool, fFalse ) 57.54/57.78 ( bool, fTrue ) 57.54/57.78 ( nat, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com) ) 57.54/57.78 ( pname, pn ) 57.54/57.78 ( (fun pname bool), u ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1 ) 57.54/57.78 ( (fun int int), succ ) 57.54/57.78 ( (fun nat nat), suc ) 57.54/57.78 ( (fun x_a bool), g ) 57.54/57.78 ( (fun int bool), nat_neg ) 57.54/57.78 ( (fun bool bool), fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.78 ( (fun com x_a), mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.78 ( (fun pname (option com)), body ) 57.54/57.78 ( (fun com bool), wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25004 $$unsorted) (BOUND_VARIABLE_25005 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25005) BOUND_VARIABLE_25004)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25004) BOUND_VARIABLE_25005))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (minus T_1)) (minus (fun T_2 T_1))) ) 57.54/57.78 ( bool, bool ) 57.54/57.78 ( bool, (fun bool bool) ) 57.54/57.78 ( nat, bool ) 57.54/57.78 ( nat, nat ) 57.54/57.78 ( nat, int ) 57.54/57.78 ( (fun nat bool), (fun int bool) ) 57.54/57.78 ( com, bool ) 57.54/57.78 ( com, x_a ) 57.54/57.78 ( (option com), com ) 57.54/57.78 ( pname, bool ) 57.54/57.78 ( pname, (option com) ) 57.54/57.78 ( pname, x_a ) 57.54/57.78 ( (fun pname bool), bool ) 57.54/57.78 ( (fun pname bool), (fun x_a bool) ) 57.54/57.78 ( int, bool ) 57.54/57.78 ( int, int ) 57.54/57.78 ( int, (fun int int) ) 57.54/57.78 ( x_a, bool ) 57.54/57.78 ( (fun x_a bool), bool ) 57.54/57.78 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.78 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25089 $$unsorted) (BOUND_VARIABLE_25090 $$unsorted) (BOUND_VARIABLE_25091 $$unsorted) (BOUND_VARIABLE_25092 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25091) BOUND_VARIABLE_25092))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25089) BOUND_VARIABLE_25090))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_25091) BOUND_VARIABLE_25089)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_25092) BOUND_VARIABLE_25090)))))))) ) 57.54/57.78 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (minus_minus _let_0))) (let ((_let_4 (hAPP _let_0 _let_2 _let_3 A_3))) (let ((_let_5 (insert X_b))) (let ((_let_6 (hAPP X_b _let_2 _let_5 X_1))) (let ((_let_7 (bot_bot _let_0))) (let ((_let_8 (hAPP _let_0 _let_0 _let_6 _let_7))) (let ((_let_9 (hAPP _let_0 _let_0 _let_4 _let_8))) (let ((_let_10 (hAPP _let_0 nat _let_1 _let_9))) (let ((_let_11 (hAPP _let_0 nat _let_1 A_3))) (let ((_let_12 (fun _let_0 bool))) (let ((_let_13 (member X_b))) (let ((_let_14 (hAPP X_b _let_12 _let_13 X_1))) (let ((_let_15 (hBOOL (hAPP _let_0 bool _let_14 A_3)))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (and (or _let_15 (= _let_10 _let_11)) (or (not _let_15) (= _let_10 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_11) (one_one nat)))))))))))))))))))))) ) 57.54/57.78 ( pname, pn, u ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (ring_1_Ints X_b))) (or (not (ring_1 X_b)) (= _let_0 (ti (fun X_b bool) _let_0)))) ) 57.54/57.78 ( bool ) 57.54/57.78 ( nat ) 57.54/57.78 ( com ) 57.54/57.78 ( pname ) 57.54/57.78 ( (fun pname bool) ) 57.54/57.78 ( int ) 57.54/57.78 ( x_a ) 57.54/57.78 ( (fun x_a bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_25233 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (zero_zero X_b))) (or (not (linordered_idom X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_25233) _let_2)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_25233) BOUND_VARIABLE_25233)) _let_2))))))) ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25260 $$unsorted) (BOUND_VARIABLE_25261 $$unsorted) (BOUND_VARIABLE_25262 $$unsorted) (BOUND_VARIABLE_25263 $$unsorted)) (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))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25262) BOUND_VARIABLE_25263))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25260) BOUND_VARIABLE_25261))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_25262))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_25260))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_25262) BOUND_VARIABLE_25260)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_25263) BOUND_VARIABLE_25261)))))))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (= (= (bot_bot _let_1) (hAPP _let_0 _let_1 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F) A_3)) (= (ti _let_0 A_3) (bot_bot _let_0))))) ) 57.54/57.78 ( int, nat, (semiring_1_of_nat int), (bot_bot (fun nat bool)) ) 57.54/57.78 ( x_a, pname, mgt_call, u ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (C_2 $$unsorted) (D_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (insert X_b))) (let ((_let_5 (hAPP X_b _let_3 _let_4 A_2))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 C_2) D_3))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 _let_5 C_2)) (hAPP _let_0 _let_0 _let_5 D_3)))))))))) ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn), g, g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25336 $$unsorted) (BOUND_VARIABLE_25337 $$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)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25337) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_25336) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_25337) BOUND_VARIABLE_25336))))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (or (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_3)) (not (hBOOL (hAPP _let_0 bool (finite_finite X_c) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_3)))) (not (forall ((X_2 $$unsorted)) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun X_b X_c))) (let ((_let_4 (member X_b))) (let ((_let_5 (fun X_b _let_2))) (let ((_let_6 (fun X_b _let_0))) (let ((_let_7 (fun _let_1 _let_1))) (let ((_let_8 (fun _let_1 bool))) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_b _let_8 _let_4 X_2) A_3))) (hBOOL (hAPP _let_1 bool (finite_finite X_b) (hAPP _let_1 _let_1 (collect X_b) (hAPP _let_1 _let_1 (hAPP _let_5 _let_7 (combs X_b bool bool) (hAPP _let_1 _let_5 (hAPP (fun bool _let_2) (fun _let_1 _let_5) (combb bool _let_2 X_b) fconj) (hAPP _let_1 _let_1 (hAPP (fun X_b _let_8) _let_7 (combc X_b _let_1 bool) _let_4) A_3))) (hAPP X_c _let_1 (hAPP _let_6 (fun X_c _let_1) (combc X_b X_c bool) (hAPP _let_3 _let_6 (hAPP (fun X_c _let_0) (fun _let_3 _let_6) (combb X_c _let_0 X_b) (fequal X_c)) F)) (hAPP X_b X_c F X_2)))))))))))))) ))))) ) 57.54/57.78 ( int, nat, (semiring_1_of_nat int), (bot_bot (fun nat bool)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25395 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_25395))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_25395) (ti X_a BOUND_VARIABLE_25395))) ) 57.54/57.78 ( bool, fFalse ) 57.54/57.78 ( bool, fTrue ) 57.54/57.78 ( nat, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com) ) 57.54/57.78 ( pname, pn ) 57.54/57.78 ( (fun pname bool), u ) 57.54/57.78 ( int, (one_one int) ) 57.54/57.78 ( (fun int int), bit1 ) 57.54/57.78 ( (fun int int), succ ) 57.54/57.78 ( (fun nat nat), suc ) 57.54/57.78 ( (fun x_a bool), g ) 57.54/57.78 ( (fun int bool), nat_neg ) 57.54/57.78 ( (fun bool bool), fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.78 ( (fun com x_a), mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.78 ( (fun pname (option com)), body ) 57.54/57.78 ( (fun com bool), wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (= (ti X_b B_3) (ti X_b A_2)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) B_3) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) (bot_bot _let_0)))))) ) 57.54/57.78 ( bool, fFalse, fFalse ) 57.54/57.78 ( bool, fTrue, fTrue ) 57.54/57.78 ( nat, na, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.78 ( pname, pn, pn ) 57.54/57.78 ( (fun pname bool), u, u ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1, bit1 ) 57.54/57.78 ( (fun int int), succ, succ ) 57.54/57.78 ( (fun nat nat), suc, suc ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.78 ( (fun bool bool), fNot, fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.78 ( (fun com x_a), mgt, mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.78 ( (fun pname (option com)), body, body ) 57.54/57.78 ( (fun com bool), wt, wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc N) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) N)) ) 57.54/57.78 ( (zero_zero nat) ) 57.54/57.78 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.78 ( na ) 57.54/57.78 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_25456 $$unsorted) (BOUND_VARIABLE_25457 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (linorder X_b)) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_25456) BOUND_VARIABLE_25457))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_25457) BOUND_VARIABLE_25456))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ( int, (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25477 $$unsorted) (BOUND_VARIABLE_25478 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_25477) BOUND_VARIABLE_25478))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_25478) BOUND_VARIABLE_25477))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ( int, (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_25582 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (ring_1 X_b)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) (hAPP nat X_b (semiring_1_of_nat X_b) BOUND_VARIABLE_25582)) (ring_1_Ints X_b))))) ) 57.54/57.78 ( int, (one_one nat) ) 57.54/57.78 ( int, (zero_zero nat) ) 57.54/57.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25597 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP nat X_a _let_0 BOUND_VARIABLE_25597)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_25597))))) ) 57.54/57.78 ( nat, (zero_zero nat) ) 57.54/57.78 ( int, (zero_zero nat) ) 57.54/57.78 ( int, na ) 57.54/57.78 ( int, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (plus_plus X_b))) (or (not (cancel_semigroup_add X_b)) (= _let_0 (ti (fun X_b (fun X_b X_b)) _let_0)))) ) 57.54/57.78 ( bool ) 57.54/57.78 ( nat ) 57.54/57.78 ( int ) 57.54/57.78 ( (fun x_a bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (zero_zero X_a))))) ) 57.54/57.78 ( bool ) 57.54/57.78 ( nat ) 57.54/57.78 ( com ) 57.54/57.78 ( pname ) 57.54/57.78 ( (fun pname bool) ) 57.54/57.78 ( int ) 57.54/57.78 ( x_a ) 57.54/57.78 ( (fun x_a bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_25679 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (number_ring X_b)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_25679)) (ring_1_Ints X_b))))) ) 57.54/57.78 ( nat, (zero_zero int) ) 57.54/57.78 ( nat, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.78 ( nat, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( int, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.78 ( int, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M_1))) (= M_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M_1) N)) N)))) ) 57.54/57.78 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M_1) N)) (= M_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M_1) N))))) ) 57.54/57.78 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) (hAPP nat nat suc N)))))) ) 57.54/57.78 ( (zero_zero nat), (zero_zero nat) ) 57.54/57.78 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.78 ( na, na ) 57.54/57.78 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (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 (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0))))) ) 57.54/57.78 ( bool ) 57.54/57.78 ( nat ) 57.54/57.78 ( com ) 57.54/57.78 ( pname ) 57.54/57.78 ( (fun pname bool) ) 57.54/57.78 ( int ) 57.54/57.78 ( x_a ) 57.54/57.78 ( (fun x_a bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) (bot_bot _let_0)) (hAPP _let_0 _let_0 (collect X_b) (hAPP X_b _let_0 (fequal X_b) A_2)))) ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_25954 $$unsorted) (BOUND_VARIABLE_25955 $$unsorted) (BOUND_VARIABLE_25956 $$unsorted) (BOUND_VARIABLE_25957 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (minus_minus X_b))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less_eq X_b))) (or (not (ordered_ab_group_add X_b)) (not (= (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_25954) BOUND_VARIABLE_25955) (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_25956) BOUND_VARIABLE_25957))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_25954) BOUND_VARIABLE_25955)) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_25956) BOUND_VARIABLE_25957)))))))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_2 _let_3 M_1) L_1)) (hAPP nat nat (hAPP nat _let_2 _let_3 N) L_1)))))))) ) 57.54/57.78 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26012 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (let ((_let_1 (fun X_b bool))) (or (not (ring_char_0 X_b)) (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) BOUND_VARIABLE_26012) (ring_1_Ints X_b)))) (= (= _let_0 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_26012) BOUND_VARIABLE_26012)) (= _let_0 (ti X_b BOUND_VARIABLE_26012)))))) ) 57.54/57.78 ( bool, fFalse ) 57.54/57.78 ( bool, fTrue ) 57.54/57.78 ( nat, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com) ) 57.54/57.78 ( pname, pn ) 57.54/57.78 ( (fun pname bool), u ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1 ) 57.54/57.78 ( (fun int int), succ ) 57.54/57.78 ( (fun nat nat), suc ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.78 ( (fun x_a bool), g ) 57.54/57.78 ( (fun int bool), nat_neg ) 57.54/57.78 ( (fun bool bool), fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.78 ( (fun com x_a), mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.78 ( (fun pname (option com)), body ) 57.54/57.78 ( (fun com bool), wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 57.54/57.78 ( nat ) 57.54/57.78 ( int ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (insert X_b))) (let ((_let_4 (hAPP X_b _let_2 _let_3 X_1))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 _let_4 A_3)) (hAPP nat nat suc (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 _let_4 (bot_bot _let_0)))))))))))) ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (= (ti _let_0 A_3) (ti _let_0 B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B_1) A_3)))) ) 57.54/57.78 ( bool, fNot, fNot ) 57.54/57.78 ( com, wt, wt ) 57.54/57.78 ( pname, u, u ) 57.54/57.78 ( int, nat_neg, nat_neg ) 57.54/57.78 ( x_a, g, g ) 57.54/57.78 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_26113 $$unsorted) (BOUND_VARIABLE_26114 $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (or (not (ord X_c)) (= (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less _let_0) BOUND_VARIABLE_26113) BOUND_VARIABLE_26114)) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_26113) BOUND_VARIABLE_26114)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_26114) BOUND_VARIABLE_26113))))))))) ) 57.54/57.78 ( x_a, bool, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( x_a, bool, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( x_a, bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.78 ( x_a, bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26133 $$unsorted) (BOUND_VARIABLE_26134 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (ordered_ab_group_add X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_26133) BOUND_VARIABLE_26134)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) BOUND_VARIABLE_26133) BOUND_VARIABLE_26134)) (zero_zero X_b))))))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26150 $$unsorted)) (or (not (bot X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_26150) (bot_bot X_a))))) ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (one_one X_a)))) ) 57.54/57.78 ( bool ) 57.54/57.78 ( nat ) 57.54/57.78 ( com ) 57.54/57.78 ( pname ) 57.54/57.78 ( (fun pname bool) ) 57.54/57.78 ( x_a ) 57.54/57.78 ( (fun x_a bool) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool Pa A_3))) (not (forall ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (fun _let_0 _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_5))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_4) A_5))) (not (hBOOL (hAPP _let_0 bool Pa A_5))) (hBOOL (hAPP _let_0 bool Pa (hAPP _let_0 _let_0 (hAPP _let_0 _let_1 (minus_minus _let_0) A_5) (hAPP _let_0 _let_0 (hAPP X_b _let_1 (insert X_b) A_4) (bot_bot _let_0))))))) )) (hBOOL (hAPP _let_0 bool Pa (bot_bot _let_0))))) ) 57.54/57.78 ( pname, (finite_finite pname), u ) 57.54/57.78 ( pname, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.54/57.78 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26300 $$unsorted) (BOUND_VARIABLE_26301 