0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.23 % Computer : n167.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:27:10 CDT 2018 0.03/0.23 % CPUTime : 0.03/0.29 %----Proving without arithmetic mode 0.03/0.29 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.03/0.29 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 0.41/0.62 % SZS status Theorem for theBenchmark 0.41/0.62 % SZS output start Proof for theBenchmark 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (forall ((M $$unsorted)) (not (= (hAPP nat nat suc M) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ))) 0.41/0.62 ( skv_1 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (hAPP x_a (fun _let_1 bool) (member x_a) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) )))) 0.41/0.62 ( skv_2 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) AA) u))) (not (= (ti _let_1 g) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) AA)))) ))) 0.41/0.62 ( skv_3 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (forall ((C_2 $$unsorted)) (or (not (= (ti _let_1 g) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) C_2))) (not (hBOOL (hAPP _let_0 bool (finite_finite pname) C_2))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) C_2) u)))) ))) 0.41/0.62 ( skv_4 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (forall ((C_2 $$unsorted)) (or (not (= (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) C_2) (ti _let_1 (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)))) (not (hBOOL (hAPP _let_0 bool (finite_finite pname) C_2))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) C_2) u)))) ))) 0.41/0.62 ( skv_5 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (hAPP x_a (fun _let_1 bool) (member x_a) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_2 g))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) )))) 0.41/0.62 ( skv_6 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 bool))) (let ((_let_5 (member pname))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun pname _let_2))) (forall ((X_1 $$unsorted)) (or (hBOOL (hAPP _let_0 bool (finite_finite pname) (hAPP _let_0 _let_0 (collect pname) (hAPP _let_0 _let_0 (hAPP _let_7 _let_6 (combs pname bool bool) (hAPP _let_0 _let_7 (hAPP (fun bool _let_1) (fun _let_0 _let_7) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname _let_4) _let_6 (combc pname _let_0 bool) _let_5) u))) (hAPP x_a _let_0 (hAPP _let_8 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_8 (hAPP (fun x_a _let_2) (fun _let_3 _let_8) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call X_1)))))) (not (hBOOL (hAPP _let_0 bool (hAPP pname _let_4 _let_5 X_1) u)))) )))))))))) 0.41/0.62 ( skv_7 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fdisj X_1) (hAPP bool _let_0 fconj X_1)) )) 0.41/0.62 ( skv_8 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fimplies X_1) (hAPP bool _let_0 fconj X_1)) )) 0.41/0.62 ( skv_9 ) 0.41/0.62 ) 0.41/0.62 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fdisj X_1) (hAPP bool _let_0 fimplies X_1)) )) 0.41/0.62 ( skv_10 ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (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_2) A_1)) B)) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (member X_b) X_2) B)))) )))) 0.41/0.62 ( 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))) ) 0.41/0.62 ( 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)) ) 0.41/0.62 ( x_a, (hAPP pname x_a mgt_call pn), (ti (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))) ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_finite X_b))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_1))) (hBOOL (hAPP _let_0 bool _let_1 A_1))) ))) 0.41/0.62 ( pname, pn, u ) 0.41/0.62 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.41/0.62 ( x_a, (hAPP pname x_a mgt_call pn), (ti (fun x_a bool) g) ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1) A_1)) )) 0.41/0.62 ( pname, skv_3 ) 0.41/0.62 ( pname, skv_4 ) 0.41/0.62 ( pname, skv_5 ) 0.41/0.62 ( x_a, g ) 0.41/0.62 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.41/0.62 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (fequal X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)) )) 0.41/0.62 ( bool ) 0.41/0.62 ( pname ) 0.41/0.62 ( (fun pname bool) ) 0.41/0.62 ( nat ) 0.41/0.62 ( (fun nat bool) ) 0.41/0.62 ( x_a ) 0.41/0.62 ( (fun x_a bool) ) 0.41/0.62 ( (fun (fun x_a bool) bool) ) 0.41/0.62 ( (fun (fun pname bool) bool) ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (image X_b X_c))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_b bool) (fun X_c bool))) _let_0)) )) 0.41/0.62 ( bool, bool ) 0.41/0.62 ( pname, pname ) 0.41/0.62 ( pname, (fun pname bool) ) 0.41/0.62 ( pname, x_a ) 0.41/0.62 ( (fun pname bool), (fun pname bool) ) 0.41/0.62 ( nat, nat ) 0.41/0.62 ( x_a, x_a ) 0.41/0.62 ( x_a, (fun x_a bool) ) 0.41/0.62 ( (fun x_a bool), (fun x_a bool) ) 0.41/0.62 ) 0.41/0.62 (instantiation (let ((_let_0 (combc X_a X_b X_c))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun X_b (fun X_a X_c))) _let_0)) )) 0.41/0.62 ( bool, bool, bool ) 0.41/0.62 ( bool, pname, bool ) 0.41/0.62 ( bool, (fun bool bool), bool ) 0.41/0.62 ( bool, (fun bool (fun bool bool)), (fun bool bool) ) 0.41/0.62 ( bool, x_a, bool ) 0.41/0.62 ( pname, pname, bool ) 0.41/0.62 ( pname, (fun pname bool), bool ) 0.41/0.62 ( pname, (fun pname bool), (fun bool bool) ) 0.41/0.62 ( pname, x_a, bool ) 0.41/0.62 ( pname, (fun pname x_a), (fun x_a bool) ) 0.41/0.62 ( pname, (fun pname x_a), (fun (fun x_a bool) bool) ) 0.41/0.62 ( pname, (fun pname x_a), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.41/0.62 ( (fun pname bool), pname, bool ) 0.41/0.62 ( (fun pname bool), pname, (fun pname bool) ) 0.41/0.62 ( (fun pname bool), (fun pname bool), bool ) 0.41/0.62 ( (fun pname bool), x_a, bool ) 0.41/0.62 ( (fun pname bool), (fun pname x_a), (fun x_a bool) ) 0.41/0.62 ( (fun pname bool), (fun (fun pname bool) (fun x_a bool)), bool ) 0.41/0.62 ( (fun pname bool), (fun (fun pname bool) (fun x_a bool)), nat ) 0.41/0.62 ( (fun pname bool), (fun (fun pname bool) bool), bool ) 0.41/0.62 ( (fun pname bool), (fun x_a (fun (fun pname bool) bool)), (fun x_a bool) ) 0.41/0.62 ( nat, nat, bool ) 0.41/0.62 ( nat, nat, nat ) 0.41/0.62 ( nat, (fun nat bool), bool ) 0.41/0.62 ( nat, (fun nat nat), nat ) 0.41/0.62 ( nat, (fun nat nat), (fun nat bool) ) 0.41/0.62 ( nat, (fun nat (fun nat nat)), (fun nat nat) ) 0.41/0.62 ( nat, (fun x_a bool), nat ) 0.41/0.62 ( (fun nat bool), nat, (fun nat bool) ) 0.41/0.63 ( (fun bool bool), bool, (fun bool bool) ) 0.41/0.63 ( x_a, pname, bool ) 0.41/0.63 ( x_a, (fun pname bool), bool ) 0.41/0.63 ( x_a, x_a, bool ) 0.41/0.63 ( x_a, (fun x_a bool), bool ) 0.41/0.63 ( x_a, (fun x_a bool), (fun bool bool) ) 0.41/0.63 ( x_a, (fun x_a bool), (fun x_a bool) ) 0.41/0.63 ( x_a, (fun pname x_a), bool ) 0.41/0.63 ( (fun x_a bool), pname, bool ) 0.41/0.63 ( (fun x_a bool), pname, (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), (fun bool bool), (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), x_a, bool ) 0.41/0.63 ( (fun x_a bool), x_a, (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), (fun x_a bool), bool ) 0.41/0.63 ( (fun x_a bool), (fun (fun x_a bool) bool), bool ) 0.41/0.63 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (fun (fun x_a bool) bool) ) 0.41/0.63 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (fun (fun x_a bool) bool) ) 0.41/0.63 ( (fun x_a bool), (fun x_a (fun x_a bool)), (fun (fun x_a bool) bool) ) 0.41/0.63 ( (fun x_a bool), (fun x_a x_a), (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), (fun x_a (fun (fun x_a bool) bool)), (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), (fun x_a (fun bool bool)), (fun x_a bool) ) 0.41/0.63 ( (fun x_a bool), (fun (fun x_a bool) nat), bool ) 0.41/0.63 ( (fun x_a bool), (fun (fun x_a bool) nat), (fun nat nat) ) 0.41/0.63 ( (fun (fun x_a bool) bool), (fun x_a bool), (fun (fun x_a bool) bool) ) 0.41/0.63 ( (fun pname x_a), (fun pname bool), (fun x_a bool) ) 0.41/0.63 ( (fun (fun pname bool) bool), (fun pname bool), (fun (fun pname bool) bool) ) 0.41/0.63 ) 0.41/0.63 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (forall ((M_3 $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc Na)) M_3)) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_3) Na)))) ))) 0.41/0.63 ( na, na ) 0.41/0.63 ( 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)))) ) 0.41/0.63 ( na, skv_1 ) 0.41/0.63 ( (hAPP nat nat suc na), na ) 0.41/0.63 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.41/0.63 ( (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)))) ) 0.41/0.63 ( (hAPP nat nat suc na), skv_1 ) 0.41/0.63 ( (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 ) 0.41/0.63 ( (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) ) 0.41/0.63 ( (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.63 ( (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 nat (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)))) ) 0.41/0.63 ( (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 x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.63 ( (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 (fun pname bool) nat (finite_card pname) u) ) 0.41/0.63 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.41/0.63 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.63 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), skv_1 ) 0.41/0.63 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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)))) ) 0.41/0.63 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), skv_1 ) 0.41/0.63 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.41/0.63 ( (hAPP (fun pname bool) nat (finite_card pname) u), skv_1 ) 0.41/0.63 ) 0.41/0.63 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) B))) )) 0.41/0.63 ( pname, u, pn ) 0.41/0.63 ( x_a, g, (hAPP pname x_a mgt_call pn) ) 0.41/0.63 ) 0.41/0.63 (instantiation (let ((_let_0 (hAPP X_a X_c B_1_1 B_2))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= _let_0 (ti X_c _let_0)) )) 0.41/0.63 ( bool, pname, u, pn ) 0.41/0.63 ( bool, pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) u)), pn ) 0.41/0.63 ( bool, (fun pname bool), (finite_finite pname), u ) 0.41/0.63 ( bool, (fun pname bool), (finite_finite pname), skv_4 ) 0.41/0.63 ( bool, (fun pname bool), (finite_finite pname), skv_5 ) 0.41/0.63 ( bool, (fun pname bool), (finite_finite pname), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (fun pname _let_2))) (hAPP _let_0 _let_0 (collect pname) (hAPP _let_0 _let_0 (hAPP _let_5 _let_4 (combs pname bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_1) (fun _let_0 _let_5) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) _let_4 (combc pname _let_0 bool) (member pname)) u))) (hAPP x_a _let_0 (hAPP _let_6 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_6 (hAPP (fun x_a _let_2) (fun _let_3 _let_6) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7))))))))))) ) 0.41/0.63 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 0.41/0.63 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun _let_0 bool))) (hAPP _let_3 _let_4 (hAPP _let_2 (fun _let_3 _let_4) (combb _let_1 bool _let_0) (hAPP _let_1 _let_2 (ord_less_eq _let_1) g)) (hAPP (fun pname x_a) _let_3 (image pname x_a) mgt_call))))))), u ) 0.41/0.63 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun _let_0 bool))) (hAPP _let_3 _let_4 (hAPP _let_2 (fun _let_3 _let_4) (combb _let_1 bool _let_0) (hAPP _let_1 _let_2 (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) (hAPP (fun pname x_a) _let_3 (image pname x_a) mgt_call))))))), u ) 0.41/0.63 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_3)), u ) 0.41/0.63 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_4)), u ) 0.41/0.63 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_5)), u ) 0.41/0.63 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_7), u ) 0.41/0.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), na ) 0.41/0.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (hAPP nat nat suc na) ) 0.41/0.63 ( 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)))) ) 0.41/0.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP (fun x_a bool) nat (finite_card x_a) g)), (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)))) ) 0.41/0.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP (fun x_a bool) nat (finite_card x_a) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.63 ( bool, nat, (let ((_let_0 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat (finite_card x_a) (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_1 nat (finite_card x_a) (hAPP _let_0 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) 0.41/0.