%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 21:53:30 EDT 2023

% Result   : Unsatisfiable 0.41s 0.93s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.16  % Problem    : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.17  % Command    : do_cvc5 %s %d
% 0.18/0.38  % Computer : n006.cluster.edu
% 0.18/0.38  % Model    : x86_64 x86_64
% 0.18/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38  % Memory   : 8042.1875MB
% 0.18/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38  % CPULimit   : 300
% 0.18/0.38  % WCLimit    : 300
% 0.18/0.38  % DateTime   : Tue Aug 29 05:27:06 EDT 2023
% 0.18/0.38  % CPUTime    : 
% 0.24/0.55  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3e6vr8BMfT/cvc5---1.0.5_8526.p...
% 0.41/0.64  ------- get file name : TPTP file name is SWV840-1
% 0.41/0.65  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8526.smt2...
% 0.41/0.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.41/0.93  % SZS status Unsatisfiable for SWV840-1
% 0.41/0.93  % SZS output start Proof for SWV840-1
% 0.41/0.94  (
% 0.41/0.94  (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) tptp.v_P))) (let ((_let_4 (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody tptp.v_pn))) tptp.v_Q) (tptp.c_Orderings_Obot__class_Obot _let_2) _let_1))) (let ((_let_5 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP tptp.c_Com_Ocom_OBODY tptp.v_pn)) tptp.v_Q))) (let ((_let_6 (tptp.c_Set_Oinsert _let_5 tptp.v_G _let_1))) (let ((_let_7 (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_6 _let_4 tptp.t_a))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G _let_4 tptp.t_a))) (let ((_let_10 (tptp.hAPP tptp.v_P tptp.v_R))) (let ((_let_11 (tptp.hAPP tptp.v_Q tptp.v_R))) (let ((_let_12 (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_G_H V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))))) (let ((_let_13 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_14 (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (let ((_let_15 (not _let_9))) (let ((_let_16 (tptp.c_lessequals tptp.v_G _let_6 _let_2))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_7 _let_17 _let_15))) (let ((_let_19 (_let_12))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (not _let_18))) (let ((_let_22 (_let_14))) (let ((_let_23 (ASSUME :args _let_22))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_6 _let_4 tptp.t_a tptp.v_G QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) true)) (not (= (tptp.c_lessequals V_G_H V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool)) false))))) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_7 _let_15 _let_17 _let_21))) (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.v_G _let_5 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Set_Oinsert V_a V_B T_a)))) :args _let_22)) _let_23 :args (_let_16 false _let_14)) :args (_let_21 true _let_7 false _let_9 false _let_16)) _let_20 :args (false true _let_18 false _let_12)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_X $$unsorted) (V_pn $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_pn V_a)) (not (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn))))) (forall ((V_P $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P)) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_P V_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_s2) (not (tptp.c_Natural_Oevalc V_c1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c0 V_s0 V_s1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (tptp.c_Natural_Oevalc V_c0 V_s V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (tptp.c_Com_OWT tptp.c_Com_Ocom_OSKIP) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c0 V_s0 V_n V_s1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevalc _let_1 V_s0 V_s2) (not (tptp.c_Natural_Oevalc _let_1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c V_s0 V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((T_a $$unsorted) (V_a_H $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.c_Option_Ooption_OSome V_a_H T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.c_Option_Ooption_OSome V_y T_a)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevaln _let_1 V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln _let_1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c V_s0 V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c0 V_s V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f8 V_vname) V_pname) V_fun))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 V_f V_A T_a) (tptp.c_The (tptp.c_Finite__Set_Ofold1Set V_f V_A T_a) T_a))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.hAPP V_M V_i) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_a T_b) T_b) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_pname V_pname_H))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_vname V_vname_H))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.c_Collect V_P T_a) V_P)) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_n $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_t T_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) V_t T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_A V_x) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_I T_b))) (not (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_b _let_1) V_B _let_1))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp (tptp.c_COMBK V_c T_b T_c) V_f T_c T_b tptp.t_a) tptp.v_x) V_c)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) V_a)) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_a _let_1))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_A V_k) _let_2 _let_1) _let_2) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_fun V_fun_H))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_b V_d T_a)) (not (tptp.c_lessequals V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_b V_d T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_c V_a T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Option_Ooption_OSome V_a_H T_a) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Option_Ooption_OSome V_xa T_a) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted)) (or (not (= (tptp.c_Option_Ooption_OSome V_a T_a) (tptp.c_Option_Ooption_OSome V_a_H T_a))) (= V_a V_a_H))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_lessequals V_a V_b T_a))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 tptp.c_Com_Ocom_OSKIP T_a) V_f1)) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((T_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OSemi