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_26300) BOUND_VARIABLE_26301)) BOUND_VARIABLE_26301) (ti X_a BOUND_VARIABLE_26300)))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M_1))) (= M_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M_1) N))))) ) 57.54/57.78 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((BOUND_VARIABLE_26332 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) BOUND_VARIABLE_26332))) (= (hAPP int nat _let_0 (hAPP int int succ BOUND_VARIABLE_26332)) (hAPP nat nat suc (hAPP int nat _let_0 BOUND_VARIABLE_26332))))) ) 57.54/57.78 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.78 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((BOUND_VARIABLE_26344 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) BOUND_VARIABLE_26344)))) (= (one_one nat) (hAPP nat nat suc (hAPP int nat (number_number_of nat) BOUND_VARIABLE_26344)))) ) 57.54/57.78 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) V))) ) 57.54/57.78 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((Pa $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP nat bool Pa K))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool Pa (hAPP nat nat suc N_1)))) (hBOOL (hAPP nat bool Pa N_1))) )) (hBOOL (hAPP nat bool Pa (zero_zero nat)))) ) 57.54/57.78 ( (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26376 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (zero_zero X_b))) (or (not (linord219039673up_add X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_26376) _let_2)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_26376) BOUND_VARIABLE_26376)) _let_2))))))) ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26401 $$unsorted) (BOUND_VARIABLE_26402 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (or (not (order X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_26401) BOUND_VARIABLE_26402))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_26402) BOUND_VARIABLE_26401)) (= (ti X_b BOUND_VARIABLE_26401) (ti X_b BOUND_VARIABLE_26402)))))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26423 $$unsorted) (BOUND_VARIABLE_26424 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (linorder X_b)) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_26423) BOUND_VARIABLE_26424))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_26424) BOUND_VARIABLE_26423))))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (one_one int), (zero_zero int) ) 57.54/57.78 ( int, (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26512 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (ordere142940540dd_abs X_b)) (= (= _let_0 (ti X_b BOUND_VARIABLE_26512)) (= _let_0 (hAPP X_b X_b (abs_abs X_b) BOUND_VARIABLE_26512))))) ) 57.54/57.78 ( bool, fFalse ) 57.54/57.78 ( bool, fTrue ) 57.54/57.78 ( nat, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com) ) 57.54/57.78 ( pname, pn ) 57.54/57.78 ( (fun pname bool), u ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1 ) 57.54/57.78 ( (fun int int), succ ) 57.54/57.78 ( (fun nat nat), suc ) 57.54/57.78 ( (fun x_a bool), g ) 57.54/57.78 ( (fun int bool), nat_neg ) 57.54/57.78 ( (fun bool bool), fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.78 ( (fun com x_a), mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.78 ( (fun pname (option com)), body ) 57.54/57.78 ( (fun com bool), wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M_1)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_1) N)))) ) 57.54/57.78 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26651 $$unsorted) (BOUND_VARIABLE_26652 $$unsorted) (BOUND_VARIABLE_26653 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_26651))) (or (not (ordere1490568538miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26652) BOUND_VARIABLE_26653))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_26651))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_26652)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_26653))))))))) ) 57.54/57.78 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int), (zero_zero int) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((K_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) K_1) (one_one int)) (hAPP int int succ K_1)) ) 57.54/57.78 ( (zero_zero int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (bot_bot _let_0))) (= (= (ti _let_0 A_3) _let_1) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_3) _let_1))))) ) 57.54/57.78 ( bool, fNot ) 57.54/57.78 ( com, wt ) 57.54/57.78 ( pname, u ) 57.54/57.78 ( int, nat_neg ) 57.54/57.78 ( x_a, g ) 57.54/57.78 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26693 $$unsorted)) (or (not (ab_sem1668676832m_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_26693) BOUND_VARIABLE_26693) (ti X_a BOUND_VARIABLE_26693))) ) 57.54/57.78 ( bool, fFalse ) 57.54/57.78 ( bool, fTrue ) 57.54/57.78 ( nat, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com) ) 57.54/57.78 ( pname, pn ) 57.54/57.78 ( (fun pname bool), u ) 57.54/57.78 ( int, (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1 ) 57.54/57.78 ( (fun int int), succ ) 57.54/57.78 ( (fun nat nat), suc ) 57.54/57.78 ( (fun x_a bool), g ) 57.54/57.78 ( (fun int bool), nat_neg ) 57.54/57.78 ( (fun bool bool), fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.78 ( (fun com x_a), mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.78 ( (fun pname (option com)), body ) 57.54/57.78 ( (fun com bool), wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26715 $$unsorted) (BOUND_VARIABLE_26716 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26715) BOUND_VARIABLE_26716))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_26716) BOUND_VARIABLE_26715))) (= (ti X_a BOUND_VARIABLE_26716) (ti X_a BOUND_VARIABLE_26715))))) ) 57.54/57.78 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (ti X_a Y) (ti X_a X))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (fequal X_a) X) Y))) ) 57.54/57.78 ( bool, fFalse, fFalse ) 57.54/57.78 ( bool, fTrue, fTrue ) 57.54/57.78 ( nat, na, na ) 57.54/57.78 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.78 ( pname, pn, pn ) 57.54/57.78 ( (fun pname bool), u, u ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.78 ( (fun int int), bit1, bit1 ) 57.54/57.78 ( (fun int int), succ, succ ) 57.54/57.78 ( (fun nat nat), suc, suc ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.78 ( (fun bool bool), fNot, fNot ) 57.54/57.78 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.78 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.78 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.78 ( (fun com x_a), mgt, mgt ) 57.54/57.78 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.78 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.78 ( (fun pname (option com)), body, body ) 57.54/57.78 ( (fun com bool), wt, wt ) 57.54/57.78 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) F_1))) (hBOOL (hAPP _let_0 bool (finite_finite X_c) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) H) F_1)))))) ) 57.54/57.78 ( int, nat, (semiring_1_of_nat int), (bot_bot (fun nat bool)) ) 57.54/57.78 ( x_a, pname, mgt_call, u ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((Pn $$unsorted) (G_1 $$unsorted)) (let ((_let_0 (option com))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (insert x_a))) (let ((_let_5 (hAPP pname x_a mgt_call Pn))) (let ((_let_6 (hAPP x_a _let_3 _let_4 _let_5))) (let ((_let_7 (bot_bot _let_1))) (or (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 _let_2 p (hAPP _let_1 _let_1 _let_6 G_1)) (hAPP _let_1 _let_1 (hAPP x_a _let_3 _let_4 (hAPP com x_a mgt (hAPP _let_0 com (the_1 com) (hAPP pname _let_0 body Pn)))) _let_7)))) (hBOOL (hAPP _let_1 bool (hAPP _let_1 _let_2 p G_1) (hAPP _let_1 _let_1 _let_6 _let_7)))))))))))) ) 57.54/57.78 ( pn, g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_26852 $$unsorted) (BOUND_VARIABLE_26853 $$unsorted) (BOUND_VARIABLE_26854 $$unsorted) (BOUND_VARIABLE_26855 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (ord_less X_a))) (let ((_let_5 (fun X_a X_a))) (let ((_let_6 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_4 BOUND_VARIABLE_26854) BOUND_VARIABLE_26855))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_4 BOUND_VARIABLE_26852) BOUND_VARIABLE_26853))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_26854))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_26852))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_4 (hAPP X_a X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_26854) BOUND_VARIABLE_26852)) (hAPP X_a X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_26855) BOUND_VARIABLE_26853))))))))))) ) 57.54/57.78 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 A_2))) (or (not (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_3) A_3)))) (= (ti X_b A_2) (ti X_b B_3)) (hBOOL (hAPP _let_0 bool _let_3 A_3))))))) ) 57.54/57.78 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (minus_minus _let_0) A_3) (bot_bot _let_0)) (ti _let_0 A_3))) ) 57.54/57.78 ( bool, fNot ) 57.54/57.78 ( com, wt ) 57.54/57.78 ( pname, u ) 57.54/57.78 ( int, nat_neg ) 57.54/57.78 ( x_a, g ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_26985 $$unsorted) (BOUND_VARIABLE_26986 $$unsorted) (BOUND_VARIABLE_26987 $$unsorted)) (or (not (order X_b)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (hAPP nat X_b BOUND_VARIABLE_26987 N_1)) (hAPP nat X_b BOUND_VARIABLE_26987 (hAPP nat nat suc N_1)))) )) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (hAPP nat X_b BOUND_VARIABLE_26987 BOUND_VARIABLE_26985)) (hAPP nat X_b BOUND_VARIABLE_26987 BOUND_VARIABLE_26986))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_26985) BOUND_VARIABLE_26986)))) ) 57.54/57.78 ( bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 57.54/57.78 ( nat, (zero_zero nat), (zero_zero nat), suc ) 57.54/57.78 ( nat, (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)), suc ) 57.54/57.78 ( nat, na, na, suc ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), suc ) 57.54/57.78 ( (fun nat bool), (hAPP nat nat suc na), (hAPP nat nat suc na), (ord_less_eq nat) ) 57.54/57.78 ( int, (one_one nat), (one_one nat), (semiring_1_of_nat int) ) 57.54/57.78 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 57.54/57.78 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 57.54/57.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (semiring_1_of_nat int) ) 57.54/57.78 ( (fun nat nat), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (minus_minus nat) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP _let_0 nat (finite_card X_b) A_3)))) (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3)))) ) 57.54/57.78 ( x_a, g ) 57.54/57.78 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27030 $$unsorted) (BOUND_VARIABLE_27031 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (ordered_ring X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27031) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27030) _let_2)))) (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27031))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27030))))) (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_27031) BOUND_VARIABLE_27030)))))))) ) 57.54/57.78 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.78 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.78 ( (fun x_a bool), g, g ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27069 $$unsorted) (BOUND_VARIABLE_27070 $$unsorted) (BOUND_VARIABLE_27071 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27069))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27070) BOUND_VARIABLE_27071))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_27070))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_27071)))))) ) 57.54/57.78 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.78 ) 57.54/57.78 (instantiation (forall ((Nat_3 $$unsorted) (Nat_4 $$unsorted)) (= (= Nat_3 Nat_4) (= (hAPP nat nat suc Nat_3) (hAPP nat nat suc Nat_4))) ) 57.54/57.78 ( (zero_zero nat), na ) 57.54/57.78 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 57.54/57.78 ( na, (zero_zero nat) ) 57.54/57.78 ( na, (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.78 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_27113 $$unsorted) (BOUND_VARIABLE_27114 $$unsorted) (BOUND_VARIABLE_27115 $$unsorted) (BOUND_VARIABLE_27116 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (minus_minus X_b))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (ord_less X_b))) (or (not (ordered_ab_group_add X_b)) (not (= (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_27113) BOUND_VARIABLE_27114) (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_27115) BOUND_VARIABLE_27116))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_27113) BOUND_VARIABLE_27114)) (hBOOL (hAPP X_b bool (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_27115) BOUND_VARIABLE_27116)))))))) ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (monoid_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.79 ( bool ) 57.54/57.79 ( nat ) 57.54/57.79 ( int ) 57.54/57.79 ( (fun x_a bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_1) J_1))) (not (hBOOL (hAPP nat bool Pa J_1))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I) J_1))) (not (hBOOL (hAPP nat bool Pa (hAPP nat nat suc I)))) (hBOOL (hAPP nat bool Pa I))) )) (hBOOL (hAPP nat bool Pa I_1))) ) 57.54/57.79 ( (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 A_2))) (= (or (hBOOL (hAPP _let_0 bool _let_3 A_3)) (= (ti X_b B_3) (ti X_b A_2))) (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_3) A_3)))))))) ) 57.54/57.79 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27446 $$unsorted) (BOUND_VARIABLE_27447 $$unsorted)) (or (not (dense_linorder X_a)) (not (forall ((X_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) X_2) BOUND_VARIABLE_27447))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) X_2) BOUND_VARIABLE_27446)))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_27447) BOUND_VARIABLE_27446))) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_3) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B_1) A_3))) (= (ti _let_0 B_1) (ti _let_0 A_3)))))) ) 57.54/57.79 ( x_a, g, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.79 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.79 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27504 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_27504) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_27504))) ) 57.54/57.79 ( bool, fFalse ) 57.54/57.79 ( bool, fTrue ) 57.54/57.79 ( nat, na ) 57.54/57.79 ( (fun (option com) com), (the_1 com) ) 57.54/57.79 ( pname, pn ) 57.54/57.79 ( (fun pname bool), u ) 57.54/57.79 ( int, (zero_zero int) ) 57.54/57.79 ( (fun int int), bit1 ) 57.54/57.79 ( (fun int int), succ ) 57.54/57.79 ( (fun nat nat), suc ) 57.54/57.79 ( (fun x_a bool), g ) 57.54/57.79 ( (fun int bool), nat_neg ) 57.54/57.79 ( (fun bool bool), fNot ) 57.54/57.79 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.79 ( (fun bool (fun bool bool)), fconj ) 57.54/57.79 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.79 ( (fun com x_a), mgt ) 57.54/57.79 ( (fun pname x_a), mgt_call ) 57.54/57.