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less_eq nat) 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)))) ) 0.41/0.63 ( bool, nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun nat (fun nat bool)))) (let ((_let_2 (fun x_a bool))) (hAPP nat (fun nat bool) (hAPP _let_1 _let_1 (combc nat nat bool) (ord_less_eq nat)) (hAPP _let_2 nat (finite_card x_a) (hAPP _let_0 _let_2 (hAPP (fun pname x_a) (fun _let_0 _let_2) (image pname x_a) mgt_call) u)))))), (hAPP nat nat suc na) ) 0.41/0.63 ( bool, (fun nat bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun (fun nat bool) bool) (member 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 (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.41/0.63 ( 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g)), g ) 0.41/0.63 ( 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))) ) 0.41/0.63 ( 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 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)) ) 0.41/0.63 ( 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))) ) 0.41/0.63 ( bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 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((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N_1) M_2)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) ))) 0.41/0.66 ( na, (hAPP nat nat suc na) ) 0.41/0.66 ( 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)))) ) 0.41/0.66 ( (hAPP nat nat suc na), na ) 0.41/0.66 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.41/0.66 ( (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)))) ) 0.41/0.66 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.41/0.66 ( (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 ) 0.41/0.66 ( (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) ) 0.41/0.66 ( (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.66 ( (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 x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.66 ( (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 (fun pname bool) nat (finite_card pname) u) ) 0.41/0.66 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.41/0.66 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.66 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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)))) ) 0.41/0.66 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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 x_a bool) nat (finite_card x_a) g) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.41/0.66 ( (hAPP (fun pname bool) nat (finite_card pname) 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)))) ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (forall ((Na $$unsorted) (M_3 $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc Na)) (hAPP nat nat suc M_3))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Na) M_3))) ))) 0.41/0.66 ( na, na ) 0.41/0.66 ( na, skv_1 ) 0.41/0.66 ( (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 ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), skv_1 ) 0.41/0.66 ( skv_1, na ) 0.41/0.66 ( skv_1, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))) ) 0.41/0.66 ) 0.41/0.66 (instantiation (forall ((B_1_1 $$unsorted)) (= (hBOOL (ti bool B_1_1)) (hBOOL B_1_1)) ) 0.41/0.66 ( (hAPP (fun pname bool) bool (finite_finite pname) u) ) 0.41/0.66 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 bool (hAPP x_a (fun _let_0 bool) (member x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) g) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) pn) u)) ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (combb X_b X_c X_a))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_a X_b) (fun X_a X_c))) _let_0)) )) 0.41/0.66 ( bool, bool, bool ) 0.41/0.66 ( bool, bool, pname ) 0.41/0.66 ( bool, bool, (fun pname bool) ) 0.41/0.66 ( bool, bool, nat ) 0.41/0.66 ( bool, bool, x_a ) 0.41/0.66 ( bool, bool, (fun x_a bool) ) 0.41/0.66 ( bool, (fun bool bool), pname ) 0.41/0.66 ( bool, (fun bool bool), x_a ) 0.41/0.66 ( bool, (fun x_a bool), x_a ) 0.41/0.66 ( nat, bool, (fun x_a bool) ) 0.41/0.66 ( nat, nat, nat ) 0.41/0.66 ( nat, (fun nat bool), nat ) 0.41/0.66 ( nat, (fun nat nat), (fun x_a bool) ) 0.41/0.66 ( (fun nat nat), (fun nat nat), nat ) 0.41/0.66 ( (fun bool bool), (fun bool bool), bool ) 0.41/0.66 ( x_a, (fun x_a bool), pname ) 0.41/0.66 ( x_a, (fun (fun x_a bool) bool), pname ) 0.41/0.66 ( x_a, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), pname ) 0.41/0.66 ( (fun x_a bool), bool, (fun pname bool) ) 0.41/0.66 ( (fun x_a bool), nat, (fun pname bool) ) 0.41/0.66 ( (fun x_a bool), (fun (fun x_a bool) bool), (fun x_a bool) ) 0.41/0.66 ( (fun (fun x_a bool) bool), (fun (fun x_a bool) bool), (fun x_a bool) ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (finite_card X_c))) (forall ((X_c $$unsorted)) (= _let_0 (ti (fun (fun X_c bool) nat) _let_0)) )) 0.41/0.66 ( bool ) 0.41/0.66 ( pname ) 0.41/0.66 ( (fun pname bool) ) 0.41/0.66 ( nat ) 0.41/0.66 ( (fun nat bool) ) 0.41/0.66 ( x_a ) 0.41/0.66 ( (fun x_a bool) ) 0.41/0.66 ( (fun (fun x_a bool) bool) ) 0.41/0.66 ( (fun (fun pname bool) bool) ) 0.41/0.66 ) 0.41/0.66 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) N_1)) ) 0.41/0.66 ( na ) 0.41/0.66 ( (hAPP nat nat suc na) ) 0.41/0.66 ( (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)))) ) 0.41/0.66 ( (hAPP (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.66 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.66 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) B))) )) 0.41/0.66 ( pname, pn, u ) 0.41/0.66 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (combi X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun X_a X_a) _let_0)) )) 0.41/0.66 ( bool ) 0.41/0.66 ( pname ) 0.41/0.66 ( (fun pname bool) ) 0.41/0.66 ( nat ) 0.41/0.66 ( (fun nat bool) ) 0.41/0.66 ( (fun nat nat) ) 0.41/0.66 ( (fun bool bool) ) 0.41/0.66 ( (fun bool (fun bool bool)) ) 0.41/0.66 ( (fun nat (fun nat nat)) ) 0.41/0.66 ( x_a ) 0.41/0.66 ( (fun x_a bool) ) 0.41/0.66 ( (fun (fun x_a bool) bool) ) 0.41/0.66 ( (fun pname x_a) ) 0.41/0.66 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.41/0.66 ( (fun (fun pname bool) bool) ) 0.41/0.66 ) 0.41/0.66 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_1)) (hBOOL (hAPP X_b bool A_1 X_2))) )) 0.41/0.66 ( pname, pn, u ) 0.41/0.66 ( pname, pn, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) u)) ) 0.41/0.66 ( pname, skv_7, u ) 0.41/0.66 ( (fun pname bool), u, (finite_finite pname) ) 0.41/0.66 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.41/0.66 ( (fun pname bool), u, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun _let_0 bool))) (hAPP _let_3 _let_4 (hAPP _let_2 (fun _let_3 _let_4) (combb _let_1 bool _let_0) (hAPP _let_1 _let_2 (ord_less_eq _let_1) g)) (hAPP (fun pname x_a) _let_3 (image pname x_a) mgt_call))))))) ) 0.41/0.66 ( (fun pname bool), u, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun _let_0 bool))) (hAPP _let_3 _let_4 (hAPP _let_2 (fun _let_3 _let_4) (combb _let_1 bool _let_0) (hAPP _let_1 _let_2 (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) (hAPP (fun pname x_a) _let_3 (image pname x_a) mgt_call))))))) ) 0.41/0.66 ( (fun pname bool), u, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_3)) ) 0.41/0.66 ( (fun pname bool), u, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_4)) ) 0.41/0.66 ( (fun pname bool), u, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_5)) ) 0.41/0.66 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) skv_7) ) 0.41/0.66 ( (fun pname bool), skv_4, (finite_finite pname) ) 0.41/0.66 ( (fun pname bool), skv_5, (finite_finite pname) ) 0.41/0.66 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (fun pname _let_2))) (hAPP _let_0 _let_0 (collect pname) (hAPP _let_0 _let_0 (hAPP _let_5 _let_4 (combs pname bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_1) (fun _let_0 _let_5) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) _let_4 (combc pname _let_0 bool) (member pname)) u))) (hAPP x_a _let_0 (hAPP _let_6 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_6 (hAPP (fun x_a _let_2) (fun _let_3 _let_6) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7))))))))))), (finite_finite pname) ) 0.41/0.66 ( nat, na, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.41/0.66 ( nat, na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq 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))))) ) 0.41/0.66 ( nat, (hAPP nat nat suc na), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.41/0.66 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq 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))))) ) 0.41/0.66 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc (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)))))) ) 0.41/0.67 ( nat, (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun nat (fun nat bool)))) (let ((_let_2 (fun x_a bool))) (hAPP nat (fun nat bool) (hAPP _let_1 _let_1 (combc nat nat bool) (ord_less_eq nat)) (hAPP _let_2 nat (finite_card x_a) (hAPP _let_0 _let_2 (hAPP (fun pname x_a) (fun _let_0 _let_2) (image pname x_a) mgt_call) u)))))) ) 0.41/0.67 ( 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)) ) 0.41/0.67 ( 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 (fun x_a bool) nat (finite_card x_a) g)) ) 0.41/0.67 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 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(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))) ) 0.41/0.67 ( 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)) ) 0.41/0.67 ( x_a, (ti (fun x_a bool) g), g ) 0.41/0.67 ( x_a, (ti (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))) ) 0.41/0.67 ( x_a, (ti (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)) ) 0.41/0.67 ) 0.41/0.67 (instantiation (let ((_let_0 (fun nat (fun nat bool)))) (forall ((Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat nat suc Na) (hAPP _let_0 nat (finite_card nat) (hAPP _let_0 _let_0 (collect nat) (hAPP nat _let_0 (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) Na))))) )) 0.41/0.67 ( na ) 0.41/0.67 ( (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)))) ) 0.41/0.67 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))) ) 0.41/0.67 ( (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.41/0.67 ( skv_1 ) 0.41/0.67 ) 0.41/0.67 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_b _let_1 (member X_b) X_2))) (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_2 A_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_1) B))) (hBOOL (hAPP _let_0 bool _let_2 B))) )))) 0.41/0.67 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 0.41/0.67 ( x_a, g, (hAPP pname x_a mgt_call pn), (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))) ) 0.41/0.67 ( 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))), (hAPP pname x_a mgt_call pn), g ) 0.41/0.67 ( 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))), (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)) ) 0.41/0.67 ( 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))), skv_6, g ) 0.41/0.67 ( 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)), skv_2, (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))) ) 0.41/0.67 ( 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)), skv_2, (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)) ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (let ((_let_2 (hAPP nat (fun nat bool) (ord_less_eq nat) K))) (forall ((Na $$unsorted) (K $$unsorted) (M_3 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_2 M_3))) (not (hBOOL (hAPP nat bool _let_2 Na))) (= (= Na M_3) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M_3) K) (hAPP nat nat (hAPP nat _let_0 _let_1 Na) K)))) )))) 0.41/0.68 ( 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)))) ) 0.41/0.68 ( 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)))), na ) 0.41/0.68 ( 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) ) 0.41/0.68 ( (hAPP nat nat suc na), (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.41/0.68 ( (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)))), na ) 0.41/0.68 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.41/0.68 ( (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, (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)))) ) 0.41/0.68 ( (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), na ) 0.41/0.68 ( (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)))) ) 0.41/0.68 ( (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 (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.41/0.68 ( (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 (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.68 ( (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 x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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)))) ) 0.41/0.68 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.68 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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 x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.68 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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 (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.68 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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 x_a bool) nat (finite_card x_a) g), (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)))) ) 0.41/0.68 ( (hAPP (fun pname bool) nat (finite_card pname) 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 (fun pname bool) nat (finite_card pname) u) ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (let ((_let_2 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (image X_c X_b) F))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B) (hAPP _let_1 _let_0 _let_2 A_1)))) (not (forall ((C_2 $$unsorted)) (or (not (= (hAPP _let_1 _let_0 _let_2 C_2) (ti _let_0 B))) (not (hBOOL (hAPP _let_1 bool (finite_finite X_c) C_2))) (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) C_2) A_1)))) ))) )))) 0.41/0.68 ( pname, pname, (combi pname), u, skv_3 ) 0.41/0.68 ( pname, pname, (combi pname), u, skv_4 ) 0.41/0.68 ( pname, pname, (combi pname), u, skv_5 ) 0.41/0.68 ( pname, x_a, mgt_call, u, g ) 0.41/0.68 ( pname, x_a, mgt_call, u, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.41/0.68 ( pname, x_a, mgt_call, skv_4, g ) 0.41/0.68 ( pname, x_a, mgt_call, skv_4, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.41/0.68 ( pname, x_a, mgt_call, skv_5, g ) 0.41/0.68 ( pname, x_a, mgt_call, skv_5, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.41/0.68 ( pname, x_a, mgt_call, skv_5, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (minus_minus nat))) (forall ((L $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_2 _let_3 M_2) L)) (hAPP nat nat (hAPP nat _let_2 _let_3 N_1) L)))) ))))) 0.41/0.68 ( (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 nat suc (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))))) ) 0.41/0.68 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 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(finite_finite X_b) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1) B))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 A_1)) (hAPP _let_0 nat _let_1 B)))) ))) 0.41/0.68 ( pname, skv_3, u ) 0.41/0.68 ( pname, skv_4, u ) 0.41/0.68 ( pname, skv_5, u ) 0.41/0.68 ( nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) na))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) na))) ) 0.41/0.68 ( x_a, g, g ) 0.41/0.68 ( 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))) ) 0.41/0.68 ( 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)) ) 0.41/0.68 ( 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 ) 0.41/0.68 ( 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)) ) 0.41/0.68 ( 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))) ) 0.41/0.68 ( 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)) ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (hAPP X_b (fun (fun X_b bool) (fun X_b bool)) (insert X_b) X_2))) (let ((_let_1 (hAPP (fun X_b bool) (fun X_b bool) _let_0 A_1))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= _let_1 (hAPP _let_0 _let_0 _let_0 _let_1))) ))) 0.41/0.68 ( pname, pn, u ) 0.41/0.68 ) 0.41/0.68 (instantiation (forall ((N_1 $$unsorted) (M_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N_1)) M_1))) (not (forall ((M $$unsorted)) (not (= M_1 (hAPP nat nat suc M))) ))) ) 0.41/0.68 ( na, na ) 0.41/0.68 ( na, (hAPP nat nat suc na) ) 0.41/0.68 ( 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)))) ) 0.41/0.68 ( (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) ) 0.41/0.68 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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)))) ) 0.41/0.68 ( skv_1, na ) 0.41/0.68 ( skv_1, (hAPP nat nat suc na) ) 0.41/0.68 ( skv_1, (hAPP (fun x_a bool) nat (finite_card x_a) g) ) 0.41/0.68 ( skv_1, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.41/0.68 ( skv_1, (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP X_b (fun _let_0 bool) (member X_b) A_2))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (or (and (not (hBOOL (hAPP _let_0 bool _let_1 B))) (not (= (ti X_b A_2) (ti X_b B_1)))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_1) B)))) ))) 0.41/0.68 ( pname, pn, pn, u ) 0.41/0.68 ( pname, pn, skv_7, u ) 0.41/0.68 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 0.41/0.68 ( x_a, (hAPP pname x_a mgt_call pn), skv_2, g ) 0.41/0.68 ) 0.41/0.68 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) A_2) A_1))) (= (ti _let_0 A_1) (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_1))) )) 0.41/0.68 ( pname, pn, u ) 0.41/0.68 ( pname, skv_7, u ) 0.41/0.68 ( (fun pname bool), u, (finite_finite pname) ) 0.41/0.68 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.41/0.68 ( 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)) ) 0.41/0.68 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.41/0.68 ( x_a, (hAPP pname x_a mgt_call pn), (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))) ) 0.41/0.68 ( 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)) ) 0.41/0.68 ( x_a, skv_2, (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))) ) 0.41/0.68 ( x_a, skv_2, (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)) ) 0.41/0.68 ( x_a, skv_6, g ) 0.41/0.68 ( x_a, skv_6, (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))) ) 0.41/0.68 ( (fun x_a bool), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.41/0.68 ( (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)) ) 0.41/0.69 ( (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))) ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (= (not (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) AA) A_1))) (not (= (hAPP _let_0 _let_1 _let_2 AA) (ti _let_1 B)))) )) (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) B) (hAPP _let_0 _let_1 _let_2 A_1)))) )))) 0.41/0.69 ( pname, pname, skv_3, (combi pname), u ) 0.41/0.69 ( pname, pname, skv_4, (combi pname), u ) 0.41/0.69 ( pname, pname, skv_5, (combi pname), u ) 0.41/0.69 ( x_a, pname, g, mgt_call, u ) 0.41/0.69 ( x_a, pname, g, mgt_call, skv_4 ) 0.41/0.69 ( x_a, pname, g, mgt_call, skv_5 ) 0.41/0.69 ( x_a, pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), mgt_call, skv_4 ) 0.41/0.69 ( x_a, pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), mgt_call, skv_5 ) 0.41/0.69 ( x_a, pname, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), mgt_call, u ) 0.41/0.69 ( x_a, pname, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), mgt_call, skv_5 ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1) B))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 B)) (hAPP _let_0 nat _let_1 A_1)))) (= (ti _let_0 A_1) (ti _let_0 B))) ))) 0.41/0.69 ( pname, skv_3, u ) 0.41/0.69 ( pname, skv_4, u ) 0.41/0.69 ( pname, skv_5, u ) 0.41/0.69 ( nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) na))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) na))) ) 0.41/0.69 ( x_a, g, g ) 0.41/0.69 ( 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))) ) 0.41/0.69 ( 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)) ) 0.41/0.69 ( 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 ) 0.41/0.69 ( 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)) ) 0.41/0.69 ( 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 ) 0.41/0.69 ( 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))) ) 0.41/0.69 ( 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)) ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (insert X_b))) (forall ((X_b $$unsorted)) (= _let_1 (ti (fun X_b (fun _let_0 _let_0)) _let_1)) ))) 0.41/0.69 ( bool ) 0.41/0.69 ( pname ) 0.41/0.69 ( (fun pname bool) ) 0.41/0.69 ( nat ) 0.41/0.69 ( (fun nat bool) ) 0.41/0.69 ( x_a ) 0.41/0.69 ( (fun x_a bool) ) 0.41/0.69 ( (fun (fun x_a bool) bool) ) 0.41/0.69 ( (fun (fun pname bool) bool) ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 B))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_1) B)))) ))) 0.41/0.69 ( pname, pn, skv_3, u ) 0.41/0.69 ( pname, pn, skv_4, u ) 0.41/0.69 ( pname, pn, skv_5, u ) 0.41/0.69 ( x_a, (hAPP pname x_a mgt_call pn), g, g ) 0.41/0.69 ( x_a, (hAPP pname x_a mgt_call pn), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 0.41/0.69 ( x_a, (hAPP pname x_a mgt_call pn), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (collect X_b))) (forall ((X_b $$unsorted)) (= _let_1 (ti (fun _let_0 _let_0) _let_1)) ))) 0.41/0.69 ( bool ) 0.41/0.69 ( pname ) 0.41/0.69 ( (fun pname bool) ) 0.41/0.69 ( nat ) 0.41/0.69 ( (fun nat bool) ) 0.41/0.69 ( x_a ) 0.41/0.69 ( (fun x_a bool) ) 0.41/0.69 ( (fun (fun x_a bool) bool) ) 0.41/0.69 ( (fun (fun pname bool) bool) ) 0.41/0.69 ) 0.41/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (forall ((X_b $$unsorted) (BOUND_VARIABLE_2846 $$unsorted) (BOUND_VARIABLE_2847 $$unsorted) (BOUND_VARIABLE_2848 $$unsorted)) (or (not (order X_b)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP nat X_b BOUND_VARIABLE_2848 N_2)) (hAPP nat X_b BOUND_VARIABLE_2848 (hAPP nat nat suc N_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_2846) BOUND_VARIABLE_2847))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP nat X_b BOUND_VARIABLE_2848 BOUND_VARIABLE_2846)) (hAPP nat X_b BOUND_VARIABLE_2848 BOUND_VARIABLE_2847)))) ))) 0.41/0.69 ( nat, na, skv_1, suc ) 0.41/0.69 ( 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)))), na, suc ) 0.41/0.69 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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))))) ) 0.41/0.69 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), skv_1, suc ) 0.41/0.69 ( nat, skv_1, na, suc ) 0.41/0.69 ( nat, skv_1, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), suc ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (= (ti _let_0 A_1) (ti _let_0 B))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1) B))) )) 0.49/0.69 ( pname, skv_3, u ) 0.49/0.69 ( pname, skv_4, u ) 0.49/0.69 ( pname, skv_5, u ) 0.49/0.69 ( x_a, g, g ) 0.49/0.69 ( 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))) ) 0.49/0.69 ( 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)) ) 0.49/0.69 ( 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 ) 0.49/0.69 ( 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)) ) 0.49/0.69 ( 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))) ) 0.49/0.69 ( 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)) ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1))) (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_1)) (= (hBOOL (hAPP _let_0 bool _let_1 B)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) B))))) ))) 0.49/0.69 ( pname, u, pn, skv_3 ) 0.49/0.69 ( pname, u, pn, skv_4 ) 0.49/0.69 ( pname, u, pn, skv_5 ) 0.49/0.69 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 0.49/0.69 ( x_a, g, (hAPP pname x_a mgt_call pn), (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))) ) 0.49/0.69 ( x_a, g, (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)) ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (let ((_let_2 (hAPP nat (fun nat nat) (minus_minus nat) L))) (forall ((L $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat _let_2 N_1)) (hAPP nat nat _let_2 M_2)))) )))) 0.49/0.69 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (let ((_let_3 (hAPP _let_0 _let_1 _let_2 A_1))) (forall ((X_b $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_3 B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) C))) (hBOOL (hAPP _let_0 bool _let_3 C))) ))))) 0.49/0.69 ( x_a, 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))) ) 0.49/0.69 ( 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))), g ) 0.49/0.69 ( 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, g ) 0.49/0.69 ( 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)), (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)) ) 0.49/0.69 ( 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))), (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)) ) 0.49/0.69 ( 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)), (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))) ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP X_b (fun _let_0 bool) (member X_b) A_2))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (= (or (= (ti X_b B_1) (ti X_b A_2)) (hBOOL (hAPP _let_0 bool _let_1 A_1))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_1) A_1)))) ))) 0.49/0.69 ( pname, pn, pn, u ) 0.49/0.69 ( pname, skv_7, pn, u ) 0.49/0.69 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 0.49/0.69 ( x_a, skv_2, (hAPP pname x_a mgt_call pn), g ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun (fun X_b bool) (fun X_b bool)))) (let ((_let_1 (insert X_b))) (let ((_let_2 (hAPP X_b _let_0 _let_1 X_2))) (let ((_let_3 (hAPP X_b _let_0 _let_1 Y_2))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 _let_3 (hAPP _let_0 _let_0 _let_2 A_1)) (hAPP _let_0 _let_0 _let_2 (hAPP _let_0 _let_0 _let_3 A_1)))) ))))) 0.49/0.69 ( pname, pn, pn, u ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_1))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) X_2) A_1))) (= _let_2 (hAPP _let_0 _let_0 (hAPP X_c (fun _let_0 _let_0) (insert X_c) (hAPP X_b X_c F X_2)) _let_2))) )))) 0.49/0.69 ( pname, pname, (combi pname), pn, u ) 0.49/0.69 ( x_a, pname, mgt_call, pn, skv_4 ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) A_1))) (= (ti _let_0 A_1) (ti _let_0 B))) )))) 0.49/0.69 ( pname, u, skv_3 ) 0.49/0.69 ( pname, u, skv_4 ) 0.49/0.69 ( pname, u, skv_5 ) 0.49/0.69 ( pname, skv_3, u ) 0.49/0.69 ( pname, skv_4, u ) 0.49/0.69 ( pname, skv_5, u ) 0.49/0.69 ( x_a, g, g ) 0.49/0.69 ( 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))) ) 0.49/0.69 ( 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)) ) 0.49/0.69 ( 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 ) 0.49/0.69 ( 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)) ) 0.49/0.69 ( 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 ) 0.49/0.69 ( 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))) ) 0.49/0.69 ( 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)) ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (collect X_b))) (let ((_let_2 (fun X_b _let_0))) (let ((_let_3 (fun (fun X_b bool) (fun X_b bool)))) (let ((_let_4 (fun X_b (fun X_b bool)))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (let ((_let_0 (fun X_b bool))) (= (hAPP _let_0 _let_0 (hAPP X_b _let_3 (insert X_b) A_2) (hAPP _let_0 _let_0 _let_1 Pa)) (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 (hAPP _let_2 _let_3 (combs X_b bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_0) (fun _let_0 _let_2) (combb bool _let_0 X_b) fimplies) (hAPP _let_0 _let_0 (hAPP _let_0 _let_3 (combb bool bool X_b) fNot) (hAPP X_b _let_0 (hAPP _let_4 _let_4 (combc X_b X_b bool) (fequal X_b)) A_2)))) Pa)))) )))))) 0.49/0.69 ( pname, pn, u ) 0.49/0.69 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.49/0.69 ) 0.49/0.69 (instantiation (forall ((N_1 $$unsorted)) (not (= N_1 (hAPP nat nat suc N_1))) ) 0.49/0.69 ( na ) 0.49/0.69 