V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP V_f4 V_com1) V_com2))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((V_b $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_Y $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_Y $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_n $$unsorted) (V_P $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (= V_n (tptp.c_Suc (tptp.c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 V_P V_n V_s V_s1))) (not (tptp.c_Natural_Oevaln (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P) V_s V_n V_s1)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a))))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_t)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1))))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_x $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_x V_t)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Collect V_P T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) V_x)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) _let_14 (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_Procs $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.tc_fun T_a (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun _let_2 _let_1))) (let ((_let_4 (tptp.c_COMBB (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P _let_2 (tptp.tc_fun tptp.tc_Com_Ocom _let_3) tptp.tc_Com_Opname))) (let ((_let_5 (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS _let_4 tptp.c_Com_Ocom_OBODY tptp.tc_Com_Opname tptp.tc_Com_Ocom _let_3) V_Q tptp.tc_Com_Opname _let_2 _let_1) V_Procs tptp.tc_Com_Opname _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G _let_5 T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G _let_5 (tptp.tc_fun _let_1 tptp.tc_bool)) (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS _let_4 (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Opname tptp.tc_Com_Ocom _let_3) V_Q tptp.tc_Com_Opname _let_2 _let_1) V_Procs tptp.tc_Com_Opname _let_1) T_a))))))))) (forall ((V_pname_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s_H $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s (tptp.c_Suc V_n) V_s_H) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c1 V_s V_n V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_s $$unsorted)) (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_s)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_u $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (= V_u V_t) (not (tptp.c_Natural_Oevalc V_c V_s V_u)) (not (tptp.c_Natural_Oevalc V_c V_s V_t)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_s $$unsorted) (V_n $$unsorted)) (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_s)) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_Q $$unsorted) (V_Z $$unsorted) (V_s_H $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q V_Z) V_s_H)) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_Z) V_s))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) tptp.t_a)))) (= (tptp.hAPP _let_13 tptp.v_x) (tptp.c_in tptp.v_x _let_13 tptp.t_a)) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (tptp.c_Natural_Oevalc V_c1 V_s V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oinsert V_a V_A T_b) V_B T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_1)))) (forall ((V_c2 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((V_c1 $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a) V_x T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a))) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f3 V_loc) V_fun) V_com))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OWhile V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP V_f6 V_fun) V_com))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_c T_b tptp.t_a) tptp.v_x) (tptp.hAPP V_f (tptp.hAPP V_g tptp.v_x)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_loc V_loc_H))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Ocomp V_f V_g T_c T_a T_b) V_r T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_r T_b T_c) T_c T_a))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK _let_2 _let_1 T_b) T_b _let_1) _let_2)))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_t)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f5 V_fun) V_com1) V_com2))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_t)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) V_M T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_B V_M T_b _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_fequal T_a) V_x) T_a) V_x)) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c2 $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_c1 $$unsorted) (V_b $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_pname_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_pname $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname)))) (forall ((V_pname_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_pname $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) T_a) (tptp.hAPP V_f7 V_pname))) (forall ((V_pname_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) V_Q) T_a)) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (V_xc $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Hoare__Mirabelle_Otriple_Otriple__case V_f1 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_b) V_xa) V_xb) V_xc) tptp.t_b tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f1 V_xa) V_xb) V_xc))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Hoare__Mirabelle_Otriple_Otriple__case V_f1 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_b) V_fun1) V_com) V_fun2) tptp.t_b tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f1 V_fun1) V_com) V_fun2))))) (forall ((V_f1 $$unsorted) (T_b $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple__rec V_f1 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_b) V_fun1) V_com) V_fun2) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f1 V_fun1) V_com) V_fun2))) (forall ((V_f1 $$unsorted) (T_b $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple__case V_f1 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_b) V_fun1) V_com) V_fun2) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f1 V_fun1) V_com) V_fun2))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_ts_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_ts_H (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts_H T_a)))) _let_12 (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))))) (= (tptp.hAPP (tptp.c_COMBI tptp.t_a) tptp.v_P) tptp.v_P) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool))) (let ((_let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_COMBK (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal tptp.tc_Com_Ostate) tptp.tc_Com_Ostate tptp.tc_Com_Ostate tptp.tc_bool) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)) _let_3 tptp.t_a)) V_c) (tptp.c_COMBK (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) _let_3 tptp.t_a)) _let_2 _let_1) tptp.t_a)))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted) (V_Procs $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.tc_fun T_a (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun _let_2 _let_1))) (let ((_let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (let ((_let_5 (tptp.c_COMBB _let_4 V_P _let_2 (tptp.tc_fun tptp.tc_Com_Ocom _let_3) tptp.tc_Com_Opname))) (let ((_let_6 (tptp.tc_fun _let_1 tptp.tc_bool))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP V_P V_pn)) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) (tptp.hAPP V_Q V_pn)) (tptp.c_Orderings_Obot__class_Obot _let_6) _let_1) T_a) (not (tptp.hBOOL (tptp.c_in V_pn V_Procs tptp.tc_Com_Opname))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS _let_5 tptp.c_Com_Ocom_OBODY tptp.tc_Com_Opname tptp.tc_Com_Ocom _let_3) V_Q tptp.tc_Com_Opname _let_2 _let_1) V_Procs tptp.tc_Com_Opname _let_1) _let_6) (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS _let_5 (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Opname tptp.tc_Com_Ocom _let_3) V_Q tptp.tc_Com_Opname _let_2 _let_1) V_Procs tptp.tc_Com_Opname _let_1) T_a)))))))))) (forall ((V_pn $$unsorted)) (or (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) (= (tptp.hAPP tptp.c_Com_Obody V_pn) (tptp.c_Option_Ooption_ONone tptp.tc_Com_Ocom)))) (= (tptp.hAPP (tptp.c_COMBB tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP tptp.v_P _let_11)) (= (tptp.hAPP (tptp.c_COMBS tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP _let_10 _let_11)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.v_P tptp.t_a tptp.t_b tptp.t_c) tptp.v_Q) tptp.v_R) (tptp.hAPP _let_10 tptp.v_Q)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Option_Othe T_a) (tptp.c_Option_Ooption_OSome V_x T_a)) V_x)) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) (tptp.c_Com_Ocom_OWhile V_b V_c)) (tptp.c_Hoare__Mirabelle_Opeek__and V_P (tptp.c_Fun_Ocomp tptp.c_Not V_b tptp.tc_bool tptp.tc_bool tptp.tc_Com_Ostate) T_a)) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Opeek__and V_P V_b T_a)) V_c) V_P) _let_2 _let_1) T_a))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) (tptp.c_Com_Ocom_OCond V_b V_c V_d)) V_Q) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Opeek__and V_P (tptp.c_Fun_Ocomp tptp.c_Not V_b tptp.tc_bool tptp.tc_bool tptp.tc_Com_Ostate) T_a)) V_d) V_Q) _let_2 _let_1) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Opeek__and V_P V_b T_a)) V_c) V_Q) _let_2 _let_1) T_a))))))) (forall ((V_P $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_P)) V_s (tptp.c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 V_P V_n V_s V_s1) V_s1) (not (tptp.c_Natural_Oevaln (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P) V_s V_n V_s1)))) (forall ((V_pn $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn) V_s0 (tptp.c_Suc V_n) V_s1) (not (tptp.c_Natural_Oevaln (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn)) V_s0 V_n V_s1)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_fequal T_a) V_a) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a))))) (forall ((V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_The (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_x)) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_b))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ocontents (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_x)) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (or (= V_y (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_a T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted) (V_Z_H $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)))))) (= (tptp.hAPP (tptp.c_COMBK tptp.v_P tptp.t_a tptp.t_b) tptp.v_Q) tptp.v_P) (forall ((V_n $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) V_Q) T_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn))) V_Q) T_a))))) (forall ((V_n $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn))) V_Q) T_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) V_Q) T_a))))) (forall ((V_pn $$unsorted) (V_s0 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn) V_s0 V_s1) (not (tptp.c_Natural_Oevalc (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn)) V_s0 V_s1)))) (forall ((V_P $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_P)) V_s V_s1) (not (tptp.c_Natural_Oevalc (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P) V_s V_s1)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P) tptp.c_Com_Ocom_OSKIP) V_P) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (let ((_let_4 (tptp.hAPP _let_3 V_P))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Com_Ocom_OSemi V_c V_d)) V_R) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_Q) V_d) V_R) _let_2 _let_1) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_4 V_c) V_Q) _let_2 _let_1) T_a)))))))) (forall ((V_G $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_G_H T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_fun2 V_fun2_H)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_com V_com_H)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_fun1 V_fun1_H)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_G $$unsorted) (T_a $$unsorted)) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool)) T_a)) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) V_Q))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert _let_4 _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Set_Oinsert _let_4 V_G _let_1) (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn))) V_Q) _let_2 _let_1) T_a)))))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_pname $$unsorted) (V_pname_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H))) (= V_pname V_pname_H))) _let_9 _let_8 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y)))))))))))))))))))))))))))))))
% 0.41/0.94  )
% 0.41/0.95  % SZS output end Proof for SWV840-1
% 0.41/0.95  % cvc5---1.0.5 exiting
% 0.41/0.95  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------