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.79 ( (fun pname (option com)), body ) 57.54/57.79 ( (fun com bool), wt ) 57.54/57.79 ( (fun int (fun int int)), nat_tsub ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27579 $$unsorted) (BOUND_VARIABLE_27580 $$unsorted) (BOUND_VARIABLE_27581 $$unsorted) (BOUND_VARIABLE_27582 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (or (not (ordere779506340up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27581) BOUND_VARIABLE_27582))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27579) BOUND_VARIABLE_27580))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_27581) BOUND_VARIABLE_27579)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_27582) BOUND_VARIABLE_27580)))))))) ) 57.54/57.79 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.54/57.79 ( int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (let ((_let_2 (fun X_b X_c))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (image X_b X_c))) (let ((_let_5 (hAPP _let_2 _let_3 _let_4 F))) (let ((_let_6 (hAPP _let_0 _let_1 _let_5 A_3))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (= _let_6 (hAPP _let_1 _let_1 (hAPP X_c (fun _let_1 _let_1) (insert X_c) (hAPP X_b X_c F X_1)) _let_6)))))))))) ) 57.54/57.79 ( x_a, pname, mgt_call, pn, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((M_1 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP nat int _let_0 (hAPP nat nat suc M_1)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int _let_0 M_1)))) ) 57.54/57.79 ( (zero_zero nat) ) 57.54/57.79 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.79 ( na ) 57.54/57.79 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (finite_finite_1 T_1)) (not (finite_finite_1 T_2)) (finite_finite_1 (fun T_2 T_1))) ) 57.54/57.79 ( bool, bool ) 57.54/57.79 ( bool, (fun bool bool) ) 57.54/57.79 ( nat, bool ) 57.54/57.79 ( nat, nat ) 57.54/57.79 ( nat, int ) 57.54/57.79 ( (fun nat bool), (fun int bool) ) 57.54/57.79 ( com, bool ) 57.54/57.79 ( com, x_a ) 57.54/57.79 ( (option com), com ) 57.54/57.79 ( pname, bool ) 57.54/57.79 ( pname, (option com) ) 57.54/57.79 ( pname, x_a ) 57.54/57.79 ( (fun pname bool), bool ) 57.54/57.79 ( (fun pname bool), (fun x_a bool) ) 57.54/57.79 ( int, bool ) 57.54/57.79 ( int, int ) 57.54/57.79 ( int, (fun int int) ) 57.54/57.79 ( x_a, bool ) 57.54/57.79 ( (fun x_a bool), bool ) 57.54/57.79 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.79 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (mult_zero X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.54/57.79 ( bool ) 57.54/57.79 ( nat ) 57.54/57.79 ( int ) 57.54/57.79 ( (fun x_a bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3)) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) A_3)) (hAPP nat nat suc (hAPP _let_0 nat _let_1 A_3)))))) ) 57.54/57.79 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_27696 $$unsorted) (BOUND_VARIABLE_27697 $$unsorted) (BOUND_VARIABLE_27698 $$unsorted) (BOUND_VARIABLE_27699 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (minus_minus X_b))) (or (not (ab_group_add X_b)) (not (= (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_27698) BOUND_VARIABLE_27699) (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_27696) BOUND_VARIABLE_27697))) (= (= (ti X_b BOUND_VARIABLE_27699) (ti X_b BOUND_VARIABLE_27698)) (= (ti X_b BOUND_VARIABLE_27697) (ti X_b BOUND_VARIABLE_27696)))))) ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27743 $$unsorted) (BOUND_VARIABLE_27744 $$unsorted)) (or (not (linordered_field X_a)) (not (forall ((E_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) E_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_27743) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_27744) E_2))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_27743) BOUND_VARIABLE_27744))) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.79 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_27781 $$unsorted) (BOUND_VARIABLE_27782 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (abs_abs X_a))) (let ((_let_5 (fun X_a X_a))) (let ((_let_6 (times_times X_a))) (or (not (ordered_ring_abs X_a)) (and (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27781) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27781)))) (and (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_27782) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_27782)))) (= (hAPP X_a X_a (hAPP X_a _let_5 _let_6 (hAPP X_a X_a _let_4 BOUND_VARIABLE_27782)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_27781)) (hAPP X_a X_a _let_4 (hAPP X_a X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_27782) BOUND_VARIABLE_27781))))))))))) ) 57.54/57.79 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.54/57.79 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ( (fun x_a bool), g, g ) 57.54/57.79 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_27816 $$unsorted)) (or (not (linordered_semidom X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (zero_zero X_b)) (hAPP nat X_b (semiring_1_of_nat X_b) BOUND_VARIABLE_27816))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_27816)))) ) 57.54/57.79 ( int, (one_one nat) ) 57.54/57.79 ( int, (zero_zero nat) ) 57.54/57.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_27867 $$unsorted) (BOUND_VARIABLE_27868 $$unsorted)) (let ((_let_0 (number_number_of X_b))) (or (not (ring_char_0 X_b)) (not (number_ring X_b)) (= (= (hAPP int X_b _let_0 BOUND_VARIABLE_27868) (hAPP int X_b _let_0 BOUND_VARIABLE_27867)) (= BOUND_VARIABLE_27867 BOUND_VARIABLE_27868)))) ) 57.54/57.79 ( nat, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ( nat, (hAPP int int bit1 (zero_zero int)), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ( nat, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ( int, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.79 ( int, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_b) (bot_bot _let_0)))) ) 57.54/57.79 ( bool ) 57.54/57.79 ( nat ) 57.54/57.79 ( com ) 57.54/57.79 ( pname ) 57.54/57.79 ( (fun pname bool) ) 57.54/57.79 ( int ) 57.54/57.79 ( x_a ) 57.54/57.79 ( (fun x_a bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_27992 $$unsorted) (BOUND_VARIABLE_27993 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (ring_n68954251visors X_b)) (= (or (= _let_0 (ti X_b BOUND_VARIABLE_27993)) (= _let_0 (ti X_b BOUND_VARIABLE_27992))) (= _let_0 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (times_times X_b) BOUND_VARIABLE_27992) BOUND_VARIABLE_27993))))) ) 57.54/57.79 ( bool, fFalse, fFalse ) 57.54/57.79 ( bool, fTrue, fTrue ) 57.54/57.79 ( nat, na, na ) 57.54/57.79 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.79 ( pname, pn, pn ) 57.54/57.79 ( (fun pname bool), u, u ) 57.54/57.79 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.79 ( (fun int int), bit1, bit1 ) 57.54/57.79 ( (fun int int), succ, succ ) 57.54/57.79 ( (fun nat nat), suc, suc ) 57.54/57.79 ( (fun x_a bool), g, g ) 57.54/57.79 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.79 ( (fun bool bool), fNot, fNot ) 57.54/57.79 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.79 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.79 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.79 ( (fun com x_a), mgt, mgt ) 57.54/57.79 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.79 ( (fun pname (option com)), body, body ) 57.54/57.79 ( (fun com bool), wt, wt ) 57.54/57.79 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted) (BOUND_VARIABLE_28030 $$unsorted)) (or (not (hBOOL (hAPP X_b bool Pa A_2))) (= (hAPP (fun X_b bool) X_b (the X_b) Pa) (ti X_b A_2)) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool Pa Y_1))) (= (ti X_b Y_1) (ti X_b BOUND_VARIABLE_28030))) )) (not (hBOOL (hAPP X_b bool Pa BOUND_VARIABLE_28030)))) ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ( (fun pname bool), u, (finite_finite pname), u ) 57.54/57.79 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.54/57.79 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.54/57.79 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 V))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) _let_1))) (= _let_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_1) (one_one nat))))))) ) 57.54/57.79 ( (zero_zero int) ) 57.54/57.79 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.79 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (minus_minus nat))) (or (not (= _let_0 (hAPP nat nat (hAPP nat _let_1 _let_2 M_1) N))) (not (= _let_0 (hAPP nat nat (hAPP nat _let_1 _let_2 N) M_1))) (= M_1 N))))) ) 57.54/57.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28071 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_28071) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_28071))) ) 57.54/57.79 ( bool, fFalse ) 57.54/57.79 ( bool, fTrue ) 57.54/57.79 ( nat, na ) 57.54/57.79 ( (fun (option com) com), (the_1 com) ) 57.54/57.79 ( pname, pn ) 57.54/57.79 ( (fun pname bool), u ) 57.54/57.79 ( int, (zero_zero int) ) 57.54/57.79 ( (fun int int), bit1 ) 57.54/57.79 ( (fun int int), succ ) 57.54/57.79 ( (fun nat nat), suc ) 57.54/57.79 ( (fun x_a bool), g ) 57.54/57.79 ( (fun int bool), nat_neg ) 57.54/57.79 ( (fun bool bool), fNot ) 57.54/57.79 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.79 ( (fun bool (fun bool bool)), fconj ) 57.54/57.79 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.79 ( (fun com x_a), mgt ) 57.54/57.79 ( (fun pname x_a), mgt_call ) 57.54/57.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.79 ( (fun pname (option com)), body ) 57.54/57.79 ( (fun com bool), wt ) 57.54/57.79 ( (fun int (fun int int)), nat_tsub ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_28100 $$unsorted) (BOUND_VARIABLE_28101 $$unsorted) (BOUND_VARIABLE_28102 $$unsorted) (BOUND_VARIABLE_28103 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (ord_less X_c))) (let ((_let_2 (hAPP X_c _let_0 _let_1 BOUND_VARIABLE_28100))) (or (not (order X_c)) (not (order X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_28102) BOUND_VARIABLE_28103))) (not (hBOOL (hAPP X_c bool _let_2 (hAPP X_b X_c BOUND_VARIABLE_28101 BOUND_VARIABLE_28102)))) (not (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) Y_1) X_2))) (hBOOL (hAPP X_c bool (hAPP X_c _let_0 (ord_less_eq X_c) (hAPP X_b X_c BOUND_VARIABLE_28101 Y_1)) (hAPP X_b X_c BOUND_VARIABLE_28101 X_2)))) )) (hBOOL (hAPP X_c bool _let_2 (hAPP X_b X_c BOUND_VARIABLE_28101 BOUND_VARIABLE_28103))))))) ) 57.54/57.79 ( int, int, (zero_zero int), bit1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (= (hAPP _let_0 nat (finite_card nat) (hAPP _let_0 _let_0 (collect nat) (hAPP nat _let_0 (hAPP _let_1 _let_1 (combc nat nat bool) (ord_less_eq nat)) Na))) (hAPP nat nat suc Na)))) ) 57.54/57.79 ( (zero_zero nat) ) 57.54/57.79 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.79 ( na ) 57.54/57.79 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (= (= (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F) A_3) (bot_bot _let_0)) (= (ti _let_1 A_3) (bot_bot _let_1))))) ) 57.54/57.79 ( nat, int, (semiring_1_of_nat int), (bot_bot (fun nat bool)) ) 57.54/57.79 ( pname, x_a, mgt_call, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (K $$unsorted)) (= (not (forall ((B_5 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (= (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_5) B_4) (ti _let_0 A_3))) (not (= K (hAPP _let_0 nat (finite_card X_b) B_4))) (and (= (zero_zero nat) K) (not (= (ti _let_0 B_4) (bot_bot _let_0)))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) B_5) B_4)))) )) (= (hAPP nat nat suc K) (hAPP (fun X_b bool) nat (finite_card X_b) A_3))) ) 57.54/57.79 ( x_a, g, na ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (zero_zero nat) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((K_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) K_1)) K_1) (hAPP int int bit1 K_1)))) ) 57.54/57.79 ( (zero_zero int) ) 57.54/57.79 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))))) ) 57.54/57.79 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((N $$unsorted) (K_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (let ((_let_4 (hAPP nat _let_0 _let_1 K_1))) (let ((_let_5 (hAPP nat _let_2 _let_3 M_1))) (or (not (hBOOL (hAPP nat bool _let_4 M_1))) (not (hBOOL (hAPP nat bool _let_4 N))) (= (hAPP nat nat _let_5 N) (hAPP nat nat (hAPP nat _let_2 _let_3 (hAPP nat nat _let_5 K_1)) (hAPP nat nat (hAPP nat _let_2 _let_3 N) K_1)))))))))) ) 57.54/57.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28199 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_28199)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_28199))))) ) 57.54/57.79 ( nat, (zero_zero int) ) 57.54/57.79 ( int, (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (bot_bot X_b))) (or (not (bot X_b)) (= _let_0 (ti X_b _let_0)))) ) 57.54/57.79 ( bool ) 57.54/57.79 ( nat ) 57.54/57.79 ( (fun nat bool) ) 57.54/57.79 ( (fun int bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_28238 $$unsorted) (BOUND_VARIABLE_28239 $$unsorted) (BOUND_VARIABLE_28240 $$unsorted) (BOUND_VARIABLE_28241 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_28239))) (or (not (order X_b)) (not (order X_c)) (not (hBOOL (hAPP X_b bool _let_2 (hAPP X_c X_b BOUND_VARIABLE_28240 BOUND_VARIABLE_28241)))) (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) BOUND_VARIABLE_28241) BOUND_VARIABLE_28238))) (not (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) X_2) Y_1))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_c X_b BOUND_VARIABLE_28240 X_2)) (hAPP X_c X_b BOUND_VARIABLE_28240 Y_1)))) )) (hBOOL (hAPP X_b bool _let_2 (hAPP X_c X_b BOUND_VARIABLE_28240 BOUND_VARIABLE_28238))))))) ) 57.54/57.79 ( int, int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), bit1, (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_28360 $$unsorted) (BOUND_VARIABLE_28361 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_b))) (or (not (linordered_semidom X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP nat X_b _let_0 BOUND_VARIABLE_28360)) (hAPP nat X_b _let_0 BOUND_VARIABLE_28361))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_28360) BOUND_VARIABLE_28361))))) ) 57.54/57.79 ( int, (one_one nat), (one_one nat) ) 57.54/57.79 ( int, (one_one nat), (zero_zero nat) ) 57.54/57.79 ( int, (zero_zero nat), (one_one nat) ) 57.54/57.79 ( int, (zero_zero nat), (zero_zero nat) ) 57.54/57.79 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (ring_1 X_b)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) (zero_zero X_b)) (ring_1_Ints X_b))))) ) 57.54/57.79 ( nat ) 57.54/57.79 ( pname ) 57.54/57.79 ( int ) 57.54/57.79 ( x_a ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (not (forall ((I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I) J_2))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat F I)) (hAPP nat nat F J_2))))) )) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_1) J_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat F I_1)) (hAPP nat nat F J_1)))))) ) 57.54/57.79 ( (zero_zero nat), (zero_zero nat), suc ) 57.54/57.79 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)), suc ) 57.54/57.79 ( na, na, suc ) 57.54/57.79 ( (hAPP nat nat suc na), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))) ) 57.54/57.79 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), suc ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((BOUND_VARIABLE_28450 $$unsorted) (BOUND_VARIABLE_28451 $$unsorted)) (let ((_let_0 (fun BOUND_VARIABLE_28450 bool))) (let ((_let_1 (fun _let_0 nat))) (let ((_let_2 (fun BOUND_VARIABLE_28450 nat))) (let ((_let_3 (fun nat _let_1))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite BOUND_VARIABLE_28450) BOUND_VARIABLE_28451))) (= (hAPP _let_0 nat (finite_card BOUND_VARIABLE_28450) BOUND_VARIABLE_28451) (hAPP _let_0 nat (hAPP nat _let_1 (hAPP _let_2 _let_3 (hAPP (fun nat (fun nat nat)) (fun _let_2 _let_3) (finite_fold_image nat BOUND_VARIABLE_28450) (plus_plus nat)) (hAPP nat _let_2 (combk nat BOUND_VARIABLE_28450) (one_one nat))) (zero_zero nat)) BOUND_VARIABLE_28451))))))) ) 57.54/57.79 ( pname, u ) 57.54/57.79 ( x_a, g ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (insert X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 A_2))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) A_3))) (= (ti _let_0 A_3) (hAPP _let_0 _let_0 _let_3 (hAPP _let_0 _let_0 (hAPP _let_0 _let_1 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 _let_3 (bot_bot _let_0)))))))))) ) 57.54/57.79 ( pname, pn, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_3))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat (finite_card X_c) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_3))) (hAPP _let_1 nat (finite_card X_b) A_3)))))) ) 57.54/57.79 ( int, nat, (semiring_1_of_nat int), (bot_bot (fun nat bool)) ) 57.54/57.79 ( x_a, pname, mgt_call, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_28623 $$unsorted) (BOUND_VARIABLE_28624 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (linorder X_b)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_28623) BOUND_VARIABLE_28624)) (= (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_28624) BOUND_VARIABLE_28623))) (= (ti X_b BOUND_VARIABLE_28623) (ti X_b BOUND_VARIABLE_28624)))))) ) 57.54/57.79 ( int, (one_one int), (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M_1))) (= (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) N)) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int _let_0 M_1)) (hAPP nat int _let_0 N))))) ) 57.54/57.79 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((BOUND_VARIABLE_28668 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) BOUND_VARIABLE_28668)))) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_28668)))) ) 57.54/57.79 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28776 $$unsorted) (BOUND_VARIABLE_28777 $$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 (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28777) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28776) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_28777) BOUND_VARIABLE_28776)) _let_2)))))) ) 57.54/57.79 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28807 $$unsorted) (BOUND_VARIABLE_28808 $$unsorted) (BOUND_VARIABLE_28809 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_28807))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28808) BOUND_VARIABLE_28809))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_28807))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_28808)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_28809))))))))) ) 57.54/57.79 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (member X_b))) (= _let_0 (ti (fun X_b (fun (fun X_b bool) bool)) _let_0))) ) 57.54/57.79 ( pname ) 57.54/57.79 ( x_a ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((Na $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (ord_less_eq nat))) (let ((_let_3 (fun nat nat))) (let ((_let_4 (minus_minus nat))) (let ((_let_5 (hAPP nat _let_0 _let_2 K))) (or (not (hBOOL (hAPP nat bool _let_5 M))) (not (hBOOL (hAPP nat bool _let_5 Na))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_3 _let_4 M) K)) (hAPP nat nat (hAPP nat _let_3 _let_4 Na) K))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) Na)))))))))) ) 57.54/57.