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.49/0.69 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.49/0.69 ( (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.49/0.69 ( skv_1 ) 0.49/0.69 ) 0.49/0.69 (instantiation (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (let ((_let_2 (fun X_b X_c))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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)) )))) 0.49/0.70 ( nat, bool, nat, (ord_less_eq nat), suc, (hAPP (fun x_a bool) nat (finite_card x_a) g) ) 0.49/0.70 ( nat, bool, nat, (ord_less_eq nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc 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)))) ) 0.49/0.70 ( nat, bool, nat, (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun nat nat))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb nat _let_0 nat) (ord_less_eq nat)) suc)))), suc, na ) 0.49/0.70 ( nat, bool, nat, (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun nat nat))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb nat _let_0 nat) (ord_less_eq nat)) suc)))), (combi nat), na ) 0.49/0.70 ( nat, nat, nat, (minus_minus nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc 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)))) ) 0.49/0.70 ( x_a, bool, (fun x_a bool), (member x_a), (let ((_let_0 (fun x_a bool))) (let ((_let_1 (fun x_a _let_0))) (hAPP _let_0 _let_1 (hAPP (fun x_a (fun _let_0 _let_0)) (fun _let_0 _let_1) (combc x_a _let_0 _let_0) (insert x_a)) g))), (hAPP pname x_a mgt_call pn) ) 0.49/0.70 ( (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 ) 0.49/0.70 ( (fun x_a bool), bool, (fun x_a bool), (ord_less_eq (fun x_a bool)), (collect x_a), g ) 0.49/0.70 ( (fun x_a bool), bool, (fun x_a bool), (let ((_let_0 (fun (fun x_a bool) bool))) (let ((_let_1 (fun (fun x_a bool) (fun x_a bool)))) (let ((_let_2 (fun (fun x_a bool) _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb (fun x_a bool) _let_0 (fun x_a bool)) (ord_less_eq (fun x_a bool))) (hAPP x_a _let_1 (insert x_a) (hAPP pname x_a mgt_call pn)))))), (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 ) 0.49/0.70 ) 0.49/0.70 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP X_b (fun _let_0 bool) (member X_b) X_2))) (let ((_let_2 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2))) (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (hBOOL (hAPP _let_0 bool _let_1 A_1)) (hBOOL (hAPP _let_0 bool _let_1 B)) (= (= (hAPP _let_0 _let_0 _let_2 A_1) (hAPP _let_0 _let_0 _let_2 B)) (= (ti _let_0 B) (ti _let_0 A_1)))) )))) 0.49/0.70 ( pname, u, pn, u ) 0.49/0.70 ( pname, u, skv_7, u ) 0.49/0.70 ( (fun pname bool), (finite_finite pname), u, (finite_finite pname) ) 0.49/0.70 ( (fun pname bool), (finite_finite pname), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.49/0.70 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u, (finite_finite pname) ) 0.49/0.70 ( 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)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.49/0.70 ( x_a, g, (hAPP pname x_a mgt_call pn), g ) 0.49/0.70 ( x_a, g, (hAPP pname x_a mgt_call pn), (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))) ) 0.49/0.70 ( x_a, g, skv_6, g ) 0.49/0.70 ( x_a, g, skv_6, (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))) ) 0.49/0.70 ( 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))), (hAPP pname x_a mgt_call pn), g ) 0.49/0.70 ( 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))), skv_2, (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)) ) 0.49/0.70 ( 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))), skv_6, g ) 0.49/0.70 ( 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), (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)) ) 0.49/0.70 ( 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)), skv_2, (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))) ) 0.49/0.70 ( 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)), skv_2, (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)) ) 0.49/0.70 ( (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.49/0.70 ( (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))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.49/0.70 ( (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))), (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))) ) 0.49/0.70 ( (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))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.49/0.70 ) 0.49/0.70 (instantiation (let ((_let_0 (ord_less_eq X_a))) (forall ((X_a $$unsorted)) (or (not (preorder X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) )) 0.49/0.70 ( bool ) 0.49/0.70 ( pname ) 0.49/0.70 ( (fun pname bool) ) 0.49/0.70 ( nat ) 0.49/0.70 ( (fun nat bool) ) 0.49/0.70 ( (fun nat nat) ) 0.49/0.70 ( (fun bool bool) ) 0.49/0.70 ( (fun bool (fun bool bool)) ) 0.49/0.70 ( (fun nat (fun nat nat)) ) 0.49/0.70 ( x_a ) 0.49/0.70 ( (fun x_a bool) ) 0.49/0.70 ( (fun (fun x_a bool) bool) ) 0.49/0.70 ( (fun (fun pname bool) (fun x_a bool)) ) 0.49/0.70 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.49/0.70 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.49/0.70 ( (fun (fun pname bool) bool) ) 0.49/0.70 ) 0.49/0.70 (instantiation (let ((_let_0 (combs X_a X_b X_c))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun (fun X_a X_b) (fun X_a X_c))) _let_0)) )) 0.49/0.70 ( bool, bool, bool ) 0.49/0.70 ( bool, (fun bool bool), (fun bool bool) ) 0.49/0.70 ( pname, bool, bool ) 0.49/0.70 ( pname, bool, (fun bool bool) ) 0.49/0.70 ( pname, x_a, (fun x_a bool) ) 0.49/0.70 ( pname, x_a, (fun (fun x_a bool) bool) ) 0.49/0.70 ( pname, x_a, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.49/0.70 ( (fun pname bool), bool, bool ) 0.49/0.70 ( (fun pname bool), (fun x_a bool), bool ) 0.49/0.70 ( (fun pname bool), (fun x_a bool), nat ) 0.49/0.70 ( nat, bool, bool ) 0.49/0.70 ( nat, nat, nat ) 0.49/0.70 ( nat, nat, (fun nat bool) ) 0.49/0.70 ( nat, (fun nat nat), (fun nat nat) ) 0.49/0.70 ( x_a, bool, bool ) 0.49/0.70 ( x_a, bool, (fun bool bool) ) 0.49/0.70 ( x_a, bool, (fun x_a bool) ) 0.49/0.70 ( (fun x_a bool), bool, bool ) 0.49/0.70 ( (fun x_a bool), nat, bool ) 0.49/0.70 ( (fun x_a bool), nat, (fun nat nat) ) 0.49/0.70 ( (fun x_a bool), (fun x_a bool), (fun (fun x_a bool) bool) ) 0.49/0.70 ( (fun x_a bool), (fun (fun x_a bool) bool), (fun (fun x_a bool) bool) ) 0.49/0.70 ) 0.49/0.70 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N_1) M_2))) (= M_2 N_1)) ))) 0.49/0.70 ( na, (hAPP nat nat suc na) ) 0.49/0.70 ( 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)))) ) 0.49/0.70 ( (hAPP nat nat suc na), na ) 0.49/0.70 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.49/0.70 ( (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)))) ) 0.49/0.70 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.49/0.70 ( (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 ) 0.49/0.70 ( (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) ) 0.49/0.70 ( (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.49/0.70 ( (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 x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.49/0.70 ( (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 (fun pname bool) nat (finite_card pname) u) ) 0.49/0.70 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.49/0.70 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.49/0.70 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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)))) ) 0.49/0.70 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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 x_a bool) nat (finite_card x_a) g) ) 0.49/0.70 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.49/0.70 ( (hAPP (fun pname bool) nat (finite_card pname) 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)))) ) 0.49/0.71 ) 0.49/0.71 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (hAPP _let_1 _let_1 (hAPP X_b (fun _let_1 _let_1) (insert X_b) (hAPP X_c X_b F A_2)) (hAPP _let_0 _let_1 _let_2 B)) (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 (hAPP X_c (fun _let_0 _let_0) (insert X_c) A_2) B))) )))) 0.49/0.71 ( pname, pname, (combi pname), pn, u ) 0.49/0.71 ( pname, x_a, mgt_call, pn, u ) 0.49/0.71 ( pname, x_a, mgt_call, pn, skv_4 ) 0.49/0.71 ) 0.49/0.71 (instantiation (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP X_b X_c P (hAPP X_a X_b Q R)) (hAPP X_a X_c (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)) ))) 0.49/0.71 ( pname, bool, pname, u, (combi pname), pn ) 0.49/0.71 ( pname, bool, pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) u)), (combi pname), pn ) 0.49/0.71 ( pname, bool, x_a, g, mgt_call, pn ) 0.49/0.71 ( pname, bool, x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP (fun x_a (fun _let_0 bool)) (fun _let_0 _let_0) (combc x_a _let_0 bool) (member x_a)) g)), mgt_call, pn ) 0.49/0.71 ( pname, bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) u)), (member pname), pn ) 0.49/0.71 ( pname, pname, pname, (combi pname), (combi pname), pn ) 0.49/0.71 ( pname, (fun pname bool), x_a, (let ((_let_0 (fun x_a bool))) (let ((_let_1 (fun pname x_a))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 (fun x_a (fun pname bool)) (combc pname x_a bool) (hAPP _let_1 _let_2 (hAPP (fun x_a _let_0) (fun _let_1 _let_2) (combb x_a _let_0 pname) (fequal x_a)) mgt_call))))), mgt_call, skv_7 ) 0.49/0.71 ( pname, x_a, pname, mgt_call, (combi pname), pn ) 0.49/0.71 ( pname, (fun x_a 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((_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)))) ) 0.49/0.73 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))) ) 0.49/0.73 ( (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 ) 0.49/0.73 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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)))) ) 0.49/0.73 ( (hAPP (fun pname bool) nat (finite_card pname) u), (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.49/0.73 ( (hAPP (fun pname bool) nat (finite_card pname) u), skv_1 ) 0.49/0.73 ( skv_1, (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.49/0.74 ) 0.49/0.74 (instantiation (forall ((I $$unsorted) (Pa $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP nat bool Pa K))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool Pa (hAPP nat nat suc N_2)))) (hBOOL (hAPP nat bool Pa N_2))) )) (hBOOL (hAPP nat bool Pa (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) K) I)))) ) 0.49/0.74 ( (hAPP nat nat suc na), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP (fun x_a bool) nat (finite_card x_a) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.49/0.74 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq 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))))), (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)))) ) 0.49/0.74 ( (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq 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))))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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)))) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq 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))))), (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)))) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc (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)))) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun nat (fun nat bool)))) (let ((_let_2 (fun x_a bool))) (hAPP nat (fun nat bool) (hAPP _let_1 _let_1 (combc nat nat bool) (ord_less_eq nat)) (hAPP _let_2 nat (finite_card x_a) (hAPP _let_0 _let_2 (hAPP (fun pname x_a) (fun _let_0 _let_2) (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)))) ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP X_b (fun _let_0 bool) (member X_b) A_2))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 B))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_1) B)))) ))) 0.49/0.74 ( pname, pn, pn, u ) 0.49/0.74 ( pname, pn, skv_7, u ) 0.49/0.74 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 0.49/0.74 ( x_a, (hAPP pname x_a mgt_call pn), skv_2, g ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_2)) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) ))) 0.49/0.74 ( na, na ) 0.49/0.74 ( na, (hAPP nat nat suc na) ) 0.49/0.74 ( 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)))) ) 0.49/0.74 ( (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) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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)))) ) 0.49/0.74 ( skv_1, na ) 0.49/0.74 ( skv_1, (hAPP nat nat suc na) ) 0.49/0.74 ( skv_1, (hAPP (fun x_a bool) nat (finite_card x_a) g) ) 0.49/0.74 ( skv_1, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.49/0.74 ( skv_1, (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) B_1) (hAPP _let_0 _let_1 (hAPP (fun X_c X_b) (fun _let_0 _let_1) (image X_c X_b) F) A_1)))) (not (forall ((X_1 $$unsorted)) (or (not (= (hAPP X_c X_b F X_1) (ti X_b B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP X_c (fun _let_0 bool) (member X_c) X_1) A_1)))) ))) ))) 0.49/0.74 ( pname, pname, pn, (combi pname), u ) 0.49/0.74 ( pname, pname, skv_7, (combi pname), u ) 0.49/0.74 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, u ) 0.49/0.74 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, skv_4 ) 0.49/0.74 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, skv_5 ) 0.49/0.74 ( x_a, pname, skv_2, mgt_call, u ) 0.49/0.74 ( x_a, pname, skv_2, mgt_call, skv_5 ) 0.49/0.74 ( x_a, pname, skv_6, mgt_call, u ) 0.49/0.74 ( x_a, pname, skv_6, mgt_call, skv_4 ) 0.49/0.74 ) 0.49/0.74 