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28846 $$unsorted) (BOUND_VARIABLE_28847 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_28846)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_28847)))) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_28846) BOUND_VARIABLE_28847)))))))) ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (not (forall ((N_1 $$unsorted) (F_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun X_b bool))) (not (= (ti _let_2 A_3) (hAPP _let_0 _let_2 (hAPP (fun nat X_b) (fun _let_0 _let_2) (image nat X_b) F_2) (hAPP _let_0 _let_0 (collect nat) (hAPP nat _let_0 (hAPP _let_1 _let_1 (combc nat nat bool) (ord_less nat)) N_1)))))))) )) (hBOOL (hAPP (fun X_b bool) bool (finite_finite X_b) A_3))) ) 57.54/57.79 ( pname, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28881 $$unsorted) (BOUND_VARIABLE_28882 $$unsorted)) (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))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_28882))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_28881))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28881) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_28882) BOUND_VARIABLE_28881)) BOUND_VARIABLE_28882))))))) ) 57.54/57.79 ( int, (one_one int), (one_one int) ) 57.54/57.79 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (= (bot_bot _let_0) (ti _let_0 A_3)) (forall ((X_2 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_3))) ))) ) 57.54/57.79 ( bool, fNot ) 57.54/57.79 ( com, wt ) 57.54/57.79 ( pname, u ) 57.54/57.79 ( int, nat_neg ) 57.54/57.79 ( x_a, g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28916 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_28916) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_28916))) ) 57.54/57.79 ( bool, fFalse ) 57.54/57.79 ( bool, fTrue ) 57.54/57.79 ( nat, na ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ( (fun (option com) com), (the_1 com) ) 57.54/57.79 ( pname, pn ) 57.54/57.79 ( (fun pname bool), u ) 57.54/57.79 ( int, (zero_zero int) ) 57.54/57.79 ( (fun int int), bit1 ) 57.54/57.79 ( (fun int int), succ ) 57.54/57.79 ( (fun nat nat), suc ) 57.54/57.79 ( (fun x_a bool), g ) 57.54/57.79 ( (fun int bool), nat_neg ) 57.54/57.79 ( (fun bool bool), fNot ) 57.54/57.79 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.79 ( (fun bool (fun bool bool)), fconj ) 57.54/57.79 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.79 ( (fun com x_a), mgt ) 57.54/57.79 ( (fun pname x_a), mgt_call ) 57.54/57.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.79 ( (fun pname (option com)), body ) 57.54/57.79 ( (fun com bool), wt ) 57.54/57.79 ( (fun int (fun int int)), nat_tsub ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_b) A_3)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (= (bot_bot _let_0) (ti _let_0 A_3))))) ) 57.54/57.79 ( bool, fNot ) 57.54/57.79 ( com, wt ) 57.54/57.79 ( pname, u ) 57.54/57.79 ( int, nat_neg ) 57.54/57.79 ( x_a, g ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat _let_0 (ord_less nat) X_2) (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc X_2)))) ) 57.54/57.79 ( (zero_zero nat) ) 57.54/57.79 ( (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.79 ( na ) 57.54/57.79 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M) Na)) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) Na))) ) 57.54/57.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28954 $$unsorted) (BOUND_VARIABLE_28955 $$unsorted) (BOUND_VARIABLE_28956 $$unsorted) (BOUND_VARIABLE_28957 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28956) BOUND_VARIABLE_28957))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_28954) BOUND_VARIABLE_28955))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_28956) BOUND_VARIABLE_28954)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_28957) BOUND_VARIABLE_28955)))))))) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (one_one int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 A_2))) (or (and (not (hBOOL (hAPP _let_0 bool _let_3 B_1))) (not (= (ti X_b B_3) (ti X_b A_2)))) (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_3) B_1)))))))) ) 57.54/57.79 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_28991 $$unsorted) (BOUND_VARIABLE_28992 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_28991)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_28992))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_28991) BOUND_VARIABLE_28992)))))))) ) 57.54/57.79 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((Pa $$unsorted) (I_1 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I_1) K))) (not (hBOOL (hAPP int bool Pa K))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I) K))) (not (hBOOL (hAPP int bool Pa I))) (hBOOL (hAPP int bool Pa (hAPP int int (hAPP int (fun int int) (minus_minus int) I) (one_one int))))) )) (hBOOL (hAPP int bool Pa I_1))) ) 57.54/57.79 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int), (one_one int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (= (= (ti _let_0 B_1) (ti _let_0 A_3)) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_3) B_1)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B_1) A_3))))))) ) 57.54/57.79 ( bool, fNot, fNot ) 57.54/57.79 ( com, wt, wt ) 57.54/57.79 ( pname, u, u ) 57.54/57.79 ( int, nat_neg, nat_neg ) 57.54/57.79 ( x_a, g, g ) 57.54/57.79 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.79 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Y) X))) (= (hAPP int int (hAPP int _let_0 (minus_minus int) X) Y) (hAPP int int (hAPP int _let_0 nat_tsub X) Y)))) ) 57.54/57.79 ( (zero_zero int), (one_one int) ) 57.54/57.79 ( (zero_zero int), (zero_zero int) ) 57.54/57.79 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (collect X_b) Pa) (ti _let_0 Pa))) ) 57.54/57.79 ( bool, fNot ) 57.54/57.79 ( com, wt ) 57.54/57.79 ( pname, u ) 57.54/57.79 ( int, nat_neg ) 57.54/57.79 ( x_a, g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29167 $$unsorted) (BOUND_VARIABLE_29168 $$unsorted)) (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))) (or (not (ordere453448008miring X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29167) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_29168)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29168) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_29167))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_29168) BOUND_VARIABLE_29167)) _let_2))))))) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29206 $$unsorted) (BOUND_VARIABLE_29207 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_b))) (or (not (semiring_char_0 X_b)) (= (= BOUND_VARIABLE_29206 BOUND_VARIABLE_29207) (= (hAPP nat X_b _let_0 BOUND_VARIABLE_29207) (hAPP nat X_b _let_0 BOUND_VARIABLE_29206))))) ) 57.54/57.79 ( int, (one_one nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (one_one nat) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (number_number_of X_b))) (or (not (number X_b)) (= _let_0 (ti (fun int X_b) _let_0)))) ) 57.54/57.79 ( bool ) 57.54/57.79 ( nat ) 57.54/57.79 ( int ) 57.54/57.79 ( (fun int int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (combk X_a X_b))) (= _let_0 (ti (fun X_a (fun X_b X_a)) _let_0))) ) 57.54/57.79 ( bool, bool ) 57.54/57.79 ( bool, nat ) 57.54/57.79 ( bool, com ) 57.54/57.79 ( bool, pname ) 57.54/57.79 ( bool, (fun pname bool) ) 57.54/57.79 ( bool, int ) 57.54/57.79 ( bool, x_a ) 57.54/57.79 ( bool, (fun x_a bool) ) 57.54/57.79 ( nat, nat ) 57.54/57.79 ( com, (option com) ) 57.54/57.79 ( (option com), pname ) 57.54/57.79 ( int, nat ) 57.54/57.79 ( int, int ) 57.54/57.79 ( (fun int int), int ) 57.54/57.79 ( x_a, com ) 57.54/57.79 ( x_a, pname ) 57.54/57.79 ( (fun x_a bool), (fun pname bool) ) 57.54/57.79 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.79 ( (fun int bool), (fun nat bool) ) 57.54/57.79 ( (fun bool bool), bool ) 57.54/57.79 ( (fun (fun x_a bool) bool), (fun x_a bool) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29305 $$unsorted) (BOUND_VARIABLE_29306 $$unsorted) (BOUND_VARIABLE_29307 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (zero_zero X_b))) (let ((_let_3 (fun X_b X_b))) (let ((_let_4 (times_times X_b))) (or (not (linord581940658strict X_b)) (= (or (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_29306) _let_2)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_29307) BOUND_VARIABLE_29305))) (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_2) BOUND_VARIABLE_29306)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_29305) BOUND_VARIABLE_29307)))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 BOUND_VARIABLE_29305) BOUND_VARIABLE_29306)) (hAPP X_b X_b (hAPP X_b _let_3 _let_4 BOUND_VARIABLE_29307) BOUND_VARIABLE_29306)))))))))) ) 57.54/57.79 ( int, (one_one int), (zero_zero int), (zero_zero int) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 X_1))) (let ((_let_4 (hBOOL (hAPP _let_0 bool _let_3 A_3)))) (let ((_let_5 (ord_less_eq _let_0))) (let ((_let_6 (hAPP _let_0 _let_1 _let_5 A_3))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (insert X_b))) (let ((_let_9 (hAPP X_b _let_7 _let_8 X_1))) (= (and (or _let_4 (hBOOL (hAPP _let_0 bool _let_6 B_1))) (or (not _let_4) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_5 (hAPP _let_0 _let_0 (hAPP _let_0 _let_7 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 _let_9 (bot_bot _let_0)))) B_1)))) (hBOOL (hAPP _let_0 bool _let_6 (hAPP _let_0 _let_0 _let_9 B_1)))))))))))))) ) 57.54/57.79 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29350 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (let ((_let_1 (hAPP nat X_a _let_0 BOUND_VARIABLE_29350))) (or (not (linordered_idom X_a)) (= _let_1 (hAPP X_a X_a (abs_abs X_a) _let_1))))) ) 57.54/57.79 ( int, (one_one nat) ) 57.54/57.79 ( int, (zero_zero nat) ) 57.54/57.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (= (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_3) B_1)) (not (= (ti _let_0 B_1) (ti _let_0 A_3)))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less _let_0) A_3) B_1))))) ) 57.54/57.79 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.54/57.79 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29437 $$unsorted) (BOUND_VARIABLE_29438 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_b))) (or (not (linordered_semidom X_b)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_29437) BOUND_VARIABLE_29438)) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) (hAPP nat X_b _let_0 BOUND_VARIABLE_29437)) (hAPP nat X_b _let_0 BOUND_VARIABLE_29438)))))) ) 57.54/57.79 ( int, (zero_zero nat), (one_one nat) ) 57.54/57.79 ( int, (zero_zero nat), (zero_zero nat) ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (= (ti X_a X) (ti X_a Y)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (fequal X_a) X) Y)))) ) 57.54/57.79 ( bool, fFalse, fTrue ) 57.54/57.79 ( bool, fTrue, fFalse ) 57.54/57.79 ( (fun int int), bit1, succ ) 57.54/57.79 ( (fun int int), succ, bit1 ) 57.54/57.79 ( (fun bool (fun bool bool)), fconj, fimplies ) 57.54/57.79 ( (fun bool (fun bool bool)), fimplies, fconj ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 (hAPP X_b _let_2 (insert X_b) X_1) (bot_bot _let_0))))) (hAPP _let_0 nat _let_1 A_3)))))) ) 57.54/57.79 ( pname, pn, u ) 57.54/57.79 ) 57.54/57.79 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29477 $$unsorted) (BOUND_VARIABLE_29478 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (linorder X_b)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_29477) BOUND_VARIABLE_29478)) (= (= (ti X_b BOUND_VARIABLE_29477) (ti X_b BOUND_VARIABLE_29478)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_29477) BOUND_VARIABLE_29478))))) ) 57.54/57.79 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.79 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.79 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B_1) A_3))) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (minus_minus _let_0) A_3) B_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_0 nat _let_1 A_3)) (hAPP _let_0 nat _let_1 B_1)))))) ) 57.54/57.80 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29511 $$unsorted) (BOUND_VARIABLE_29512 $$unsorted) (BOUND_VARIABLE_29513 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (semiri532925092at_aux X_b))) (let ((_let_3 (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_29511))) (or (not (semiring_1 X_b)) (= (hAPP X_b X_b (hAPP nat _let_0 _let_3 BOUND_VARIABLE_29512) (hAPP X_b X_b BOUND_VARIABLE_29511 BOUND_VARIABLE_29513)) (hAPP X_b X_b (hAPP nat _let_0 _let_3 (hAPP nat nat suc BOUND_VARIABLE_29512)) BOUND_VARIABLE_29513))))))) ) 57.54/57.80 ( int, bit1, (zero_zero nat), (zero_zero int) ) 57.54/57.80 ( int, bit1, na, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.80 ( int, (number_number_of int), (hAPP nat nat suc (zero_zero nat)), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ( int, (number_number_of int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero int) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (insert X_b))) (= _let_1 (ti (fun X_b (fun _let_0 _let_0)) _let_1)))) ) 57.54/57.80 ( bool ) 57.54/57.80 ( nat ) 57.54/57.80 ( com ) 57.54/57.80 ( pname ) 57.54/57.80 ( (fun pname bool) ) 57.54/57.80 ( int ) 57.54/57.80 ( x_a ) 57.54/57.80 ( (fun x_a bool) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29568 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_29568)) (zero_zero X_a))))) ) 57.54/57.80 ( int, (one_one nat) ) 57.54/57.80 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29586 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_29586) (hAPP int X_a (number_number_of X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_29586)))) ) 57.54/57.80 ( nat, (one_one nat) ) 57.54/57.80 ( nat, (zero_zero nat) ) 57.54/57.80 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (or (not (= (ti _let_0 B_1) (ti _let_0 A_3))) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_3) B_1)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B_1) A_3))))))) ) 57.54/57.80 ( bool, fNot, fNot ) 57.54/57.80 ( com, wt, wt ) 57.54/57.80 ( pname, u, u ) 57.54/57.80 ( int, nat_neg, nat_neg ) 57.54/57.80 ( x_a, g, g ) 57.54/57.80 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.54/57.80 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3)) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) A_3)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP _let_0 nat _let_1 A_3)))))) ) 57.54/57.80 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((BOUND_VARIABLE_29698 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 BOUND_VARIABLE_29698))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) BOUND_VARIABLE_29698))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_1) _let_1)) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_29698)))))) ) 57.54/57.80 ( (zero_zero int) ) 57.54/57.80 ( (hAPP int int bit1 (zero_zero int)) ) 57.54/57.80 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((BOUND_VARIABLE_29712 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) BOUND_VARIABLE_29712)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 BOUND_VARIABLE_29712)))) ) 57.54/57.80 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((Pa $$unsorted)) (hBOOL Pa) ) 57.54/57.80 ( fFalse ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (order T_1)) (order (fun T_2 T_1))) ) 57.54/57.80 ( bool, bool ) 57.54/57.80 ( bool, (fun bool bool) ) 57.54/57.80 ( nat, bool ) 57.54/57.80 ( nat, nat ) 57.54/57.80 ( nat, int ) 57.54/57.80 ( (fun nat bool), (fun int bool) ) 57.54/57.80 ( com, bool ) 57.54/57.80 ( com, x_a ) 57.54/57.80 ( (option com), com ) 57.54/57.80 ( pname, bool ) 57.54/57.80 ( pname, (option com) ) 57.54/57.80 ( pname, x_a ) 57.54/57.80 ( (fun pname bool), bool ) 57.54/57.80 ( (fun pname bool), (fun x_a bool) ) 57.54/57.80 ( int, bool ) 57.54/57.80 ( int, int ) 57.54/57.80 ( int, (fun int int) ) 57.54/57.80 ( x_a, bool ) 57.54/57.80 ( (fun x_a bool), bool ) 57.54/57.80 ( (fun x_a bool), (fun x_a bool) ) 57.54/57.80 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29809 $$unsorted) (BOUND_VARIABLE_29810 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_29810))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_29809))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29809) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_29809) BOUND_VARIABLE_29810)) BOUND_VARIABLE_29810))))))) ) 57.54/57.80 ( int, (one_one int), (one_one int) ) 57.54/57.80 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_29842 $$unsorted) (BOUND_VARIABLE_29843 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_29842) BOUND_VARIABLE_29843)) (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_29842) BOUND_VARIABLE_29843)) (not (= (ti X_b BOUND_VARIABLE_29843) (ti X_b BOUND_VARIABLE_29842))))))) ) 57.54/57.80 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ( int, (zero_zero int), (one_one int) ) 57.54/57.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.54/57.80 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29912 $$unsorted) (BOUND_VARIABLE_29913 $$unsorted) (BOUND_VARIABLE_29914 $$unsorted) (BOUND_VARIABLE_29915 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_29914) BOUND_VARIABLE_29915))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_29912) BOUND_VARIABLE_29913))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_29914) BOUND_VARIABLE_29912)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_29915) BOUND_VARIABLE_29913)))))))) ) 57.54/57.80 ( int, (zero_zero int), (one_one int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_29954 $$unsorted) (BOUND_VARIABLE_29955 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (no_zero_divisors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_29955)) (= _let_0 (ti X_a BOUND_VARIABLE_29954)) (not (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_29955) BOUND_VARIABLE_29954))))) ) 57.54/57.80 ( bool, fFalse, fFalse ) 57.54/57.80 ( bool, fTrue, fTrue ) 57.54/57.80 ( nat, na, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.80 ( pname, pn, pn ) 57.54/57.80 ( (fun pname bool), u, u ) 57.54/57.80 ( (fun int int), bit1, bit1 ) 57.54/57.80 ( (fun int int), succ, succ ) 57.54/57.80 ( (fun nat nat), suc, suc ) 57.54/57.80 ( (fun x_a bool), g, g ) 57.54/57.80 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.80 ( (fun bool bool), fNot, fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.80 ( (fun com x_a), mgt, mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.80 ( (fun pname (option com)), body, body ) 57.54/57.80 ( (fun com bool), wt, wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30064 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_30064) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_30064))) ) 57.54/57.80 ( bool, fFalse ) 57.54/57.80 ( bool, fTrue ) 57.54/57.80 ( nat, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( (fun pname bool), u ) 57.54/57.80 ( int, (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1 ) 57.54/57.80 ( (fun int int), succ ) 57.54/57.80 ( (fun nat nat), suc ) 57.54/57.80 ( (fun x_a bool), g ) 57.54/57.80 ( (fun int bool), nat_neg ) 57.54/57.80 ( (fun bool bool), fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.80 ( (fun com x_a), mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.80 ( (fun pname (option com)), body ) 57.54/57.80 ( (fun com bool), wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((Na $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (let ((_let_4 (hAPP nat _let_0 _let_1 K))) (or (not (hBOOL (hAPP nat bool _let_4 M))) (not (hBOOL (hAPP nat bool _let_4 Na))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_2 _let_3 M) K)) (hAPP nat nat (hAPP nat _let_2 _let_3 Na) K))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) Na))))))))) ) 57.54/57.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30234 $$unsorted) (BOUND_VARIABLE_30243 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (semiring_1_of_nat X_a))) (or (not (number_ring X_a)) (and (or (hBOOL (hAPP int bool nat_neg (hAPP int int _let_1 BOUND_VARIABLE_30234))) (= (hAPP nat X_a _let_2 (hAPP int nat _let_0 BOUND_VARIABLE_30234)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_30234))) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int _let_1 BOUND_VARIABLE_30243)))) (= (zero_zero X_a) (hAPP nat X_a _let_2 (hAPP int nat _let_0 BOUND_VARIABLE_30243))))))))) ) 57.54/57.80 ( int, (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (P $$unsorted)) (= (ti X_a P) (hAPP X_a X_a (combi X_a) P)) ) 57.54/57.80 ( bool, fFalse ) 57.54/57.80 ( bool, fTrue ) 57.54/57.80 ( nat, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( (fun pname bool), u ) 57.54/57.80 ( int, (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1 ) 57.54/57.80 ( (fun int int), succ ) 57.54/57.80 ( (fun nat nat), suc ) 57.54/57.80 ( (fun x_a bool), g ) 57.54/57.80 ( (fun int bool), nat_neg ) 57.54/57.80 ( (fun bool bool), fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.80 ( (fun com x_a), mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.80 ( (fun pname (option com)), body ) 57.54/57.80 ( (fun com bool), wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((Ts $$unsorted) (G_1 $$unsorted)) (let ((_let_0 (fun x_a bool))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) Ts) G_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 p G_1) Ts))))) ) 57.54/57.80 ( g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_0 (hAPP X_a X_c B_1_1 B_2_1))) (= _let_0 (ti X_c _let_0))) ) 57.54/57.80 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ( bool, (fun pname bool), (finite_finite pname), u ) 57.54/57.80 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int) ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ( bool, int, nat_neg, (one_one int) ) 57.54/57.80 ( bool, int, nat_neg, (hAPP int int (number_number_of int) (zero_zero int)) ) 57.54/57.80 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.54/57.80 ( bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( bool, (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g ) 57.54/57.80 ( bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( nat, nat, suc, (zero_zero nat) ) 57.54/57.80 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 57.54/57.80 ( nat, nat, suc, na ) 57.54/57.80 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.54/57.80 ( nat, nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), (hAPP nat nat suc na) ) 57.54/57.80 ( nat, int, (number_number_of nat), (zero_zero int) ) 57.54/57.80 ( nat, int, (number_number_of nat), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.80 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ( nat, (fun x_a bool), (finite_card x_a), g ) 57.54/57.80 ( nat, (fun x_a bool), (finite_card x_a), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.54/57.80 ( (fun nat bool), nat, (ord_less_eq nat), (hAPP nat nat suc na) ) 57.54/57.80 ( (fun (fun pname bool) bool), pname, (member pname), pn ) 57.54/57.80 ( int, nat, (semiring_1_of_nat int), (one_one nat) ) 57.54/57.80 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ( int, int, bit1, (zero_zero int) ) 57.54/57.80 ( int, int, bit1, (hAPP int int bit1 (zero_zero int)) ) 57.54/57.80 ( int, int, (number_number_of int), (hAPP int int bit1 (zero_zero int)) ) 57.54/57.80 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ( int, int, succ, (zero_zero int) ) 57.54/57.80 ( (fun nat nat), nat, (minus_minus nat), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ( x_a, pname, mgt_call, pn ) 57.54/57.80 ( (fun x_a bool), (fun pname bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u ) 57.54/57.80 ( (fun x_a bool), (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn))), g ) 57.54/57.80 ( (fun int bool), (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) (fun int bool)) (image nat int) (semiring_1_of_nat int)), (bot_bot (fun nat bool)) ) 57.54/57.80 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 57.54/57.80 ( (fun int bool), int, (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 57.54/57.80 ( (fun (fun nat bool) (fun int bool)), (fun nat int), (image nat int), (semiring_1_of_nat int) ) 57.54/57.80 ( (fun (fun x_a bool) bool), x_a, (member x_a), (hAPP pname x_a mgt_call pn) ) 57.54/57.80 ( (fun (fun x_a bool) bool), (fun x_a bool), (ord_less_eq (fun x_a bool)), g ) 57.54/57.80 ( (fun (fun x_a bool) bool), (fun x_a bool), (ord_less_eq (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), x_a, (insert x_a), (hAPP pname x_a mgt_call pn) ) 57.54/57.80 ( (fun (fun pname bool) (fun x_a bool)), (fun pname x_a), (image pname x_a), mgt_call ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30512 $$unsorted) (BOUND_VARIABLE_30513 $$unsorted) (BOUND_VARIABLE_30514 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30513) BOUND_VARIABLE_30514))) (not (= (ti X_a BOUND_VARIABLE_30513) (ti X_a BOUND_VARIABLE_30512))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30512) BOUND_VARIABLE_30514))))) ) 57.54/57.80 ( nat, na, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (= (not (forall ((K_2 $$unsorted)) (not (= Na (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) K_2))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M) Na))) ) 57.54/57.80 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (semiring_1_of_nat int))) (= (and (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Y_2) X_1))) (hBOOL (hAPP int bool Pa (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int _let_1 X_1)) (hAPP nat int _let_1 Y_2))))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) X_1) Y_2))) (hBOOL (hAPP int bool Pa (zero_zero int))))) (hBOOL (hAPP int bool Pa (hAPP nat int _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) X_1) Y_2))))))) ) 57.54/57.80 ( nat_neg, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) Na))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Na) (hAPP nat nat suc M))) (= M Na)))) ) 57.54/57.80 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (let ((_let_2 (fun X_b X_c))) (= (hAPP X_b X_c (hAPP X_a _let_2 P R) (hAPP X_a X_b Q R)) (hAPP X_a X_c (hAPP _let_0 _let_1 (hAPP (fun X_a _let_2) (fun _let_0 _let_1) (combs X_a X_b X_c) P) Q) R))))) ) 57.54/57.80 ( nat, bool, nat, (ord_less_eq nat), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), (hAPP nat nat suc na) ) 57.54/57.80 ( int, bool, int, (ord_less_eq int), bit1, (zero_zero int) ) 57.54/57.80 ( int, bool, int, (ord_less_eq int), bit1, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.54/57.80 ( int, bool, int, (ord_less_eq int), (number_number_of int), (zero_zero int) ) 57.54/57.80 ( int, bool, int, (ord_less_eq int), succ, (zero_zero int) ) 57.54/57.80 ( int, bool, int, (ord_less int), (number_number_of int), (zero_zero int) ) 57.54/57.80 ( int, bool, int, (ord_less int), succ, (zero_zero int) ) 57.54/57.80 ( (fun x_a bool), bool, (fun x_a bool), (ord_less_eq (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn))), g ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_30696 $$unsorted) (BOUND_VARIABLE_30697 $$unsorted)) (or (not (ab_group_add X_b)) (= (= (ti X_b BOUND_VARIABLE_30697) (ti X_b BOUND_VARIABLE_30696)) (= (zero_zero X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) BOUND_VARIABLE_30696) BOUND_VARIABLE_30697)))) ) 57.54/57.80 ( bool, fFalse, fFalse ) 57.54/57.80 ( bool, fTrue, fTrue ) 57.54/57.80 ( nat, na, na ) 57.54/57.80 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.80 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.80 ( pname, pn, pn ) 57.54/57.80 ( (fun pname bool), u, u ) 57.54/57.80 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1, bit1 ) 57.54/57.80 ( (fun int int), succ, succ ) 57.54/57.80 ( (fun nat nat), suc, suc ) 57.54/57.80 ( (fun x_a bool), g, g ) 57.54/57.80 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.80 ( (fun bool bool), fNot, fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.80 ( (fun com x_a), mgt, mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.80 ( (fun pname (option com)), body, body ) 57.54/57.80 ( (fun com bool), wt, wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_30733 $$unsorted) (BOUND_VARIABLE_30734 $$unsorted)) (or (not (semiri456707255roduct X_b)) (= (= (ti X_b BOUND_VARIABLE_30733) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_30733) BOUND_VARIABLE_30734)) (= (zero_zero X_b) (ti X_b BOUND_VARIABLE_30734)))) ) 57.54/57.80 ( bool, fFalse, fFalse ) 57.54/57.80 ( bool, fTrue, fTrue ) 57.54/57.80 ( nat, na, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.80 ( pname, pn, pn ) 57.54/57.80 ( (fun pname bool), u, u ) 57.54/57.80 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1, bit1 ) 57.54/57.80 ( (fun int int), succ, succ ) 57.54/57.80 ( (fun nat nat), suc, suc ) 57.54/57.80 ( (fun x_a bool), g, g ) 57.54/57.80 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.80 ( (fun bool bool), fNot, fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.80 ( (fun com x_a), mgt, mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.80 ( (fun pname (option com)), body, body ) 57.54/57.80 ( (fun com bool), wt, wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (ring_1 X_b)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) (one_one X_b)) (ring_1_Ints X_b))))) ) 57.54/57.80 ( nat ) 57.54/57.80 ( pname ) 57.54/57.80 ( int ) 57.54/57.80 ( x_a ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 X_b (the X_b) (hAPP X_b _let_0 (fequal X_b) X_1)) (ti X_b X_1))) ) 57.54/57.80 ( bool, fFalse ) 57.54/57.80 ( bool, fTrue ) 57.54/57.80 ( nat, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( (fun pname bool), u ) 57.54/57.80 ( int, (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1 ) 57.54/57.80 ( (fun int int), succ ) 57.54/57.80 ( (fun nat nat), suc ) 57.54/57.80 ( (fun x_a bool), g ) 57.54/57.80 ( (fun int bool), nat_neg ) 57.54/57.80 ( (fun bool bool), fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.80 ( (fun com x_a), mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.80 ( (fun pname (option com)), body ) 57.54/57.80 ( (fun com bool), wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_30790 $$unsorted) (BOUND_VARIABLE_30791 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (ord_less_eq X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 _let_0))) (or (not (ordere216010020id_add X_b)) (not (hBOOL (hAPP X_b bool _let_3 BOUND_VARIABLE_30791))) (not (hBOOL (hAPP X_b bool _let_3 BOUND_VARIABLE_30790))) (= (= _let_0 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (plus_plus X_b) BOUND_VARIABLE_30791) BOUND_VARIABLE_30790)) (and (= _let_0 (ti X_b BOUND_VARIABLE_30791)) (= _let_0 (ti X_b BOUND_VARIABLE_30790))))))))) ) 57.54/57.80 ( int, (one_one int), (one_one int) ) 57.54/57.80 ( int, (zero_zero int), (zero_zero int) ) 57.54/57.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M_1) N))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) N))) ) 57.54/57.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.54/57.80 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M_1 $$unsorted)) (= M_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M_1) (zero_zero nat))) ) 57.54/57.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (combi X_a))) (= _let_0 (ti (fun X_a X_a) _let_0))) ) 57.54/57.80 ( bool ) 57.54/57.80 ( nat ) 57.54/57.80 ( int ) 57.54/57.80 ( (fun x_a bool) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30965 $$unsorted) (BOUND_VARIABLE_30966 $$unsorted) (BOUND_VARIABLE_30967 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_30966))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_30967))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_30967) BOUND_VARIABLE_30965))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_30965)))))) ) 57.54/57.80 ( int, (zero_zero int), (zero_zero int), (one_one int) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_30991 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_30991) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_30991) (one_one X_a)))) ) 57.54/57.80 ( bool, fFalse ) 57.54/57.80 ( bool, fTrue ) 57.54/57.80 ( nat, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( (fun pname bool), u ) 57.54/57.80 ( int, (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1 ) 57.54/57.80 ( (fun int int), succ ) 57.54/57.80 ( (fun nat nat), suc ) 57.54/57.80 ( (fun x_a bool), g ) 57.54/57.80 ( (fun int bool), nat_neg ) 57.54/57.80 ( (fun bool bool), fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.80 ( (fun com x_a), mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.80 ( (fun pname (option com)), body ) 57.54/57.80 ( (fun com bool), wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (= _let_0 Na) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) Na) _let_0)))) ) 57.54/57.80 ( (hAPP nat nat suc na) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (= (hAPP _let_0 nat _let_1 A_3) (hAPP nat nat suc (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 (hAPP X_b _let_2 (insert X_b) X_1) (bot_bot _let_0)))))))))) ) 57.54/57.80 ( pname, pn, u ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M_1 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (let ((_let_1 (hAPP nat int _let_0 M_1))) (= _let_1 (hAPP int int (abs_abs int) _let_1)))) ) 57.54/57.80 ( (one_one nat) ) 57.54/57.80 ( (zero_zero nat) ) 57.54/57.