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_2992 $$unsorted)) (or (not (finite_finite_1 X_b)) (hBOOL (hAPP (fun X_b bool) bool (finite_finite X_b) BOUND_VARIABLE_2992))) ) 0.49/0.74 ( pname, u ) 0.49/0.74 ( pname, skv_4 ) 0.49/0.74 ( pname, skv_5 ) 0.49/0.74 ( pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (fun pname _let_2))) (hAPP _let_0 _let_0 (collect pname) (hAPP _let_0 _let_0 (hAPP _let_5 _let_4 (combs pname bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_1) (fun _let_0 _let_5) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) _let_4 (combc pname _let_0 bool) (member pname)) u))) (hAPP x_a _let_0 (hAPP _let_6 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_6 (hAPP (fun x_a _let_2) (fun _let_3 _let_6) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7))))))))))) ) 0.49/0.74 ( x_a, g ) 0.49/0.74 ( 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))) ) 0.49/0.74 ( 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)) ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat _let_1 A_1)) (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) A_1))))) ))) 0.49/0.74 ( pname, pn, u ) 0.49/0.74 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun x_a bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((Ts $$unsorted) (G_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) Ts) G_1))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 p G_1) Ts))) ))) 0.49/0.74 ( g, g ) 0.49/0.74 ( g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.49/0.74 ( g, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.49/0.74 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.49/0.74 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less_eq nat) M_2))) (let ((_let_1 (hAPP nat nat suc N_1))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 _let_1))) (hBOOL (hAPP nat bool _let_0 N_1)) (= M_2 _let_1)) ))) 0.49/0.74 ( na, skv_1 ) 0.49/0.74 ( (hAPP nat nat suc na), na ) 0.49/0.74 ( (hAPP nat nat suc na), skv_1 ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.49/0.74 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.49/0.74 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), skv_1 ) 0.49/0.74 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), skv_1 ) 0.49/0.74 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), na ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP _let_0 nat (finite_card X_c) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_1))) (hAPP _let_1 nat (finite_card X_b) A_1)))) ))) 0.49/0.74 ( bool, bool, (combi bool), fNot ) 0.49/0.74 ( pname, pname, (combi pname), u ) 0.49/0.74 ( x_a, pname, mgt_call, u ) 0.49/0.74 ( x_a, pname, mgt_call, skv_3 ) 0.49/0.74 ( x_a, pname, mgt_call, skv_4 ) 0.49/0.74 ( x_a, pname, mgt_call, skv_5 ) 0.49/0.74 ( x_a, x_a, (combi x_a), g ) 0.49/0.74 ) 0.49/0.74 (instantiation (let ((_let_0 (fun X_b X_c))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (= (hAPP X_b X_c F X_1) (hAPP X_b X_c G X_1)) )) (= (ti _let_0 G) (ti _let_0 F))) )) 0.49/0.74 ( bool, bool, fNot, fNot ) 0.49/0.74 ( bool, bool, fNot, (ti (fun bool bool) fNot) ) 0.49/0.74 ( bool, bool, fNot, (combi bool) ) 0.49/0.74 ( bool, bool, (ti (fun bool bool) fNot), fNot ) 0.49/0.74 ( bool, bool, (combi bool), (ti (fun bool bool) fNot) ) 0.49/0.74 ( bool, (fun bool bool), fdisj, fdisj ) 0.49/0.74 ( bool, (fun bool bool), fdisj, fimplies ) 0.49/0.74 ( bool, (fun bool bool), fdisj, fconj ) 0.49/0.74 ( bool, (fun bool bool), fdisj, (fequal bool) ) 0.49/0.74 ( bool, (fun bool bool), fdisj, (ord_less_eq bool) ) 0.49/0.74 ( bool, (fun bool bool), (ti (fun bool (fun bool bool)) fdisj), fconj ) 0.49/0.74 ( bool, (fun bool bool), fimplies, fdisj ) 0.49/0.74 ( bool, (fun bool bool), fimplies, fimplies ) 0.49/0.74 ( bool, (fun bool bool), fimplies, fconj ) 0.49/0.74 ( bool, (fun bool bool), fimplies, (fequal bool) ) 0.49/0.74 ( bool, (fun bool bool), (ti (fun bool (fun bool bool)) fimplies), (ti (fun bool (fun bool bool)) fdisj) ) 0.49/0.74 ( bool, (fun bool bool), fconj, fdisj ) 0.49/0.74 ( bool, (fun bool bool), fconj, (ti (fun bool (fun bool bool)) fdisj) ) 0.49/0.74 ( bool, (fun bool bool), fconj, fimplies ) 0.49/0.74 ( bool, (fun bool bool), fconj, (ti (fun bool (fun bool bool)) fimplies) ) 0.49/0.74 ( bool, (fun bool bool), fconj, fconj ) 0.49/0.74 ( bool, (fun bool bool), (ti (fun bool (fun bool bool)) fconj), (ti (fun bool (fun bool bool)) fconj) ) 0.49/0.74 ( bool, (fun bool bool), (fequal bool), fdisj ) 0.49/0.74 ( bool, (fun bool bool), (ord_less_eq bool), fimplies ) 0.49/0.74 ( bool, (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (insert bool), (insert bool) ) 0.49/0.74 ( pname, bool, u, u ) 0.49/0.74 ( pname, bool, u, (ti (fun pname bool) u) ) 0.49/0.74 ( pname, bool, (ti (fun pname bool) u), u ) 0.49/0.74 ( pname, (fun pname bool), (fequal pname), (fequal pname) ) 0.49/0.74 ( pname, (fun pname bool), (fequal pname), (ord_less_eq pname) ) 0.49/0.74 ( pname, (fun pname bool), (ord_less_eq pname), (fequal pname) ) 0.49/0.74 ( pname, x_a, mgt_call, mgt_call ) 0.49/0.74 ( pname, x_a, mgt_call, (ti (fun pname x_a) mgt_call) ) 0.49/0.74 ( pname, x_a, (ti (fun pname x_a) mgt_call), mgt_call ) 0.49/0.74 ( pname, (fun (fun pname bool) bool), (member pname), (member pname) ) 0.49/0.74 ( pname, (let ((_let_0 (fun pname bool))) (fun _let_0 _let_0)), (insert pname), (insert pname) ) 0.49/0.74 ( (fun pname bool), bool, (finite_finite pname), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.49/0.74 ( (fun pname bool), bool, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), (finite_finite pname) ) 0.49/0.74 ( (fun pname bool), bool, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.49/0.74 ( (fun pname bool), (fun pname bool), (collect pname), (collect pname) ) 0.49/0.74 ( (fun pname bool), nat, (finite_card pname), (finite_card pname) ) 0.49/0.74 ( (fun pname bool), (fun x_a bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call) ) 0.49/0.74 ( (fun pname bool), (fun (fun pname bool) bool), (ord_less_eq (fun pname bool)), (fequal (fun pname bool)) ) 0.49/0.74 ( (fun pname bool), (fun (fun pname bool) bool), (fequal (fun pname bool)), (ord_less_eq (fun pname bool)) ) 0.49/0.74 ( (fun pname bool), (fun (fun pname bool) bool), (fequal (fun pname bool)), (fequal (fun pname bool)) ) 0.49/0.74 ( (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (fun _let_0 _let_0)), (insert (fun pname bool)), (insert (fun pname bool)) ) 0.49/0.75 ( nat, bool, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.49/0.75 ( nat, nat, suc, suc ) 0.49/0.75 ( nat, nat, suc, (ti (fun nat nat) suc) ) 0.49/0.75 ( nat, nat, suc, (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))))) ) 0.49/0.75 ( nat, nat, (ti (fun nat nat) suc), (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))))) ) 0.49/0.75 ( 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 ) 0.49/0.75 ( nat, nat, (combi nat), (combi nat) ) 0.49/0.75 ( nat, (fun nat bool), (ord_less_eq nat), (fequal nat) ) 0.49/0.75 ( nat, (fun nat bool), (fequal nat), (ord_less_eq nat) ) 0.49/0.75 ( nat, (fun nat bool), (fequal nat), (fequal nat) ) 0.49/0.75 ( nat, (fun nat nat), (minus_minus nat), (minus_minus nat) ) 0.49/0.75 ( nat, (fun nat nat), (minus_minus nat), (ti (fun nat (fun nat nat)) (minus_minus nat)) ) 0.49/0.75 ( nat, (fun nat nat), (ti (fun nat (fun nat nat)) (minus_minus nat)), (minus_minus nat) ) 0.49/0.75 ( nat, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (insert nat), (insert nat) ) 0.49/0.75 ( (fun nat bool), nat, (finite_card nat), (finite_card nat) ) 0.49/0.75 ( (fun nat bool), (fun nat bool), (collect nat), (collect nat) ) 0.49/0.75 ( (fun bool bool), nat, (finite_card bool), (finite_card bool) ) 0.49/0.75 ( (fun bool bool), (fun bool bool), (collect bool), (collect bool) ) 0.49/0.75 ( (fun bool bool), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (combb bool bool x_a), (combb bool bool x_a) ) 0.49/0.75 ( (fun bool (fun bool bool)), (fun bool (fun bool bool)), (combc bool bool bool), (combc bool bool bool) ) 0.49/0.75 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (combc nat nat nat) ) 0.49/0.75 ( x_a, bool, g, g ) 0.49/0.75 ( 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))) ) 0.49/0.75 ( 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)) ) 0.49/0.75 ( 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 ) 0.49/0.75 ( 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))) ) 0.49/0.75 ( x_a, bool, (ti (fun x_a bool) g), (ti (fun x_a bool) g) ) 0.49/0.75 ( x_a, (fun x_a bool), (fequal x_a), (fequal x_a) ) 0.49/0.75 ( x_a, (fun x_a bool), (fequal x_a), (ord_less_eq x_a) ) 0.49/0.75 ( x_a, (fun x_a bool), (ord_less_eq x_a), (fequal x_a) ) 0.49/0.75 ( x_a, (fun (fun x_a bool) bool), (member x_a), (member x_a) ) 0.49/0.75 ( x_a, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (insert x_a), (insert x_a) ) 0.49/0.75 ( (fun x_a bool), bool, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.49/0.75 ( (fun x_a bool), bool, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.49/0.75 ( (fun x_a bool), bool, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), (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))) ) 0.49/0.75 ( (fun x_a bool), bool, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.49/0.75 ( (fun x_a bool), 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 x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.49/0.75 ( (fun x_a bool), bool, (finite_finite x_a), (finite_finite x_a) ) 0.49/0.75 ( (fun x_a bool), nat, (finite_card x_a), (finite_card x_a) ) 0.49/0.75 ( (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))), (collect x_a) ) 0.49/0.75 ( (fun x_a bool), (fun x_a bool), (collect x_a), (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))) ) 0.49/0.75 ( (fun x_a bool), (fun x_a bool), (collect x_a), (collect x_a) ) 0.49/0.75 ( (fun x_a bool), (fun x_a bool), (collect x_a), (combi (fun x_a bool)) ) 0.49/0.75 ( (fun x_a bool), (fun x_a bool), (combi (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))) ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), (ord_less_eq (fun x_a bool)), (fequal (fun x_a bool)) ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), p, (ord_less_eq (fun x_a bool)) ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), p, p ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), p, (fequal (fun x_a bool)) ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), (let ((_let_0 (fun x_a bool))) (ti (fun _let_0 (fun _let_0 bool)) p)), (let ((_let_0 (fun x_a bool))) (ti (fun _let_0 (fun _let_0 bool)) p)) ) 0.49/0.75 ( (fun x_a bool), (fun (fun x_a bool) bool), (fequal (fun x_a bool)), p ) 0.49/0.75 ( (fun x_a bool), (let ((_let_0 (fun (fun x_a bool) bool))) (fun _let_0 _let_0)), (insert (fun x_a bool)), (insert (fun x_a bool)) ) 0.49/0.75 ( (fun (fun x_a bool) bool), nat, (finite_card (fun x_a bool)), (finite_card (fun x_a bool)) ) 0.49/0.75 ( (fun (fun x_a bool) bool), (fun (fun x_a bool) bool), (collect (fun x_a bool)), (collect (fun x_a bool)) ) 0.49/0.75 ( (fun pname x_a), (fun (fun pname bool) (fun x_a bool)), (image pname x_a), (image pname x_a) ) 0.49/0.75 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun x_a bool))) (combc _let_0 _let_0 bool)), (let ((_let_0 (fun x_a bool))) (combc _let_0 _let_0 bool)) ) 0.49/0.75 ( (fun (fun pname bool) bool), nat, (finite_card (fun pname bool)), (finite_card (fun pname bool)) ) 0.49/0.75 ( (fun (fun pname bool) bool), (fun (fun pname bool) bool), (collect (fun pname bool)), (collect (fun pname bool)) ) 0.49/0.75 ( (fun x_a (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (image x_a (fun x_a bool)), (image x_a (fun x_a bool)) ) 0.49/0.75 ( (fun x_a x_a), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (image x_a x_a), (image x_a x_a) ) 0.49/0.75 ( (fun x_a (fun (fun pname bool) bool)), (fun (fun pname bool) (fun x_a bool)), (combc x_a (fun pname bool) bool), (combc x_a (fun pname bool) bool) ) 0.49/0.75 ( (fun x_a (fun (fun x_a bool) bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (combc x_a (fun x_a bool) bool), (combc x_a (fun x_a bool) bool) ) 0.49/0.75 ( (fun x_a (fun bool bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (combs x_a bool bool), (combs x_a bool bool) ) 0.49/0.75 ) 0.49/0.75 (instantiation (let ((_let_0 (member X_b))) (forall ((X_b $$unsorted)) (= _let_0 (ti (fun X_b (fun (fun X_b bool) bool)) _let_0)) )) 0.49/0.75 ( pname ) 0.49/0.75 ( (fun pname bool) ) 0.49/0.75 ( nat ) 0.49/0.75 ( x_a ) 0.49/0.75 ( (fun x_a bool) ) 0.49/0.75 ) 0.49/0.75 (instantiation (let ((_let_0 (fun nat nat))) (let ((_let_1 (minus_minus nat))) (forall ((N_1 $$unsorted) (M_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) M_2))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M_2) N_1)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M_2)) N_1))) ))) 0.49/0.75 ( 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)))) ) 0.49/0.75 ( (hAPP nat nat suc na), na ) 0.49/0.75 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.49/0.75 ( (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)))) ) 0.49/0.75 ( (hAPP nat nat suc na), skv_1 ) 0.49/0.75 ( (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 ) 0.49/0.75 ( (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) ) 0.49/0.75 ( (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.49/0.75 ( (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)))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.49/0.75 ( (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 (fun pname bool) nat (finite_card pname) u) ) 0.49/0.75 ( 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(let ((_let_4 (fun X_b _let_1))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (hAPP _let_1 _let_1 (hAPP X_b _let_3 (insert X_b) A_2) B) (hAPP _let_1 _let_1 (collect X_b) (hAPP _let_1 _let_1 (hAPP _let_2 _let_3 (combs X_b bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 X_b) fdisj) (hAPP X_b _let_1 (hAPP _let_4 _let_4 (combc X_b X_b bool) (fequal X_b)) A_2))) (hAPP _let_1 _let_1 (hAPP (fun X_b (fun _let_1 bool)) _let_3 (combc X_b _let_1 bool) (member X_b)) B)))) )))))) 0.49/0.77 ( pname, pn, u ) 0.49/0.77 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.49/0.77 ) 0.49/0.77 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP X_b (fun _let_0 bool) (member X_b) A_2))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) B_1) A_1)))) (= (ti X_b B_1) (ti X_b A_2)) (hBOOL (hAPP _let_0 bool _let_1 A_1))) ))) 0.49/0.77 ( pname, pn, pn, u ) 0.49/0.77 ( pname, skv_7, pn, u ) 0.49/0.77 ( x_a, (hAPP pname x_a mgt_call pn), (hAPP pname x_a mgt_call pn), g ) 0.49/0.77 ( x_a, skv_2, (hAPP pname x_a mgt_call pn), g ) 0.49/0.77 ) 0.49/0.77 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) F_1))) (hBOOL (hAPP _let_1 bool (finite_finite X_c) (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (image X_b X_c) H) F_1)))) ))) 0.49/0.77 ( bool, bool, (combi bool), fNot ) 0.49/0.77 ( pname, pname, (combi pname), u ) 0.49/0.77 ( x_a, pname, mgt_call, u ) 0.49/0.77 ( x_a, pname, mgt_call, skv_3 ) 0.49/0.77 ( x_a, pname, mgt_call, skv_4 ) 0.49/0.77 ( x_a, pname, mgt_call, skv_5 ) 0.49/0.77 ( x_a, x_a, (combi x_a), g ) 0.49/0.77 ) 0.49/0.77 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= 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mgt_call)) (hAPP pname x_a mgt_call skv_7))))))))))) ) 0.49/0.77 ( (fun pname bool), bool, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), u ) 0.49/0.77 ( (fun pname bool), (fun pname bool), (collect pname), u ) 0.49/0.77 ( (fun pname bool), (fun pname bool), (collect pname), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (fun pname _let_2))) (hAPP _let_0 _let_0 (hAPP _let_5 _let_4 (combs pname bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_1) (fun _let_0 _let_5) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) _let_4 (combc pname _let_0 bool) (member pname)) u))) (hAPP x_a _let_0 (hAPP _let_6 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_6 (hAPP (fun x_a _let_2) (fun _let_3 _let_6) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7)))))))))) ) 0.49/0.77 ( (fun pname bool), nat, (finite_card pname), u ) 0.49/0.77 ( (fun pname bool), (fun x_a bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u ) 0.49/0.77 ( (fun pname bool), (fun x_a bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), skv_3 ) 0.49/0.77 ( (fun pname bool), (fun x_a bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), skv_4 ) 0.49/0.77 ( (fun pname bool), (fun x_a bool), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), skv_5 ) 0.49/0.77 ( (fun pname bool), (fun (fun pname bool) bool), (ord_less_eq (fun pname bool)), skv_3 ) 0.49/0.77 ( (fun pname bool), (fun (fun pname bool) bool), (ord_less_eq (fun pname bool)), skv_4 ) 0.49/0.77 ( (fun pname bool), (fun (fun pname bool) bool), (ord_less_eq (fun pname bool)), skv_5 ) 0.49/0.77 ( nat, bool, (hAPP nat (fun nat bool) 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pname x_a), (fun pname (fun (fun x_a bool) bool)) ) 0.58/0.79 ( (fun pname x_a), (let ((_let_0 (fun x_a bool))) (fun pname (fun _let_0 _let_0))) ) 0.58/0.79 ( (fun pname x_a), (fun pname (fun x_a bool)) ) 0.58/0.79 ( (fun (fun pname bool) (fun x_a bool)), (fun (fun pname bool) bool) ) 0.58/0.79 ( (fun (fun pname bool) (fun x_a bool)), (fun (fun pname bool) nat) ) 0.58/0.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.58/0.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.58/0.79 ( (fun (fun pname bool) bool), bool ) 0.58/0.79 ( (fun (fun pname bool) bool), nat ) 0.58/0.79 ( (fun (fun pname bool) bool), (fun (fun pname bool) bool) ) 0.58/0.79 ( (fun x_a (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.58/0.79 ( (fun x_a x_a), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.58/0.79 ( (fun x_a (fun (fun pname bool) bool)), (fun (fun pname bool) (fun x_a bool)) ) 0.58/0.79 ( (fun x_a (fun (fun x_a bool) bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.58/0.79 ( (fun x_a (fun bool bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.58/0.79 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) bool) ) 0.58/0.79 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) (fun nat nat)) ) 0.58/0.79 ) 0.58/0.79 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) X_2) A_1))) (not (= (ti X_c B_1) (hAPP X_b X_c F X_2))) (hBOOL (hAPP _let_0 bool (hAPP X_c (fun _let_0 bool) (member X_c) B_1) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_1)))) ))) 0.58/0.79 ( bool, (fun pname bool), (hAPP (fun pname bool) bool (finite_finite pname) u), (finite_finite pname), u, (finite_finite pname) ) 0.58/0.79 ( bool, nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) g) (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)))), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.58/0.79 ( bool, x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) (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 (fun x_a (fun _let_0 bool)) (fun _let_0 _let_0) (combc x_a _let_0 bool) (member x_a)) g)), (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)) ) 0.58/0.79 ( bool, (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 bool (hAPP x_a (fun _let_0 bool) (member x_a) (hAPP pname x_a mgt_call pn)) g)), (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))), (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))) ) 0.58/0.79 ( bool, (fun x_a bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) (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 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))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.58/0.79 ( bool, (fun x_a bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) pn) u)), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.58/0.79 ( x_a, pname, (hAPP pname x_a mgt_call pn), mgt_call, pn, u ) 0.58/0.79 ( (fun x_a bool), (fun pname bool), g, (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.58/0.79 ( (fun (fun x_a bool) bool), x_a, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)), (member x_a), (hAPP pname x_a mgt_call pn), g ) 0.58/0.79 ( (fun (fun x_a bool) bool), x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)), (member x_a), skv_2, (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)) ) 0.58/0.79 ( (fun (fun x_a bool) bool), 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))), (member x_a), skv_6, g ) 0.58/0.79 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), x_a, (collect x_a), (insert x_a), (hAPP pname x_a mgt_call pn), (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))) ) 0.58/0.79 ( (fun (fun pname bool) bool), pname, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), (member pname), skv_7, u ) 0.58/0.79 ) 0.58/0.79 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (let ((_let_2 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (image X_b X_c) F))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1) B))) (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) (hAPP _let_0 _let_1 _let_2 A_1)) (hAPP _let_0 _let_1 _let_2 B)))) )))) 0.58/0.79 ( x_a, pname, mgt_call, u, skv_4 ) 0.58/0.79 ( x_a, pname, mgt_call, u, skv_5 ) 0.58/0.79 ( x_a, pname, mgt_call, skv_4, u ) 0.58/0.79 ( x_a, pname, mgt_call, skv_4, skv_4 ) 0.58/0.79 ( x_a, pname, mgt_call, skv_4, skv_5 ) 0.58/0.79 ( x_a, pname, mgt_call, skv_5, u ) 0.58/0.79 ( x_a, pname, mgt_call, skv_5, skv_5 ) 0.58/0.79 ) 0.58/0.79 (instantiation (let ((_let_0 (hAPP nat (fun nat nat) (minus_minus nat) N_1))) (forall ((I_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_1) N_1))) (= I_1 (hAPP nat nat _let_0 (hAPP nat nat _let_0 I_1)))) )) 0.58/0.79 ( 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)))) ) 0.58/0.79 ( (hAPP nat nat suc na), na ) 0.58/0.79 ( (hAPP nat nat suc na), (hAPP nat nat suc na) ) 0.58/0.79 ( (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)))) ) 0.58/0.79 ( (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)))), na ) 0.58/0.79 ( (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) ) 0.58/0.79 ( (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 (fun x_a bool) nat (finite_card x_a) g) ) 0.58/0.79 ( (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)))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.58/0.79 ( (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 (fun pname bool) nat (finite_card pname) u) ) 0.58/0.79 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.58/0.79 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.58/0.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))), (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)))) ) 0.58/0.79 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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_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)))) ) 0.58/0.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.58/0.79 ) 0.58/0.79 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (= (ti _let_0 B) (ti _let_0 A_1))) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) A_1)))) )))) 0.58/0.79 ( pname, u, skv_3 ) 0.58/0.79 ( pname, u, skv_4 ) 0.58/0.79 ( pname, u, skv_5 ) 0.58/0.79 ( pname, skv_3, u ) 0.58/0.79 ( pname, skv_4, u ) 0.58/0.79 ( pname, skv_5, u ) 0.58/0.79 ( x_a, g, g ) 0.58/0.79 ( 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))) ) 0.58/0.79 ( 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)) ) 0.58/0.79 ( 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 ) 0.58/0.79 ( 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)) ) 0.58/0.79 ( 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 ) 0.58/0.79 ( 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))) ) 0.58/0.79 ( 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)) ) 0.58/0.79 ) 0.58/0.79 (instantiation (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))) (forall ((Na $$unsorted) (K $$unsorted) (M_3 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_4 M_3))) (not (hBOOL (hAPP nat bool _let_4 Na))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_3) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_2 _let_3 M_3) K)) (hAPP nat nat (hAPP nat _let_2 _let_3 Na) K))))) )))))) 0.58/0.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.58/0.79 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), (hAPP nat nat suc na), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.58/0.79 ) 0.58/0.79 (instantiation (let ((_let_0 (fun (fun X_b bool) bool))) (let ((_let_1 (ord_less_eq (fun X_b bool)))) (let ((_let_2 (hAPP X_b (fun (fun X_b bool) (fun X_b bool)) (insert X_b) A_2))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_0 _let_1 C) D))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 _let_2 C)) (hAPP _let_0 _let_0 _let_2 D))))) )))) 0.58/0.80 ( x_a, (hAPP pname x_a mgt_call pn), g, g ) 0.58/0.80 ) 0.58/0.80 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP nat nat suc X) (hAPP nat nat suc Y))) (= X Y)) ) 0.58/0.80 ( na, na ) 0.58/0.80 ( na, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.58/0.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 0.58/0.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.58/0.80 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))), na ) 0.58/0.80 ( (hAPP (fun pname bool) nat (finite_card pname) u), (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.58/0.80 ( (hAPP (fun pname bool) nat (finite_card pname) u), skv_1 ) 0.58/0.80 ( skv_1, (hAPP (fun pname bool) nat (finite_card pname) u) ) 0.58/0.80 ) 0.58/0.80 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_b bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool (hAPP X_b (fun _let_2 bool) (member X_b) X_1) A_1))) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (member X_c) (hAPP X_b X_c F X_1)) B))) )) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) (hAPP _let_2 _let_0 (hAPP (fun X_b X_c) (fun _let_2 _let_0) (image X_b X_c) F) A_1)) B))) )))) 0.58/0.80 ( x_a, pname, mgt_call, g, u ) 0.58/0.80 ( x_a, pname, mgt_call, g, skv_4 ) 0.58/0.80 ( x_a, pname, mgt_call, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), skv_4 ) 0.58/0.80 ( x_a, pname, mgt_call, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), skv_5 ) 0.58/0.80 ( x_a, pname, mgt_call, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), u ) 0.58/0.80 ( x_a, pname, mgt_call, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), skv_4 ) 0.58/0.80 ( x_a, pname, mgt_call, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), skv_5 ) 0.58/0.80 ) 0.58/0.80 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_c bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_1))) (hBOOL (hAPP _let_1 bool (hAPP X_c (fun _let_1 bool) (member X_c) (hAPP X_b X_c F X_2)) (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (image X_b X_c) F) A_1)))) ))) 0.58/0.80 ( pname, pname, (combi pname), pn, u ) 0.58/0.80 ( x_a, pname, mgt_call, pn, u ) 0.58/0.80 ( x_a, pname, mgt_call, pn, skv_4 ) 0.58/0.80 ( x_a, pname, mgt_call, pn, skv_5 ) 0.58/0.80 ) 0.58/0.