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (one_one nat)))) ) 57.54/57.80 ( nat ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_31134 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_31134) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_31134))) ) 57.54/57.80 ( bool, fFalse ) 57.54/57.80 ( bool, fTrue ) 57.54/57.80 ( nat, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( (fun pname bool), u ) 57.54/57.80 ( int, (zero_zero int) ) 57.54/57.80 ( (fun int int), bit1 ) 57.54/57.80 ( (fun int int), succ ) 57.54/57.80 ( (fun nat nat), suc ) 57.54/57.80 ( (fun x_a bool), g ) 57.54/57.80 ( (fun int bool), nat_neg ) 57.54/57.80 ( (fun bool bool), fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies ) 57.54/57.80 ( (fun com x_a), mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.54/57.80 ( (fun pname (option com)), body ) 57.54/57.80 ( (fun com bool), wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (= (bot_bot _let_0) (ti _let_0 A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) A_3))))) ) 57.54/57.80 ( pname, pn, u ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (finite_card X_b))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (minus_minus _let_0))) (let ((_let_6 (insert X_b))) (let ((_let_7 (bot_bot _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 X_1) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 Y_2) A_3))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP _let_0 nat _let_3 (hAPP _let_0 _let_0 (hAPP _let_0 _let_4 _let_5 (hAPP _let_0 _let_0 (hAPP _let_0 _let_4 _let_5 A_3) (hAPP _let_0 _let_0 (hAPP X_b _let_4 _let_6 X_1) _let_7))) (hAPP _let_0 _let_0 (hAPP X_b _let_4 _let_6 Y_2) _let_7)))) (hAPP _let_0 nat _let_3 A_3)))))))))))) ) 57.54/57.80 ( pname, pn, pn, u ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_31183 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_b X_b))) (let ((_let_2 (plus_plus X_b))) (or (not (ring_char_0 X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) BOUND_VARIABLE_31183) (ring_1_Ints X_b)))) (not (= (zero_zero X_b) (hAPP X_b X_b (hAPP X_b _let_1 _let_2 (hAPP X_b X_b (hAPP X_b _let_1 _let_2 (one_one X_b)) BOUND_VARIABLE_31183)) BOUND_VARIABLE_31183))))))) ) 57.54/57.80 ( pname, pn ) 57.54/57.80 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M_1))) (or (not (hBOOL (hAPP nat bool _let_2 N))) (hBOOL (hAPP nat bool _let_2 (hAPP nat nat suc N))))))) ) 57.54/57.80 ( (hAPP nat nat suc na), (zero_zero nat) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_31210 $$unsorted) (BOUND_VARIABLE_31211 $$unsorted) (BOUND_VARIABLE_31212 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (fun X_b X_b))) (let ((_let_3 (times_times X_b))) (let ((_let_4 (hAPP X_b _let_2 _let_3 BOUND_VARIABLE_31212))) (or (not (linord581940658strict X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (zero_zero X_b)) BOUND_VARIABLE_31212))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_31210) BOUND_VARIABLE_31211)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b _let_4 BOUND_VARIABLE_31210)) (hAPP X_b X_b _let_4 BOUND_VARIABLE_31211)))))))))) ) 57.54/57.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (one_one int) ) 57.54/57.80 ) 57.54/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_31245 $$unsorted) (BOUND_VARIABLE_31246 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (linorder X_b)) (= (not (= (ti X_b BOUND_VARIABLE_31246) (ti X_b BOUND_VARIABLE_31245))) (or (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_31246) BOUND_VARIABLE_31245)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_31245) BOUND_VARIABLE_31246))))))) ) 57.54/57.80 ( bool, fFalse, fFalse ) 57.54/57.80 ( bool, fTrue, fTrue ) 57.54/57.80 ( nat, na, na ) 57.54/57.80 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.54/57.80 ( pname, pn, pn ) 57.54/57.80 ( (fun pname bool), u, u ) 57.54/57.80 ( int, (one_one int), (zero_zero int) ) 57.54/57.80 ( int, (zero_zero int), (one_one int) ) 57.54/57.80 ( (fun int int), bit1, bit1 ) 57.54/57.80 ( (fun int int), succ, succ ) 57.54/57.80 ( (fun nat nat), suc, suc ) 57.54/57.80 ( (fun x_a bool), g, g ) 57.54/57.80 ( (fun int bool), nat_neg, nat_neg ) 57.54/57.80 ( (fun bool bool), fNot, fNot ) 57.54/57.80 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.54/57.80 ( (fun bool (fun bool bool)), fconj, fconj ) 57.54/57.80 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.54/57.80 ( (fun com x_a), mgt, mgt ) 57.54/57.80 ( (fun pname x_a), mgt_call, mgt_call ) 57.54/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.54/57.80 ( (fun pname (option com)), body, body ) 57.54/57.80 ( (fun com bool), wt, wt ) 57.54/57.80 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.54/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 X_1))) (let ((_let_4 (hBOOL (hAPP _let_0 bool _let_3 B_1)))) (let ((_let_5 (hBOOL (hAPP _let_0 bool _let_3 A_3)))) (let ((_let_6 (ord_less _let_0))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (insert X_b))) (let ((_let_9 (hAPP X_b _let_7 _let_8 X_1))) (let ((_let_10 (hAPP _let_0 _let_1 _let_6 A_3))) (= (and (or _let_4 (and (or _let_5 (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_3) B_1))) (or (not _let_5) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_6 (hAPP _let_0 _let_0 (hAPP _let_0 _let_7 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 _let_9 (bot_bot _let_0)))) B_1))))) (or (not _let_4) (hBOOL (hAPP _let_0 bool _let_10 B_1)))) (hBOOL (hAPP _let_0 bool _let_10 (hAPP _let_0 _let_0 _let_9 B_1))))))))))))))) ) 57.63/57.80 ( pname, u, pn, u ) 57.63/57.80 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (not (forall ((N_1 $$unsorted)) (not (= Z_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) N_1)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W_1) Z_2))) ) 57.63/57.80 ( (zero_zero int), (one_one int) ) 57.63/57.80 ( (zero_zero int), (zero_zero int) ) 57.63/57.80 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N) M_1))) (= M_1 N)))) ) 57.63/57.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.63/57.80 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (= (hAPP X_a X_c (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (combb X_b X_c X_a) P) Q) R) (hAPP X_b X_c P (hAPP X_a X_b Q R))))) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( nat, bool, int, nat_neg, (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, bool, int, nat_neg, (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int)))), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, nat, nat, suc, suc, (zero_zero nat) ) 57.63/57.80 ( nat, nat, nat, suc, suc, (hAPP nat nat suc (zero_zero nat)) ) 57.63/57.80 ( nat, nat, nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), suc, na ) 57.63/57.80 ( nat, nat, int, (number_number_of nat), (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, nat, int, (number_number_of nat), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, nat, int, (number_number_of nat), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( nat, (fun nat bool), nat, (ord_less_eq nat), suc, na ) 57.63/57.80 ( nat, int, nat, (semiring_1_of_nat int), suc, (zero_zero nat) ) 57.63/57.80 ( nat, int, nat, (semiring_1_of_nat int), suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.63/57.80 ( nat, int, int, bit1, (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, int, int, bit1, (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, int, int, (number_number_of int), (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, int, int, (number_number_of int), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, int, int, (number_number_of int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( nat, int, int, succ, (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, (fun int bool), int, (ord_less_eq int), (semiring_1_of_nat int), (one_one nat) ) 57.63/57.80 ( nat, (fun int bool), int, (ord_less_eq int), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( nat, (fun int bool), int, (ord_less int), (semiring_1_of_nat int), (zero_zero nat) ) 57.63/57.80 ( pname, (fun (fun x_a bool) bool), x_a, (member x_a), mgt_call, pn ) 57.63/57.80 ( pname, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), x_a, (insert x_a), mgt_call, pn ) 57.63/57.80 ( (fun pname bool), bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u ) 57.63/57.80 ( (fun pname bool), bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u ) 57.63/57.80 ( (fun pname bool), nat, (fun x_a bool), (finite_card x_a), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u ) 57.63/57.80 ( int, nat, nat, suc, (number_number_of nat), (zero_zero int) ) 57.63/57.80 ( int, int, nat, (semiring_1_of_nat int), (number_number_of nat), (zero_zero int) ) 57.63/57.80 ( (fun x_a bool), bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (finite_card x_a), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( (fun x_a bool), (fun nat nat), nat, (minus_minus nat), (finite_card x_a), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( (fun x_a bool), (fun (fun x_a bool) bool), (fun x_a bool), (ord_less_eq (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn))), g ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_31365 $$unsorted) (BOUND_VARIABLE_31366 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_b)) (= (or (= (ti X_b BOUND_VARIABLE_31366) (ti X_b BOUND_VARIABLE_31365)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_31365) BOUND_VARIABLE_31366))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_31365) BOUND_VARIABLE_31366))))) ) 57.63/57.80 ( bool, fFalse, fFalse ) 57.63/57.80 ( bool, fTrue, fTrue ) 57.63/57.80 ( nat, na, na ) 57.63/57.80 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.80 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.63/57.80 ( pname, pn, pn ) 57.63/57.80 ( (fun pname bool), u, u ) 57.63/57.80 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.80 ( (fun int int), bit1, bit1 ) 57.63/57.80 ( (fun int int), succ, succ ) 57.63/57.80 ( (fun nat nat), suc, suc ) 57.63/57.80 ( (fun x_a bool), g, g ) 57.63/57.80 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( (fun int bool), nat_neg, nat_neg ) 57.63/57.80 ( (fun bool bool), fNot, fNot ) 57.63/57.80 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.63/57.80 ( (fun bool (fun bool bool)), fconj, fconj ) 57.63/57.80 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.63/57.80 ( (fun com x_a), mgt, mgt ) 57.63/57.80 ( (fun pname x_a), mgt_call, mgt_call ) 57.63/57.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.63/57.80 ( (fun pname (option com)), body, body ) 57.63/57.80 ( (fun com bool), wt, wt ) 57.63/57.80 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_31403 $$unsorted) (BOUND_VARIABLE_31404 $$unsorted) (BOUND_VARIABLE_31405 $$unsorted) (BOUND_VARIABLE_31406 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_c)) (not (order X_b)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_31404) (hAPP X_c X_b BOUND_VARIABLE_31405 BOUND_VARIABLE_31406)))) (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less X_c) BOUND_VARIABLE_31406) BOUND_VARIABLE_31403))) (not (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less X_c) X_2) Y_1))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_c X_b BOUND_VARIABLE_31405 X_2)) (hAPP X_c X_b BOUND_VARIABLE_31405 Y_1)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_31404) (hAPP X_c X_b BOUND_VARIABLE_31405 BOUND_VARIABLE_31403))))) ) 57.63/57.80 ( int, int, (one_one int), (zero_zero int), bit1, (zero_zero int) ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (B_3 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) B_3) (hAPP _let_0 _let_1 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F) A_3)))) (not (forall ((X_2 $$unsorted)) (or (not (= (ti X_b B_3) (hAPP X_c X_b F X_2))) (not (hBOOL (hAPP _let_0 bool (hAPP X_c (fun _let_0 bool) (member X_c) X_2) A_3)))) ))))) ) 57.63/57.80 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, u ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((BOUND_VARIABLE_31580 $$unsorted) (BOUND_VARIABLE_31581 $$unsorted) (BOUND_VARIABLE_31582 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun BOUND_VARIABLE_31580 bool))) (let ((_let_2 (fun BOUND_VARIABLE_31580 _let_0))) (let ((_let_3 (fun BOUND_VARIABLE_31580 _let_1))) (or (hBOOL (hAPP BOUND_VARIABLE_31580 bool BOUND_VARIABLE_31581 BOUND_VARIABLE_31582)) (= (hAPP _let_1 _let_1 (collect BOUND_VARIABLE_31580) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs BOUND_VARIABLE_31580 bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 BOUND_VARIABLE_31580) fconj) (hAPP BOUND_VARIABLE_31580 _let_1 (hAPP _let_3 _let_3 (combc BOUND_VARIABLE_31580 BOUND_VARIABLE_31580 bool) (fequal BOUND_VARIABLE_31580)) BOUND_VARIABLE_31582))) BOUND_VARIABLE_31581)) (bot_bot _let_1))))))) ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int) ) 57.63/57.80 ( int, nat_neg, (one_one int) ) 57.63/57.80 ( int, nat_neg, (hAPP int int (number_number_of int) (zero_zero int)) ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.63/57.80 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((BOUND_VARIABLE_31607 $$unsorted) (BOUND_VARIABLE_31608 $$unsorted) (BOUND_VARIABLE_31609 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun BOUND_VARIABLE_31607 bool))) (let ((_let_2 (fun BOUND_VARIABLE_31607 _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun BOUND_VARIABLE_31607 _let_1))) (or (not (hBOOL (hAPP BOUND_VARIABLE_31607 bool BOUND_VARIABLE_31608 BOUND_VARIABLE_31609))) (= (hAPP _let_1 _let_1 (collect BOUND_VARIABLE_31607) (hAPP _let_1 _let_1 (hAPP _let_2 _let_3 (combs BOUND_VARIABLE_31607 bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 BOUND_VARIABLE_31607) fconj) (hAPP BOUND_VARIABLE_31607 _let_1 (hAPP _let_4 _let_4 (combc BOUND_VARIABLE_31607 BOUND_VARIABLE_31607 bool) (fequal BOUND_VARIABLE_31607)) BOUND_VARIABLE_31609))) BOUND_VARIABLE_31608)) (hAPP _let_1 _let_1 (hAPP BOUND_VARIABLE_31607 _let_3 (insert BOUND_VARIABLE_31607) BOUND_VARIABLE_31609) (bot_bot _let_1))))))))) ) 57.63/57.80 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.80 ( (fun pname bool), (finite_finite pname), u ) 57.63/57.80 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.63/57.80 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) F_1))) (= (bot_bot _let_0) (ti _let_0 F_1)) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP _let_0 bool Pa (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) (bot_bot _let_0)))) )) (not (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) F_3))) (= (bot_bot _let_0) (ti _let_0 F_3)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) F_3)) (not (hBOOL (hAPP _let_0 bool Pa F_3))) (hBOOL (hAPP _let_0 bool Pa (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) F_3)))) )) (hBOOL (hAPP _let_0 bool Pa F_1)))) ) 57.63/57.80 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ( x_a, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (BOUND_VARIABLE_31672 $$unsorted) (BOUND_VARIABLE_31673 $$unsorted)) (let ((_let_0 (fun X_b X_c))) (or (not (ord X_c)) (not (forall ((X_2 $$unsorted)) (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) (hAPP X_b X_c BOUND_VARIABLE_31672 X_2)) (hAPP X_b X_c BOUND_VARIABLE_31673 X_2))) )) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_31672) BOUND_VARIABLE_31673)))) ) 57.63/57.80 ( x_a, bool, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (let ((_let_3 (hAPP _let_0 _let_1 _let_2 A_3))) (or (not (hBOOL (hAPP _let_0 bool _let_3 B_1))) (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_3) B_1)))))))) ) 57.63/57.80 ( x_a, (hAPP pname x_a mgt_call pn), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.63/57.80 ) 57.63/57.80 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (= (hAPP nat int _let_0 M) (hAPP nat int _let_0 Na)) (= M Na))) ) 57.63/57.80 ( (one_one nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (one_one nat) ) 57.63/57.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero nat) ) 57.63/57.80 ) 57.63/57.81 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M))) (let ((_let_3 (hAPP nat nat suc Na))) (= (hBOOL (hAPP nat bool _let_2 _let_3)) (or (= M _let_3) (hBOOL (hAPP nat bool _let_2 Na)))))))) ) 57.63/57.81 ( (hAPP nat nat suc na), (zero_zero nat) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((BOUND_VARIABLE_31729 $$unsorted) (BOUND_VARIABLE_31730 $$unsorted) (BOUND_VARIABLE_31731 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun BOUND_VARIABLE_31729 bool))) (let ((_let_2 (fun BOUND_VARIABLE_31729 _let_0))) (or (hBOOL (hAPP BOUND_VARIABLE_31729 bool BOUND_VARIABLE_31730 BOUND_VARIABLE_31731)) (= (hAPP _let_1 _let_1 (collect BOUND_VARIABLE_31729) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs BOUND_VARIABLE_31729 bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 BOUND_VARIABLE_31729) fconj) (hAPP BOUND_VARIABLE_31729 _let_1 (fequal BOUND_VARIABLE_31729) BOUND_VARIABLE_31731))) BOUND_VARIABLE_31730)) (bot_bot _let_1)))))) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (zero_zero int) ) 57.63/57.81 ( int, nat_neg, (one_one int) ) 57.63/57.81 ( int, nat_neg, (hAPP int int (number_number_of int) (zero_zero int)) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ( (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((BOUND_VARIABLE_31753 $$unsorted) (BOUND_VARIABLE_31754 $$unsorted) (BOUND_VARIABLE_31755 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun BOUND_VARIABLE_31753 bool))) (let ((_let_2 (fun BOUND_VARIABLE_31753 _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (or (not (hBOOL (hAPP BOUND_VARIABLE_31753 bool BOUND_VARIABLE_31754 BOUND_VARIABLE_31755))) (= (hAPP _let_1 _let_1 (collect BOUND_VARIABLE_31753) (hAPP _let_1 _let_1 (hAPP _let_2 _let_3 (combs BOUND_VARIABLE_31753 bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 BOUND_VARIABLE_31753) fconj) (hAPP BOUND_VARIABLE_31753 _let_1 (fequal BOUND_VARIABLE_31753) BOUND_VARIABLE_31755))) BOUND_VARIABLE_31754)) (hAPP _let_1 _let_1 (hAPP BOUND_VARIABLE_31753 _let_3 (insert BOUND_VARIABLE_31753) BOUND_VARIABLE_31755) (bot_bot _let_1)))))))) ) 57.63/57.81 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ( (fun pname bool), (finite_finite pname), u ) 57.63/57.81 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_31790 $$unsorted) (BOUND_VARIABLE_31791 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_31790) BOUND_VARIABLE_31791))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_31790) BOUND_VARIABLE_31791)))) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (zero_zero X_a))))) ) 57.63/57.81 ( bool ) 57.63/57.81 ( nat ) 57.63/57.81 ( com ) 57.63/57.81 ( pname ) 57.63/57.81 ( (fun pname bool) ) 57.63/57.81 ( int ) 57.63/57.81 ( x_a ) 57.63/57.81 ( (fun x_a bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (zero X_b)) (= _let_0 (ti X_b _let_0)))) ) 57.63/57.81 ( nat ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (ti X_b X_1) (hAPP _let_0 X_b (the_elem X_b) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) (bot_bot _let_0))))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_31954 $$unsorted) (BOUND_VARIABLE_31955 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (forall ((Z_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) Z_3))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 Z_3) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) Z_3) BOUND_VARIABLE_31954)) BOUND_VARIABLE_31955))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_31954) BOUND_VARIABLE_31955))) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32015 $$unsorted) (BOUND_VARIABLE_32016 $$unsorted) (BOUND_VARIABLE_32017 $$unsorted) (BOUND_VARIABLE_32018 $$unsorted) (BOUND_VARIABLE_32019 $$unsorted)) (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))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (plus_plus X_a))) (let ((_let_6 (times_times X_a))) (or (not (linord1278240602ring_1 X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_32018) BOUND_VARIABLE_32019))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_32017) BOUND_VARIABLE_32019))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_32016))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_32015))) (not (= (one_one X_a) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_32016) BOUND_VARIABLE_32015))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a (hAPP X_a _let_4 _let_6 BOUND_VARIABLE_32016) BOUND_VARIABLE_32018)) (hAPP X_a X_a (hAPP X_a _let_4 _let_6 BOUND_VARIABLE_32015) BOUND_VARIABLE_32017))) BOUND_VARIABLE_32019)))))))))) ) 57.63/57.81 ( int, (one_one int), (one_one int), (zero_zero int), (zero_zero int), (one_one int) ) 57.63/57.81 ( int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 57.63/57.81 ( nat ) 57.63/57.81 ( int ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (fun _let_0 _let_0))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 (minus_minus _let_0) A_3) (hAPP _let_0 _let_0 (hAPP X_b _let_2 (insert X_b) X_1) (bot_bot _let_0))))) (hAPP _let_0 nat _let_1 A_3))))))) ) 57.63/57.81 ( pname, pn, u ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_1)) (hAPP nat nat suc N)))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_1) N))))) ) 57.63/57.81 ( (zero_zero nat), (zero_zero nat) ) 57.63/57.81 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 57.63/57.81 ( na, na ) 57.63/57.81 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_32197 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (or (not (ordere142940540dd_abs X_b)) (= (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_b X_b (abs_abs X_b) BOUND_VARIABLE_32197)) _let_0)) (= _let_0 (ti X_b BOUND_VARIABLE_32197))))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 A_3)) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) A_3))))))) ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (the_elem X_b))) (= _let_0 (ti (fun (fun X_b bool) X_b) _let_0))) ) 57.63/57.81 ( bool ) 57.63/57.81 ( nat ) 57.63/57.81 ( com ) 57.63/57.81 ( pname ) 57.63/57.81 ( (fun pname bool) ) 57.63/57.81 ( int ) 57.63/57.81 ( x_a ) 57.63/57.81 ( (fun x_a bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_32394 $$unsorted) (BOUND_VARIABLE_32395 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (or (not (preorder X_b)) (= (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_32394) BOUND_VARIABLE_32395)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_32395) BOUND_VARIABLE_32394)))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_32394) BOUND_VARIABLE_32395)))))) ) 57.63/57.81 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (hAPP nat nat suc na) ) 57.63/57.81 ( int, (one_one int), (zero_zero int) ) 57.63/57.81 ( int, (zero_zero int), (one_one int) ) 57.63/57.81 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int) ) 57.63/57.81 ( (fun x_a bool), g, g ) 57.63/57.81 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_3))) (and (not (forall ((X_2 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) X_2) A_3))) )) (not (= (one_one nat) _let_0))) (= _let_0 (hAPP _let_1 nat (finite_card X_b) A_3))))) ) 57.63/57.81 ( pname, u ) 57.63/57.81 ( x_a, g ) 57.63/57.81 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc _let_0)))))) ) 57.63/57.81 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (ord T_1)) (ord (fun T_2 T_1))) ) 57.63/57.81 ( bool, bool ) 57.63/57.81 ( bool, (fun bool bool) ) 57.63/57.81 ( nat, bool ) 57.63/57.81 ( nat, nat ) 57.63/57.81 ( nat, int ) 57.63/57.81 ( (fun nat bool), (fun int bool) ) 57.63/57.81 ( com, bool ) 57.63/57.81 ( com, x_a ) 57.63/57.81 ( (option com), com ) 57.63/57.81 ( pname, bool ) 57.63/57.81 ( pname, (option com) ) 57.63/57.81 ( pname, x_a ) 57.63/57.81 ( (fun pname bool), bool ) 57.63/57.81 ( (fun pname bool), (fun x_a bool) ) 57.63/57.81 ( int, bool ) 57.63/57.81 ( int, int ) 57.63/57.81 ( int, (fun int int) ) 57.63/57.81 ( x_a, bool ) 57.63/57.81 ( (fun x_a bool), bool ) 57.63/57.81 ( (fun x_a bool), (fun x_a bool) ) 57.63/57.81 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((Na $$unsorted) (Pa $$unsorted)) (or (hBOOL (hAPP nat bool Pa (zero_zero nat))) (not (hBOOL (hAPP nat bool Pa Na))) (not (forall ((K_2 $$unsorted)) (or (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I) K_2))) (not (hBOOL (hAPP nat bool Pa I)))) )) (not (hBOOL (hAPP nat bool Pa K_2))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) K_2) Na)))) ))) ) 57.63/57.81 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_finite X_b))) (or (not (hBOOL (hAPP _let_0 bool _let_1 A_3))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_3)))))) ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_32642 $$unsorted) (BOUND_VARIABLE_32643 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (zero_zero X_b))) (let ((_let_3 (hAPP X_b _let_0 _let_1 _let_2))) (or (not (linord581940658strict X_b)) (= (or (and (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_32642) _let_2)) (hBOOL (hAPP X_b bool _let_3 BOUND_VARIABLE_32643))) (and (hBOOL (hAPP X_b bool _let_3 BOUND_VARIABLE_32642)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_32643) _let_2)))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (times_times X_b) BOUND_VARIABLE_32642) BOUND_VARIABLE_32643)) _let_2)))))))) ) 57.63/57.81 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (let ((_let_3 (hAPP _let_0 _let_1 _let_2 A_3))) (or (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (member X_b) X_1) A_3)) (= (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_1) B_1))) (hBOOL (hAPP _let_0 bool _let_3 B_1)))))))) ) 57.63/57.81 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) Z))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z)))))) ) 57.63/57.81 ( (one_one int) ) 57.63/57.81 ( (zero_zero int) ) 57.63/57.81 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 X_1))) (let ((_let_4 (hBOOL (hAPP _let_0 bool _let_3 A_3)))) (let ((_let_5 (finite_card X_b))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (insert X_b))) (let ((_let_8 (hAPP X_b _let_6 _let_7 X_1))) (let ((_let_9 (hAPP _let_0 _let_0 _let_8 A_3))) (let ((_let_10 (hAPP _let_0 nat _let_5 A_3))) (let ((_let_11 (hAPP _let_0 nat _let_5 _let_9))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))) (and (or _let_4 (= (hAPP nat nat suc _let_10) _let_11)) (or (not _let_4) (= _let_10 _let_11)))))))))))))))) ) 57.63/57.81 ( pname, pn, u ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (insert X_b))) (let ((_let_3 (hAPP X_b _let_1 _let_2 X_1))) (or (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_1) A_3)) (= (hAPP _let_0 _let_0 (hAPP _let_0 _let_1 (minus_minus _let_0) (hAPP _let_0 _let_0 _let_3 A_3)) (hAPP _let_0 _let_0 _let_3 (bot_bot _let_0))) (ti _let_0 A_3))))))) ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32777 $$unsorted) (BOUND_VARIABLE_32778 $$unsorted) (BOUND_VARIABLE_32779 $$unsorted)) (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 BOUND_VARIABLE_32777))) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_32779) (ti X_a BOUND_VARIABLE_32778))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_32779))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_32778)))))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), na, na ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g, g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP _let_0 nat (finite_card X_b) A_3))) (and (not (= (ti _let_0 A_3) (bot_bot _let_0))) (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_3))))) ) 57.63/57.81 ( bool, fNot ) 57.63/57.81 ( com, wt ) 57.63/57.81 ( pname, u ) 57.63/57.81 ( int, nat_neg ) 57.63/57.81 ( x_a, g ) 57.63/57.81 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_32815 $$unsorted) (BOUND_VARIABLE_32816 $$unsorted)) (or (not (group_add X_b)) (= (= (ti X_b BOUND_VARIABLE_32815) (ti X_b BOUND_VARIABLE_32816)) (= (zero_zero X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) BOUND_VARIABLE_32815) BOUND_VARIABLE_32816)))) ) 57.63/57.81 ( bool, fFalse, fFalse ) 57.63/57.81 ( bool, fTrue, fTrue ) 57.63/57.81 ( nat, na, na ) 57.63/57.81 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na) ) 57.63/57.81 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.63/57.81 ( pname, pn, pn ) 57.63/57.81 ( (fun pname bool), u, u ) 57.63/57.81 ( int, (zero_zero int), (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1, bit1 ) 57.63/57.81 ( (fun int int), succ, succ ) 57.63/57.81 ( (fun nat nat), suc, suc ) 57.63/57.81 ( (fun x_a bool), g, g ) 57.63/57.81 ( (fun int bool), nat_neg, nat_neg ) 57.63/57.81 ( (fun bool bool), fNot, fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj, fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.63/57.81 ( (fun com x_a), mgt, mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call, mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.63/57.81 ( (fun pname (option com)), body, body ) 57.63/57.81 ( (fun com bool), wt, wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32834 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_32834) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_32834) (one_one X_a))))) ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32885 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_32885) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_32885)))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na) ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))) ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32917 $$unsorted) (BOUND_VARIABLE_32918 $$unsorted) (BOUND_VARIABLE_32919 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_32918) BOUND_VARIABLE_32919))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_32917))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_32918) BOUND_VARIABLE_32917)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_32919) BOUND_VARIABLE_32917)))))))) ) 57.63/57.81 ( int, (one_one int), (zero_zero int), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((I_1 $$unsorted) (Pa $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool Pa K))) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) K) I))) (not (hBOOL (hAPP int bool Pa I))) (hBOOL (hAPP int bool Pa (hAPP int int (hAPP int (fun int int) (plus_plus int) I) (one_one int))))) )) (not (forall ((I $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I) K))) (not (hBOOL (hAPP int bool Pa I))) (hBOOL (hAPP int bool Pa (hAPP int int (hAPP int (fun int int) (minus_minus int) I) (one_one int))))) )) (hBOOL (hAPP int bool Pa I_1))) ) 57.63/57.81 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (partial_flat_lub X_b))) (= _let_0 (ti (fun X_b (fun (fun X_b bool) X_b)) _let_0))) ) 57.63/57.81 ( bool ) 57.63/57.81 ( nat ) 57.63/57.81 ( com ) 57.63/57.81 ( pname ) 57.63/57.81 ( (fun pname bool) ) 57.63/57.81 ( int ) 57.63/57.81 ( x_a ) 57.63/57.81 ( (fun x_a bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M_1) N))) (= M_1 N) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_1) N)))) ) 57.63/57.81 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((N $$unsorted) (M_4 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N)) M_4))) (not (forall ((M_2 $$unsorted)) (not (= M_4 (hAPP nat nat suc M_2))) ))) ) 57.63/57.81 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (finite2073411215e_idem X_b))) (= _let_0 (ti (fun (fun X_b (fun X_b X_b)) (fun (fun (fun X_b bool) X_b) bool)) _let_0))) ) 57.63/57.81 ( bool ) 57.63/57.81 ( nat ) 57.63/57.81 ( int ) 57.63/57.81 ( (fun x_a bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (= (or (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less _let_0) A_3) B_1)) (= (ti _let_0 A_3) (ti _let_0 B_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_3) B_1))))) ) 57.63/57.81 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33089 $$unsorted) (BOUND_VARIABLE_33090 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_33089) BOUND_VARIABLE_33090))) (= (ti X_a BOUND_VARIABLE_33089) (ti X_a BOUND_VARIABLE_33090)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_33089) BOUND_VARIABLE_33090)))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), na ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (not (forall ((N_1 $$unsorted)) (not (= Z_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1))))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) W_1) Z_2))) ) 57.63/57.81 ( (zero_zero int), (one_one int) ) 57.63/57.81 ( (zero_zero int), (zero_zero int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (ab_semigroup_mult X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 57.63/57.81 ( bool ) 57.63/57.81 ( nat ) 57.63/57.81 ( int ) 57.63/57.81 ( (fun x_a bool) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP nat nat suc X) (hAPP nat nat suc Y))) (= X Y)) ) 57.63/57.81 ( (zero_zero nat), na ) 57.63/57.81 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 57.63/57.81 ( na, (zero_zero nat) ) 57.63/57.81 ( na, (hAPP nat nat suc (zero_zero nat)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool Pa A_2))) (not (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP X_b bool Pa X_2))) (= (ti X_b A_2) (ti X_b X_2))) )) (= (ti X_b A_2) (hAPP (fun X_b bool) X_b (the X_b) Pa))) ) 57.63/57.81 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ( (fun pname bool), (finite_finite pname), u ) 57.63/57.81 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int) ) 57.63/57.