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_3151 $$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_3151) BOUND_VARIABLE_3151))) ) 0.58/0.80 ( (fun pname bool), skv_3 ) 0.58/0.80 ( (fun pname bool), skv_4 ) 0.58/0.80 ( (fun pname bool), skv_5 ) 0.58/0.80 ( nat, na ) 0.58/0.80 ( nat, (hAPP nat nat suc na) ) 0.58/0.80 ( 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)))) ) 0.58/0.80 ( nat, (hAPP (fun x_a bool) nat (finite_card x_a) g) ) 0.58/0.80 ( nat, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))) ) 0.58/0.80 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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))))) ) 0.58/0.80 ( (fun x_a bool), g ) 0.58/0.80 ( (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))) ) 0.58/0.80 ( (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)) ) 0.58/0.80 ) 0.58/0.80 (instantiation (let ((_let_0 (ti T A))) (forall ((T $$unsorted) (A $$unsorted)) (= _let_0 (ti T _let_0)) )) 0.58/0.80 ( bool, (hAPP (fun pname bool) bool (finite_finite pname) u) ) 0.58/0.80 ( bool, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 bool (hAPP x_a (fun _let_0 bool) (member x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.58/0.80 ( bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) g) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.58/0.80 ( bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))) ) 0.58/0.80 ( bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) (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))))) ) 0.58/0.80 ( bool, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) pn) u)) ) 0.58/0.80 ( pname, pn ) 0.58/0.80 ( (fun pname bool), u ) 0.58/0.80 ( nat, na ) 0.58/0.80 ( nat, (hAPP nat nat suc na) ) 0.58/0.80 ( 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)))) ) 0.58/0.80 ( nat, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))) ) 0.58/0.80 ( (fun nat bool), (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.58/0.80 ( (fun nat (fun nat bool)), (ord_less_eq nat) ) 0.58/0.80 ( (fun nat (fun nat bool)), (fequal nat) ) 0.58/0.80 ( (fun nat nat), suc ) 0.58/0.80 ( (fun 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))))) ) 0.58/0.80 ( (fun nat nat), (combi nat) ) 0.58/0.80 ( (fun bool bool), fNot ) 0.58/0.80 ( (fun bool bool), (combi bool) ) 0.58/0.80 ( (fun bool (fun bool bool)), fdisj ) 0.58/0.80 ( (fun bool (fun bool bool)), fimplies ) 0.58/0.80 ( (fun bool (fun bool bool)), fconj ) 0.58/0.80 ( (fun bool (fun bool bool)), (fequal bool) ) 0.60/0.80 ( (fun bool (fun bool bool)), (ord_less_eq bool) ) 0.60/0.80 ( (fun nat (fun nat nat)), (minus_minus nat) ) 0.60/0.80 ( x_a, (hAPP pname x_a mgt_call pn) ) 0.60/0.80 ( (fun x_a bool), g ) 0.60/0.80 ( (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))) ) 0.60/0.80 ( (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)) ) 0.60/0.80 ( (fun (fun x_a bool) bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.60/0.80 ( (fun (fun x_a bool) bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.60/0.80 ( (fun (fun x_a bool) 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))) ) 0.60/0.80 ( (fun (fun x_a bool) bool), (finite_finite x_a) ) 0.60/0.80 ( (fun pname x_a), mgt_call ) 0.60/0.80 ( (fun (fun pname bool) (fun x_a bool)), (hAPP (fun pname x_a) (fun (fun pname bool) (fun x_a bool)) (image pname x_a) mgt_call) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (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))) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (collect x_a) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (combi (fun x_a bool)) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (ord_less_eq (fun x_a bool)) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), p ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (fequal (fun x_a bool)) ) 0.60/0.80 ( (fun (fun pname bool) bool), (finite_finite pname) ) 0.60/0.80 ( (fun (fun pname bool) bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.60/0.80 ( (let ((_let_0 (fun pname bool))) (fun _let_0 _let_0)), (collect pname) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun x_a (fun _let_0 _let_0))), (insert x_a) ) 0.60/0.80 ( (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (collect bool) ) 0.60/0.80 ( (let ((_let_0 (fun bool bool))) (fun bool (fun _let_0 _let_0))), (insert bool) ) 0.60/0.80 ( (let ((_let_0 (fun pname bool))) (fun pname (fun _let_0 _let_0))), (insert pname) ) 0.60/0.80 ( (let ((_let_0 (fun (fun pname bool) bool))) (fun _let_0 _let_0)), (collect (fun pname bool)) ) 0.60/0.80 ( (let ((_let_0 (fun (fun pname bool) bool))) (fun (fun pname bool) (fun _let_0 _let_0))), (insert (fun pname bool)) ) 0.60/0.80 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (collect nat) ) 0.60/0.80 ( (let ((_let_0 (fun nat bool))) (fun nat (fun _let_0 _let_0))), (insert nat) ) 0.60/0.80 ( (let ((_let_0 (fun (fun x_a bool) bool))) (fun _let_0 _let_0)), (collect (fun x_a bool)) ) 0.60/0.80 ( (let ((_let_0 (fun (fun x_a bool) bool))) (fun (fun x_a bool) (fun _let_0 _let_0))), (insert (fun x_a bool)) ) 0.60/0.80 ( (fun pname (fun pname bool)), (fequal pname) ) 0.60/0.80 ( (let ((_let_0 (fun pname bool))) (fun _let_0 (fun _let_0 bool))), (ord_less_eq (fun pname bool)) ) 0.60/0.80 ( (let ((_let_0 (fun pname bool))) (fun _let_0 (fun _let_0 bool))), (fequal (fun pname bool)) ) 0.60/0.80 ( (fun x_a (fun x_a bool)), (fequal x_a) ) 0.60/0.80 ( (fun (fun pname x_a) (fun (fun pname bool) (fun x_a bool))), (image pname x_a) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun (fun x_a x_a) (fun _let_0 _let_0))), (image x_a x_a) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun (fun x_a _let_0) (fun _let_0 (fun _let_0 bool)))), (image x_a (fun x_a bool)) ) 0.60/0.80 ( (let ((_let_0 (fun bool (fun bool bool)))) (fun _let_0 _let_0)), (combc bool bool bool) ) 0.60/0.80 ( (let ((_let_0 (fun nat (fun nat nat)))) (fun _let_0 _let_0)), (combc nat nat nat) ) 0.60/0.80 ( (let ((_let_0 (fun pname bool))) (fun (fun x_a (fun _let_0 bool)) (fun _let_0 (fun x_a bool)))), (combc x_a (fun pname bool) bool) ) 0.60/0.80 ( (fun x_a (fun (fun x_a bool) bool)), (member x_a) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun (fun x_a (fun _let_0 bool)) (fun _let_0 _let_0))), (combc x_a (fun x_a bool) bool) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun x_a bool))) (combc _let_0 _let_0 bool)) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun (fun x_a (fun bool bool)) (fun _let_0 _let_0))), (combs x_a bool bool) ) 0.60/0.80 ( (fun (fun pname bool) nat), (finite_card pname) ) 0.60/0.80 ( (fun (fun x_a bool) nat), (finite_card x_a) ) 0.60/0.80 ( (fun pname (fun (fun pname bool) bool)), (member pname) ) 0.60/0.80 ( (let ((_let_0 (fun x_a bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (combb bool bool x_a) ) 0.60/0.80 ( (fun (fun bool bool) nat), (finite_card bool) ) 0.60/0.80 ( (fun (fun (fun pname bool) bool) nat), (finite_card (fun pname bool)) ) 0.60/0.80 ( (fun (fun nat bool) nat), (finite_card nat) ) 0.60/0.80 ( (fun (fun (fun x_a bool) bool) nat), (finite_card (fun x_a bool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_finite X_b))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 A_1))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) A_2) A_1)))) ))) 0.60/0.80 ( pname, pn, u ) 0.60/0.80 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.60/0.80 ) 0.60/0.80 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_1))) (hBOOL (hAPP _let_0 bool (finite_finite _let_0) (hAPP _let_0 _let_0 (collect _let_0) (hAPP _let_0 _let_0 (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) A_1)))))) ))) 0.60/0.80 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.60/0.80 ) 0.60/0.80 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (finite_finite X_b))) (let ((_let_3 (fun X_b _let_0))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 bool))) (let ((_let_6 (member X_b))) (let ((_let_7 (fun X_c bool))) (let ((_let_8 (fun X_b _let_7))) (let ((_let_9 (fun X_b X_c))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (or (hBOOL (hAPP _let_1 bool _let_2 A_1)) (not (hBOOL (hAPP _let_7 bool (finite_finite X_c) (hAPP _let_1 _let_7 (hAPP _let_9 (fun _let_1 _let_7) (image X_b X_c) F) A_1)))) (not (forall ((X_1 $$unsorted)) (or (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 (collect X_b) (hAPP _let_1 _let_1 (hAPP _let_3 _let_4 (combs X_b bool bool) (hAPP _let_1 _let_3 (hAPP (fun bool _let_0) (fun _let_1 _let_3) (combb bool _let_0 X_b) fconj) (hAPP _let_1 _let_1 (hAPP (fun X_b _let_5) _let_4 (combc X_b _let_1 bool) _let_6) A_1))) (hAPP X_c _let_1 (hAPP _let_8 (fun X_c _let_1) (combc X_b X_c bool) (hAPP _let_9 _let_8 (hAPP (fun X_c _let_7) (fun _let_9 _let_8) (combb X_c _let_7 X_b) (fequal X_c)) F)) (hAPP X_b X_c F X_1)))))) (not (hBOOL (hAPP _let_1 bool (hAPP X_b _let_5 _let_6 X_1) A_1)))) ))) ))))))))))) 0.60/0.80 ( bool, bool, (combi bool), fNot ) 0.60/0.80 ( pname, pname, (combi pname), u ) 0.60/0.80 ( x_a, pname, mgt_call, u ) 0.60/0.80 ( x_a, pname, mgt_call, skv_3 ) 0.60/0.80 ( x_a, pname, mgt_call, skv_4 ) 0.60/0.80 ( x_a, pname, mgt_call, skv_5 ) 0.60/0.80 ( x_a, x_a, (combi x_a), g ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (order T_1)) (order (fun T_2 T_1))) ) 0.60/0.80 ( bool, bool ) 0.60/0.80 ( bool, (fun bool bool) ) 0.60/0.80 ( bool, (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)) ) 0.60/0.80 ( pname, bool ) 0.60/0.80 ( pname, pname ) 0.60/0.80 ( pname, (fun pname bool) ) 0.60/0.80 ( pname, (fun bool bool) ) 0.60/0.80 ( pname, x_a ) 0.60/0.80 ( pname, (fun x_a bool) ) 0.60/0.80 ( pname, (fun (fun x_a bool) bool) ) 0.60/0.80 ( pname, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.80 ( pname, (fun (fun pname bool) bool) ) 0.60/0.80 ( pname, (let ((_let_0 (fun pname bool))) (fun _let_0 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bool))) (fun _let_0 _let_0)) ) 0.60/0.80 ( (fun bool (fun bool bool)), (fun bool (fun bool bool)) ) 0.60/0.80 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)) ) 0.60/0.81 ( x_a, bool ) 0.60/0.81 ( x_a, (fun pname bool) ) 0.60/0.81 ( x_a, (fun bool bool) ) 0.60/0.81 ( x_a, x_a ) 0.60/0.81 ( x_a, (fun x_a bool) ) 0.60/0.81 ( x_a, (fun (fun x_a bool) bool) ) 0.60/0.81 ( x_a, (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( x_a, (fun (fun pname bool) bool) ) 0.60/0.81 ( (fun x_a bool), bool ) 0.60/0.81 ( (fun x_a bool), nat ) 0.60/0.81 ( (fun x_a bool), (fun nat nat) ) 0.60/0.81 ( (fun x_a bool), (fun x_a bool) ) 0.60/0.81 ( (fun x_a bool), (fun (fun x_a bool) bool) ) 0.60/0.81 ( (fun x_a bool), (let ((_let_0 (fun (fun x_a bool) bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun x_a bool), (fun x_a (fun x_a bool)) ) 0.60/0.81 ( (fun x_a bool), (fun x_a (fun bool bool)) ) 0.60/0.81 ( (fun (fun x_a bool) bool), bool ) 0.60/0.81 ( (fun (fun x_a bool) bool), nat ) 0.60/0.81 ( (fun (fun x_a bool) bool), (fun (fun x_a bool) bool) ) 0.60/0.81 ( (fun pname x_a), (fun x_a bool) ) 0.60/0.81 ( (fun pname x_a), (fun (fun pname bool) (fun x_a bool)) ) 0.60/0.81 ( (fun pname x_a), (fun pname (fun (fun x_a bool) bool)) ) 0.60/0.81 ( (fun pname x_a), (let ((_let_0 (fun x_a bool))) (fun pname (fun _let_0 _let_0))) ) 0.60/0.81 ( (fun pname x_a), (fun pname (fun x_a bool)) ) 0.60/0.81 ( (fun (fun pname bool) (fun x_a bool)), (fun (fun pname bool) bool) ) 0.60/0.81 ( (fun (fun pname bool) (fun x_a bool)), (fun (fun pname bool) nat) ) 0.60/0.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.60/0.81 ( (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.60/0.81 ( (fun (fun pname bool) bool), bool ) 0.60/0.81 ( (fun (fun pname bool) bool), nat ) 0.60/0.81 ( (fun (fun pname bool) bool), (fun (fun pname bool) bool) ) 0.60/0.81 ( (fun x_a (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.60/0.81 ( (fun x_a x_a), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun x_a (fun (fun pname bool) bool)), (fun (fun pname bool) (fun x_a bool)) ) 0.60/0.81 ( (fun x_a (fun (fun x_a bool) bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun x_a (fun bool bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) bool) ) 0.60/0.81 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) (fun nat nat)) ) 0.60/0.81 ) 0.60/0.81 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (preorder T_1)) (preorder (fun T_2 T_1))) ) 0.60/0.81 ( bool, bool ) 0.60/0.81 ( bool, (fun bool bool) ) 0.60/0.81 ( bool, (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( pname, bool ) 0.60/0.81 ( pname, pname ) 0.60/0.81 ( pname, (fun pname bool) ) 0.60/0.81 ( pname, (fun bool bool) ) 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(fun x_a bool))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.60/0.81 ( (fun (fun pname bool) bool), bool ) 0.60/0.81 ( (fun (fun pname bool) bool), nat ) 0.60/0.81 ( (fun (fun pname bool) bool), (fun (fun pname bool) bool) ) 0.60/0.81 ( (fun x_a (fun x_a bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 (fun _let_0 bool))) ) 0.60/0.81 ( (fun x_a x_a), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun x_a (fun (fun pname bool) bool)), (fun (fun pname bool) (fun x_a bool)) ) 0.60/0.81 ( (fun x_a (fun (fun x_a bool) bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun x_a (fun bool bool)), (let ((_let_0 (fun x_a bool))) (fun _let_0 _let_0)) ) 0.60/0.81 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) bool) ) 0.60/0.81 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) (fun nat nat)) ) 0.60/0.81 ) 0.60/0.81 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (Y_1 $$unsorted)) (= (ti _let_0 Y_1) (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_1)) )) 0.60/0.81 ( bool, fNot ) 0.60/0.81 ( bool, (combi bool) ) 0.60/0.81 ( pname, u ) 0.60/0.81 ( (fun pname bool), (finite_finite pname) ) 0.60/0.81 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.60/0.81 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.60/0.81 ( x_a, g ) 0.60/0.81 ( 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))) ) 0.60/0.81 ( 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)) ) 0.60/0.81 ( (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.60/0.81 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq 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0.60/0.81 ( (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)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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) ) 0.60/0.81 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (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)))) ) 0.60/0.81 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (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 x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun pname bool))) (let ((_let_1 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(fun (fun x_a bool) nat), (let ((_let_0 (fun pname bool))) (fun (fun _let_0 (fun x_a bool)) (fun _let_0 nat))), (combb (fun x_a bool) nat (fun pname bool)), (finite_card x_a) ) 0.62/0.83 ( (fun (fun x_a bool) nat), (fun (fun x_a bool) (fun nat nat)), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun x_a bool))) (hAPP (fun nat _let_0) (fun (fun _let_1 nat) (fun _let_1 _let_0)) (combb nat _let_0 _let_1) (minus_minus nat)))), (finite_card x_a) ) 0.62/0.83 ( (fun pname (fun (fun pname bool) bool)), (let ((_let_0 (fun pname bool))) (fun _let_0 _let_0)), (combc pname (fun pname bool) bool), (member pname) ) 0.62/0.83 ) 0.62/0.83 (instantiation (let ((_let_0 (fun X_d bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (fun X_d X_b))) (let ((_let_3 (fun X_d X_c))) (let ((_let_4 (fun X_c X_b))) (let ((_let_5 (fun X_c bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (= (hAPP _let_5 _let_1 (hAPP _let_4 (fun _let_5 _let_1) (image X_c X_b) F) (hAPP _let_0 _let_5 (hAPP _let_3 (fun _let_0 _let_5) (image X_d X_c) G) A_1)) (hAPP _let_0 _let_1 (hAPP _let_2 (fun _let_0 _let_1) (image X_d X_b) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (combb X_c X_b X_d) F) G)) A_1)) ))))))) 0.62/0.83 ( bool, bool, bool, (combi bool), (combi bool), fNot ) 0.62/0.83 ( pname, pname, pname, (combi pname), (combi pname), u ) 0.62/0.83 ( pname, x_a, pname, mgt_call, (combi pname), u ) 0.62/0.83 ( x_a, x_a, pname, (combi x_a), mgt_call, skv_4 ) 0.62/0.83 ) 0.62/0.83 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (finite_finite X_b))) (let ((_let_3 (collect X_b))) (let ((_let_4 (fun X_b _let_0))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (or (and (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 Q_1)))) (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 Pa))))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs X_b bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_0) (fun _let_1 _let_4) (combb bool _let_0 X_b) fconj) Pa)) Q_1))))) )))))) 0.62/0.83 ( pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun pname x_a))) (let ((_let_3 (fun pname _let_1))) (hAPP x_a _let_0 (hAPP _let_3 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_2 _let_3 (hAPP (fun x_a _let_1) (fun _let_2 _let_3) (combb x_a _let_1 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7)))))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) u)) ) 0.62/0.83 ) 0.62/0.83 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less_eq nat) M_3))) (let ((_let_1 (hAPP nat nat suc Na))) (forall ((M_3 $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP nat bool _let_0 _let_1)) (or (= M_3 _let_1) (hBOOL (hAPP nat bool _let_0 Na)))) ))) 0.62/0.83 ( na, skv_1 ) 0.62/0.83 ( (hAPP nat nat suc na), na ) 0.62/0.83 ( (hAPP nat nat suc na), skv_1 ) 0.62/0.83 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), na ) 0.62/0.83 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u)))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.62/0.83 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) (hAPP nat nat suc na)))) ) 0.62/0.83 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), skv_1 ) 0.62/0.83 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), skv_1 ) 0.62/0.83 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (hAPP _let_1 nat (finite_card x_a) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))))), na ) 0.62/0.83 ) 0.62/0.83 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_1))) (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_1)) (= (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) A_1)) (hAPP nat nat suc (hAPP _let_0 nat _let_1 A_1)))) ))) 0.62/0.83 ( pname, pn, u ) 0.62/0.83 ( pname, skv_7, u ) 0.62/0.83 ( (fun pname bool), u, (finite_finite pname) ) 0.62/0.83 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.62/0.83 ( 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)) ) 0.62/0.83 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.62/0.83 ( x_a, (hAPP pname x_a mgt_call pn), (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))) ) 0.62/0.83 ( 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)) ) 0.62/0.83 ( x_a, skv_2, (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))) ) 0.62/0.83 ( x_a, skv_2, (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)) ) 0.62/0.84 ( x_a, skv_6, g ) 0.62/0.84 ( x_a, skv_6, (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))) ) 0.62/0.84 ( (fun x_a bool), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.62/0.84 ( (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)) ) 0.62/0.84 ( (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))) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (finite_card X_b))) (let ((_let_2 (hAPP _let_0 nat _let_1 A_1))) (let ((_let_3 (hAPP _let_0 nat _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) A_1)))) (let ((_let_4 (hBOOL (hAPP _let_0 bool (hAPP X_b (fun _let_0 bool) (member X_b) X_2) A_1)))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_b) A_1))) (and (or (not _let_4) (= _let_2 _let_3)) (or _let_4 (= _let_3 (hAPP nat nat suc _let_2))))) )))))) 0.62/0.84 ( pname, pn, u ) 0.62/0.84 ( pname, skv_7, u ) 0.62/0.84 ( (fun pname bool), u, (finite_finite pname) ) 0.62/0.84 ( (fun pname bool), u, (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( x_a, (hAPP pname x_a mgt_call pn), g ) 0.62/0.84 ( x_a, (hAPP pname x_a mgt_call pn), (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))) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( x_a, skv_2, (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))) ) 0.62/0.84 ( x_a, skv_2, (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)) ) 0.62/0.84 ( x_a, skv_6, g ) 0.62/0.84 ( x_a, skv_6, (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))) ) 0.62/0.84 ( (fun x_a bool), g, (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.62/0.84 ( (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)) ) 0.62/0.84 ( (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))) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (= (ti _let_0 Pa) (hAPP _let_0 _let_0 (collect X_b) Pa)) )) 0.62/0.84 ( bool, fNot ) 0.62/0.84 ( bool, (combi bool) ) 0.62/0.84 ( pname, u ) 0.62/0.84 ( pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun x_a bool))) (let ((_let_3 (fun pname x_a))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (fun pname _let_2))) (hAPP _let_0 _let_0 (hAPP _let_5 _let_4 (combs pname bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_1) (fun _let_0 _let_5) (combb bool _let_1 pname) fconj) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) _let_4 (combc pname _let_0 bool) (member pname)) u))) (hAPP x_a _let_0 (hAPP _let_6 (fun x_a _let_0) (combc pname x_a bool) (hAPP _let_3 _let_6 (hAPP (fun x_a _let_2) (fun _let_3 _let_6) (combb x_a _let_2 pname) (fequal x_a)) mgt_call)) (hAPP pname x_a mgt_call skv_7)))))))))) ) 0.62/0.84 ( (fun pname bool), (finite_finite pname) ) 0.62/0.84 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 0.62/0.84 ( nat, (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc na)) ) 0.62/0.84 ( nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) na)) ) 0.62/0.84 ( x_a, g ) 0.62/0.84 ( 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))) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( x_a, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun x_a bool))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun x_a _let_1))) (let ((_let_4 (fun x_a _let_0))) (hAPP _let_1 _let_1 (hAPP _let_4 _let_2 (combs x_a bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_0) (fun _let_1 _let_4) (combb bool _let_0 x_a) fdisj) (hAPP x_a _let_1 (hAPP _let_3 _let_3 (combc x_a x_a bool) (fequal x_a)) (hAPP pname x_a mgt_call pn)))) (hAPP _let_1 _let_1 (hAPP (fun x_a (fun _let_1 bool)) _let_2 (combc x_a _let_1 bool) (member x_a)) g))))))) ) 0.62/0.84 ( (fun x_a bool), (hAPP x_a (fun (fun x_a bool) bool) (member x_a) (hAPP pname x_a mgt_call pn)) ) 0.62/0.84 ( (fun x_a bool), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) g)) ) 0.62/0.84 ( (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))) ) 0.62/0.84 ( (fun x_a bool), (finite_finite x_a) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_b bool))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (= (ti _let_0 A_1) (ti _let_0 B))) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B) A_1))) )) 0.62/0.84 ( pname, u, skv_3 ) 0.62/0.84 ( pname, u, skv_4 ) 0.62/0.84 ( pname, u, skv_5 ) 0.62/0.84 ( x_a, g, g ) 0.62/0.84 ( 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))) ) 0.62/0.84 ( 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 ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( 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 ) 0.62/0.84 ( 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))) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (hAPP nat (fun nat bool) (ord_less_eq nat) M_2))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool _let_0 N_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N_1)))) )) 0.62/0.84 ( na, skv_1 ) 0.62/0.84 ( (hAPP nat nat suc na), na ) 0.62/0.84 ( (hAPP nat nat suc na), skv_1 ) 0.62/0.84 ( (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 ) 0.62/0.84 ( (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 nat (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)))) ) 0.62/0.84 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat (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)))) ) 0.62/0.84 ( (hAPP (fun x_a bool) nat (finite_card x_a) g), skv_1 ) 0.62/0.84 ( (let ((_let_0 (fun x_a bool))) (hAPP _let_0 nat (finite_card x_a) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g))), skv_1 ) 0.62/0.84 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP nat nat suc (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 ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) A_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B) (hAPP _let_1 _let_0 (hAPP (fun X_b X_c) (fun _let_1 _let_0) (image X_b X_c) F) A_1)))) (hBOOL (hAPP _let_0 bool (finite_finite X_c) B))) ))) 0.62/0.84 ( pname, pname, skv_3, (combi pname), u ) 0.62/0.84 ( pname, pname, skv_4, (combi pname), u ) 0.62/0.84 ( pname, pname, skv_5, (combi pname), u ) 0.62/0.84 ( x_a, pname, g, mgt_call, u ) 0.62/0.84 ( x_a, pname, g, mgt_call, skv_4 ) 0.62/0.84 ( x_a, pname, g, mgt_call, skv_5 ) 0.62/0.84 ( x_a, pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), mgt_call, skv_4 ) 0.62/0.84 ( x_a, pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), mgt_call, skv_5 ) 0.62/0.84 ( x_a, pname, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), mgt_call, u ) 0.62/0.84 ( x_a, pname, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), mgt_call, skv_5 ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_b _let_1 (member X_b) X_1))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_2 A_1))) (hBOOL (hAPP _let_0 bool _let_2 B))) )) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) A_1) B))) )))) 0.62/0.84 ( pname, u, skv_3 ) 0.62/0.84 ( pname, u, skv_4 ) 0.62/0.84 ( pname, u, skv_5 ) 0.62/0.84 ( x_a, g, g ) 0.62/0.84 ( x_a, g, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.62/0.84 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), g ) 0.62/0.84 ( x_a, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.62/0.84 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), g ) 0.62/0.84 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) u))) ) 0.62/0.84 ( x_a, (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)), (let ((_let_0 (fun x_a bool))) (hAPP _let_0 _let_0 (hAPP x_a (fun _let_0 _let_0) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (= (ti _let_0 B) (ti _let_0 A_1)) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) A_1)))) )))) 0.62/0.84 ( pname, u, skv_3 ) 0.62/0.84 ( pname, u, skv_4 ) 0.62/0.84 ( pname, u, skv_5 ) 0.62/0.84 ( pname, skv_3, u ) 0.62/0.84 ( pname, skv_4, u ) 0.62/0.84 ( pname, skv_5, u ) 0.62/0.84 ( x_a, g, g ) 0.62/0.84 ( 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))) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( 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 ) 0.62/0.84 ( 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)) ) 0.62/0.84 ( 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 ) 0.62/0.84 ( 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))) ) 0.62/0.84 ( 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)) ) 0.62/0.84 ) 0.62/0.84 (instantiation (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun x_a bool))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) AA) u))) (not (= (ti _let_1 (hAPP _let_1 _let_1 (hAPP x_a (fun _let_1 _let_1) (insert x_a) (hAPP pname x_a mgt_call pn)) g)) (hAPP _let_0 _let_1 (hAPP (fun pname x_a) (fun _let_0 _let_1) (image pname x_a) mgt_call) AA)))) ))) 0.62/0.84 ( u ) 0.62/0.84 ( skv_3 ) 0.62/0.84 ( skv_4 ) 0.62/0.84 ( skv_5 ) 0.62/0.84 ) 0.62/0.84 % SZS output end Proof for theBenchmark 0.62/0.85 EOF