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_33235 $$unsorted) (BOUND_VARIABLE_33236 $$unsorted) (BOUND_VARIABLE_33237 $$unsorted) (BOUND_VARIABLE_33238 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (order X_b)) (not (order X_c)) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_c X_b BOUND_VARIABLE_33236 BOUND_VARIABLE_33237)) BOUND_VARIABLE_33238))) (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) BOUND_VARIABLE_33235) BOUND_VARIABLE_33237))) (not (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_c bool (hAPP X_c (fun X_c bool) (ord_less_eq X_c) Y_1) X_2))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_c X_b BOUND_VARIABLE_33236 Y_1)) (hAPP X_c X_b BOUND_VARIABLE_33236 X_2)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_c X_b BOUND_VARIABLE_33236 BOUND_VARIABLE_33235)) BOUND_VARIABLE_33238))))) ) 57.63/57.81 ( nat, int, (hAPP nat nat suc na), (semiring_1_of_nat int), (zero_zero nat), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M_1))) (let ((_let_3 (hAPP nat nat suc N))) (or (not (hBOOL (hAPP nat bool _let_2 _let_3))) (hBOOL (hAPP nat bool _let_2 N)) (= M_1 _let_3)))))) ) 57.63/57.81 ( (hAPP nat nat suc na), (zero_zero nat) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 M_1))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat _let_2 (one_one nat))) N) (hAPP nat nat _let_2 (hAPP nat nat suc N)))))) ) 57.63/57.81 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33336 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_33336) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_33336) (zero_zero X_a)))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_33356 $$unsorted) (BOUND_VARIABLE_33357 $$unsorted)) (let ((_let_0 (zero_zero X_b))) (let ((_let_1 (fun X_b X_b))) (let ((_let_2 (times_times X_b))) (or (not (linord581940658strict X_b)) (= (or (not (= _let_0 (ti X_b BOUND_VARIABLE_33357))) (not (= _let_0 (ti X_b BOUND_VARIABLE_33356)))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) _let_0) (hAPP X_b X_b (hAPP X_b _let_1 (plus_plus X_b) (hAPP X_b X_b (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_33356) BOUND_VARIABLE_33356)) (hAPP X_b X_b (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_33357) BOUND_VARIABLE_33357))))))))) ) 57.63/57.81 ( bool, fFalse, fFalse ) 57.63/57.81 ( bool, fTrue, fTrue ) 57.63/57.81 ( nat, na, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com), (the_1 com) ) 57.63/57.81 ( pname, pn, pn ) 57.63/57.81 ( (fun pname bool), u, u ) 57.63/57.81 ( int, (zero_zero int), (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1, bit1 ) 57.63/57.81 ( (fun int int), succ, succ ) 57.63/57.81 ( (fun nat nat), suc, suc ) 57.63/57.81 ( (fun x_a bool), g, g ) 57.63/57.81 ( (fun int bool), nat_neg, nat_neg ) 57.63/57.81 ( (fun bool bool), fNot, fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj, fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj, fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies, fimplies ) 57.63/57.81 ( (fun com x_a), mgt, mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call, mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p ) 57.63/57.81 ( (fun pname (option com)), body, body ) 57.63/57.81 ( (fun com bool), wt, wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33389 $$unsorted) (BOUND_VARIABLE_33390 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_33389) BOUND_VARIABLE_33390))) (not (= (ti X_a BOUND_VARIABLE_33389) (ti X_a BOUND_VARIABLE_33390)))) ) 57.63/57.81 ( int, (zero_zero int), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33408 $$unsorted) (BOUND_VARIABLE_33409 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_33408)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_33409))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33409) BOUND_VARIABLE_33408)))))))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_33431 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (let ((_let_2 (fun X_b X_b))) (let ((_let_3 (plus_plus X_b))) (let ((_let_4 (zero_zero X_b))) (or (not (linordered_idom X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) BOUND_VARIABLE_33431) (ring_1_Ints X_b)))) (= (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_b X_b (hAPP X_b _let_2 _let_3 (hAPP X_b X_b (hAPP X_b _let_2 _let_3 (one_one X_b)) BOUND_VARIABLE_33431)) BOUND_VARIABLE_33431)) _let_4)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_33431) _let_4))))))))) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( x_a, (hAPP pname x_a mgt_call pn) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33531 $$unsorted) (BOUND_VARIABLE_33532 $$unsorted) (BOUND_VARIABLE_33533 $$unsorted) (BOUND_VARIABLE_33534 $$unsorted)) (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))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33533) BOUND_VARIABLE_33534))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33531) BOUND_VARIABLE_33532))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_33534))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_33531))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_33533) BOUND_VARIABLE_33531)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_33534) BOUND_VARIABLE_33532)))))))))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 57.63/57.81 ( int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 57.63/57.81 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ( (fun x_a bool), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((BOUND_VARIABLE_33603 $$unsorted) (BOUND_VARIABLE_33604 $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_33603) BOUND_VARIABLE_33604)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) nat_tsub BOUND_VARIABLE_33604) BOUND_VARIABLE_33603))) ) 57.63/57.81 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (zero_zero int))), (zero_zero int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33651 $$unsorted) (BOUND_VARIABLE_33652 $$unsorted) (BOUND_VARIABLE_33653 $$unsorted) (BOUND_VARIABLE_33654 $$unsorted) (BOUND_VARIABLE_33655 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_33655))) (or (not (semiri456707255roduct X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_33655)) (not (= (ti X_a BOUND_VARIABLE_33654) (ti X_a BOUND_VARIABLE_33653))) (= (ti X_a BOUND_VARIABLE_33652) (ti X_a BOUND_VARIABLE_33651)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33653) (hAPP X_a X_a _let_3 BOUND_VARIABLE_33651)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33654) (hAPP X_a X_a _let_3 BOUND_VARIABLE_33652))))))))) ) 57.63/57.81 ( bool, fFalse, fTrue, fTrue, fTrue, fTrue ) 57.63/57.81 ( bool, fTrue, fFalse, fFalse, fFalse, fFalse ) 57.63/57.81 ( (fun int int), bit1, succ, succ, succ, succ ) 57.63/57.81 ( (fun int int), succ, bit1, bit1, bit1, bit1 ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj, fimplies, fimplies, fimplies, fimplies ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies, fconj, fconj, fconj, fconj ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33757 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_33757) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_33757))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) Na)) (or (= M Na) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) Na))))) ) 57.63/57.81 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_33858 $$unsorted) (BOUND_VARIABLE_33859 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_b))) (let ((_let_3 (ring_1_Ints X_b))) (or (not (ring_1 X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_33859) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_33858) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) BOUND_VARIABLE_33859) BOUND_VARIABLE_33858)) _let_3))))))) ) 57.63/57.81 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) Na)) (and (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) Na)) (not (= M Na))))) ) 57.63/57.81 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_33931 $$unsorted) (BOUND_VARIABLE_33932 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33931) BOUND_VARIABLE_33932))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_33932) BOUND_VARIABLE_33931)))))) ) 57.63/57.81 ( int, (one_one int), (zero_zero int) ) 57.63/57.81 ( int, (zero_zero int), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_33969 $$unsorted) (BOUND_VARIABLE_33970 $$unsorted) (BOUND_VARIABLE_33971 $$unsorted) (BOUND_VARIABLE_33972 $$unsorted)) (let ((_let_0 (fun X_c bool))) (or (not (order X_b)) (not (order X_c)) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_33971) BOUND_VARIABLE_33972))) (not (hBOOL (hAPP X_c bool (hAPP X_c _let_0 (ord_less_eq X_c) BOUND_VARIABLE_33969) (hAPP X_b X_c BOUND_VARIABLE_33970 BOUND_VARIABLE_33971)))) (not (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) Y_1) X_2))) (hBOOL (hAPP X_c bool (hAPP X_c _let_0 (ord_less X_c) (hAPP X_b X_c BOUND_VARIABLE_33970 Y_1)) (hAPP X_b X_c BOUND_VARIABLE_33970 X_2)))) )) (hBOOL (hAPP X_c bool (hAPP X_c _let_0 (ord_less X_c) BOUND_VARIABLE_33969) (hAPP X_b X_c BOUND_VARIABLE_33970 BOUND_VARIABLE_33972))))) ) 57.63/57.81 ( int, int, (zero_zero int), bit1, (zero_zero int), (one_one int) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) (zero_zero nat)) (zero_zero X_a))) ) 57.63/57.81 ( nat ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((I_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc I_2))) N))))) ) 57.63/57.81 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_0 (ti X_b A_2))) (let ((_let_1 (ti X_b D_1))) (let ((_let_2 (ti X_b C_1))) (let ((_let_3 (ti X_b B_3))) (let ((_let_4 (fun X_b bool))) (let ((_let_5 (fun _let_4 _let_4))) (let ((_let_6 (insert X_b))) (let ((_let_7 (bot_bot _let_4))) (= (or (and (= _let_0 _let_1) (= _let_2 _let_3)) (and (= _let_1 _let_3) (= _let_0 _let_2))) (= (hAPP _let_4 _let_4 (hAPP X_b _let_5 _let_6 A_2) (hAPP _let_4 _let_4 (hAPP X_b _let_5 _let_6 B_3) _let_7)) (hAPP _let_4 _let_4 (hAPP X_b _let_5 _let_6 C_1) (hAPP _let_4 _let_4 (hAPP X_b _let_5 _let_6 D_1) _let_7)))))))))))) ) 57.63/57.81 ( bool, fFalse, fFalse, fFalse, fFalse ) 57.63/57.81 ( bool, fFalse, fTrue, fFalse, fFalse ) 57.63/57.81 ( bool, fTrue, fFalse, fTrue, fTrue ) 57.63/57.81 ( nat, na, na, na, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com), (the_1 com), (the_1 com), (the_1 com) ) 57.63/57.81 ( pname, pn, pn, pn, pn ) 57.63/57.81 ( (fun pname bool), u, u, u, u ) 57.63/57.81 ( int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1, bit1, bit1, bit1 ) 57.63/57.81 ( (fun int int), bit1, succ, bit1, bit1 ) 57.63/57.81 ( (fun int int), succ, bit1, succ, succ ) 57.63/57.81 ( (fun nat nat), suc, suc, suc, suc ) 57.63/57.81 ( (fun x_a bool), g, g, g, g ) 57.63/57.81 ( (fun int bool), nat_neg, nat_neg, nat_neg, nat_neg ) 57.63/57.81 ( (fun bool bool), fNot, fNot, fNot, fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj, fdisj, fdisj, fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj, fimplies, fconj, fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies, fconj, fimplies, fimplies ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies, fimplies, fimplies, fimplies ) 57.63/57.81 ( (fun com x_a), mgt, mgt, mgt, mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call, mgt_call, mgt_call, mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p, p, p, p ) 57.63/57.81 ( (fun pname (option com)), body, body, body, body ) 57.63/57.81 ( (fun com bool), wt, wt, wt, wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub, nat_tsub, nat_tsub, nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc (hAPP nat nat suc N))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))))) N)) ) 57.63/57.81 ( (zero_zero nat) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_31896 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_31896) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_31896) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 (zero_zero int)))))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int bit1 K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) K))))) ) 57.63/57.81 ( (one_one int) ) 57.63/57.81 ( (hAPP int int bit1 (zero_zero int)) ) 57.63/57.81 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 (zero_zero int)))) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_32698 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_32698) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_32698) (hAPP int X_a (number_number_of X_a) (zero_zero int))))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_21252 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_21252) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 (zero_zero int)))) BOUND_VARIABLE_21252))) ) 57.63/57.81 ( bool, fFalse ) 57.63/57.81 ( bool, fTrue ) 57.63/57.81 ( nat, na ) 57.63/57.81 ( (fun (option com) com), (the_1 com) ) 57.63/57.81 ( pname, pn ) 57.63/57.81 ( (fun pname bool), u ) 57.63/57.81 ( int, (zero_zero int) ) 57.63/57.81 ( (fun int int), bit1 ) 57.63/57.81 ( (fun int int), succ ) 57.63/57.81 ( (fun nat nat), suc ) 57.63/57.81 ( (fun x_a bool), g ) 57.63/57.81 ( (fun int bool), nat_neg ) 57.63/57.81 ( (fun bool bool), fNot ) 57.63/57.81 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.81 ( (fun bool (fun bool bool)), fconj ) 57.63/57.81 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.81 ( (fun com x_a), mgt ) 57.63/57.81 ( (fun pname x_a), mgt_call ) 57.63/57.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.81 ( (fun pname (option com)), body ) 57.63/57.81 ( (fun com bool), wt ) 57.63/57.81 ( (fun int (fun int int)), nat_tsub ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K)) _let_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) _let_1))))) ) 57.63/57.81 ( (zero_zero int) ) 57.63/57.81 ( (hAPP int int bit1 (zero_zero int)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((K_1 $$unsorted)) (not (= (zero_zero int) (hAPP int int bit1 K_1))) ) 57.63/57.81 ( (hAPP int int bit1 (zero_zero int)) ) 57.63/57.81 ) 57.63/57.81 (instantiation (forall ((BOUND_VARIABLE_24438 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_24438) (zero_zero int))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP int nat _let_0 BOUND_VARIABLE_24438)) (hAPP int nat _let_0 (hAPP int int succ BOUND_VARIABLE_24438))))) ) 57.63/57.81 ( (zero_zero int) ) 57.63/57.81 ) 57.63/57.82 (instantiation (forall ((BOUND_VARIABLE_24427 $$unsorted)) (let ((_let_0 (one_one nat))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_24427) (zero_zero int)))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_0) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_24427))))) ) 57.63/57.82 ( (hAPP int int bit1 (zero_zero int)) ) 57.63/57.82 ( (hAPP int int bit1 (hAPP int int bit1 (zero_zero int))) ) 57.63/57.82 ) 57.63/57.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_25984 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_25984) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a (number_number_of X_a) (zero_zero int))) BOUND_VARIABLE_25984))) ) 57.63/57.82 ( bool, fFalse ) 57.63/57.82 ( bool, fTrue ) 57.63/57.82 ( nat, na ) 57.63/57.82 ( (fun (option com) com), (the_1 com) ) 57.63/57.82 ( pname, pn ) 57.63/57.82 ( (fun pname bool), u ) 57.63/57.82 ( int, (zero_zero int) ) 57.63/57.82 ( (fun int int), bit1 ) 57.63/57.82 ( (fun int int), succ ) 57.63/57.82 ( (fun nat nat), suc ) 57.63/57.82 ( (fun x_a bool), g ) 57.63/57.82 ( (fun int bool), nat_neg ) 57.63/57.82 ( (fun bool bool), fNot ) 57.63/57.82 ( (fun bool (fun bool bool)), fdisj ) 57.63/57.82 ( (fun bool (fun bool bool)), fconj ) 57.63/57.82 ( (fun bool (fun bool bool)), fimplies ) 57.63/57.82 ( (fun com x_a), mgt ) 57.63/57.82 ( (fun pname x_a), mgt_call ) 57.63/57.82 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 57.63/57.82 ( (fun pname (option com)), body ) 57.63/57.82 ( (fun com bool), wt ) 57.63/57.82 ( (fun int (fun int int)), nat_tsub ) 57.63/57.82 ) 57.63/57.82 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) _let_2)))))) ) 57.63/57.82 ( (zero_zero int) ) 57.63/57.82 ( (hAPP int int bit1 (zero_zero int)) ) 57.63/57.82 ) 57.63/57.82 % SZS output end Proof for theBenchmark 57.63/57.82 EOF