%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV889-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 21:53:40 EDT 2023

% Result   : Unsatisfiable 0.53s 0.95s
% Output   : Proof 0.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : SWV889-1 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.19  % Command    : do_cvc5 %s %d
% 0.18/0.40  % Computer : n010.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit   : 300
% 0.18/0.40  % WCLimit    : 300
% 0.18/0.40  % DateTime   : Tue Aug 29 08:18:49 EDT 2023
% 0.18/0.40  % CPUTime    : 
% 0.25/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.25/0.59  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PuAZ6fWjgZ/cvc5---1.0.5_11625.p...
% 0.25/0.70  ------- get file name : TPTP file name is SWV889-1
% 0.25/0.71  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11625.smt2...
% 0.25/0.71  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.53/0.95  % SZS status Unsatisfiable for SWV889-1
% 0.53/0.95  % SZS output start Proof for SWV889-1
% 0.53/0.97  (
% 0.53/0.97  (let ((_let_1 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G tptp.v_ts tptp.tc_Com_Ostate))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.c_lessequals tptp.v_ts tptp.v_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate) tptp.tc_bool)))) (let ((_let_4 (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))))))) (let ((_let_5 (not _let_3))) (let ((_let_6 (or _let_1 _let_5))) (let ((_let_7 (_let_4))) (let ((_let_8 (ASSUME :args _let_7))) (let ((_let_9 (not _let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_8 :args (tptp.v_G tptp.v_ts tptp.tc_Com_Ostate QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) true))))) :args _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_1 _let_5 _let_9))) (ASSUME :args (_let_2)) (ASSUME :args (_let_3)) :args (_let_9 true _let_1 false _let_3)) _let_8 :args (false true _let_6 false _let_4)) :args ((forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1)))) (forall ((V_f $$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 ((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_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_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_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (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 ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a) (tptp.c_SetInterval_Oord__class_OgreaterThan V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeast V_l T_a)) (not (tptp.c_lessequals V_l V_u T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a)) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a)) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$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 $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_b T_a) T_b) (not (tptp.c_Fun_Oinj__on V_h (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) (tptp.c_Set_Oinsert V_u (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.c_lessequals V_l V_u T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a) (not (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_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$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_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_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (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.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 $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_SetInterval_Oord__class_OatLeast V_k T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_in V_c (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_A T_a))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_fun_H $$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_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 $$unsorted) (V_a $$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_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oimage V_f V_A T_a T_b) T_a T_b) V_A) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_com1 $$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 $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (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 $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_HOL_Oord__class_Oless V_i V_k T_a) (not (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_i V_k T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) V_B _let_1)))) (forall ((V_A $$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_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_com1 $$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_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_com1_H $$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_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a) T_aa)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OgreaterThan V_x T_a) (tptp.c_SetInterval_Oord__class_OgreaterThan V_y T_a))) (= V_x V_y))) (forall ((V_x $$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_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((T_a $$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 (tptp.c_HOL_Ouminus__class_Ouminus _let_2 _let_1) _let_1)))) (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 $$unsorted)) (or (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (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.c_in V_c V_B T_a)) (not (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 ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (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_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.c_in V_xa V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatMost V_n T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_n T_a) _let_1) (tptp.c_Set_Oinsert V_n (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_A $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((V_fun_H $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeast V_k T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Orderings_Otop__class_Otop T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Orderings_Obot__class_Obot T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_a T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) V_A _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (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_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_in V_x V_xa T_a))) (forall ((V_G $$unsorted) (V_t $$unsorted) (T_a $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (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_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (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_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_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.c_in V_x V_B T_a) (tptp.c_in V_x V_A T_a) (= V_A V_B))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.c_in V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.c_in V_a V_C T_a)))) (forall ((V_A $$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_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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((V_B $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_loc $$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 ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_HOL_Oord__class_Oless V_k V_i T_a) (not (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OgreaterThan V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OgreaterThan V_k T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_k V_i T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_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_HOL_Oord__class_Oless 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_HOL_Oord__class_Oless (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.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$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 $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$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_OatLeastLessThan V_a V_b T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_a $$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 $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_d T_a) (tptp.c_HOL_Oord__class_Oless V_c V_a T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$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 ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (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)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a) (tptp.c_SetInterval_Oord__class_OgreaterThan V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (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 T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_A $$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_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_k (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) _let_1) _let_2))))) (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.c_in V_x 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_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_lessequals V_k V_i T_a) (not (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OatLeast V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OatLeast V_k T_a) T_a) (not (tptp.c_lessequals V_k V_i T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (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_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (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 ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) _let_1))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))) (tptp.c_lessequals V_C V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_a $$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_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 ((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_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Otop__class_Otop _let_1) V_A _let_1)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (not (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (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_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_loc $$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 $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (not (tptp.c_lessequals V_m V_u T_a)) (not (tptp.c_lessequals V_l V_m T_a)))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (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_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 $$unsorted) (V_B $$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_Lattices_Oupper__semilattice__class_Osup 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))) (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 ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_SetInterval_Oord__class_OatMost V_k T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OgreaterThan V_k T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_m V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.c_lessequals V_m V_u T_a)) (not (tptp.c_lessequals V_l V_m T_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 ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_lessequals V_i V_k T_a) (not (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OatMost V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OatMost V_k T_a) T_a) (not (tptp.c_lessequals V_i V_k T_a)))) (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_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C 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))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _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_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless 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_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_in V_x V_A T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop _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_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) V_A))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_l (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) (tptp.c_SetInterval_Oord__class_OgreaterThan V_l T_a) _let_1) (tptp.c_SetInterval_Oord__class_OatLeast V_l 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))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_m V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (= V_a V_b) (not (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1))) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_d T_a)) (not (tptp.c_lessequals V_b V_d T_a)) (not (tptp.c_lessequals V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless (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_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_a T_a)) (not (tptp.c_lessequals V_b V_d T_a)) (not (tptp.c_lessequals V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OlessThan V_u T_a) (tptp.c_Set_Oinsert V_u (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) (tptp.c_SetInterval_Oord__class_OatMost V_u T_a))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals V_A (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A _let_1) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_x $$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.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_b)) (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 $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a) (not (tptp.c_in V_x V_A T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_c V_a T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_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_HOL_Oord__class_Oless (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 $$unsorted) (V_B $$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_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_a 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_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus 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(tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$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 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(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_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (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)) (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 $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$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_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) 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(tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not 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(forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals V_f V_g _let_1) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1) (tptp.c_lessequals V_g V_f _let_1) (not (tptp.c_lessequals V_f V_g _let_1))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (not (tptp.c_lessequals V_g V_f _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (= V_A V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_x $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((V_loc_H $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((V_A $$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 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) V_A))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F 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_HOL_Oord__class_Oless 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.c_in V_x V_A T_a) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$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_b V_d)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OlessThan V_u T_a)) (not (tptp.c_lessequals V_l V_u T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeast V_x T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_y T_a))) (= V_x V_y))) (forall ((V_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (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 $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.c_in V_a V_C 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))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.c_in V_a V_A T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) T_a)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_vname V_vname_H))) (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 ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (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_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _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))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (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 ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatMost V_u T_a)) (not (tptp.c_lessequals V_l V_u T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (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.c_in V_c V_B T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (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.c_in V_c V_A T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a) (not (tptp.c_in V_a V_B T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_c V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (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 $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (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_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_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (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_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_n T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_m T_a)) (not (tptp.c_lessequals V_i V_n T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatMost V_x T_a) (tptp.c_SetInterval_Oord__class_OatMost V_y T_a))) (= V_x V_y))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Oimage V_f V_A T_a T_b) _let_2) _let_2) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1))))) (forall ((V_A $$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_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_SetInterval_Oord__class_OgreaterThan V_k T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatMost V_k T_a)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_G $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$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_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((V_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((T_a $$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_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeast V_l T_a)) (not (tptp.c_lessequals V_l V_u T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_c V_d T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((V_com1_H $$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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_f $$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_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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B 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_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (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_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_t V_B T_a) (not (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_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (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.c_in V_x V_A T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (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 $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (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_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 ((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_P $$unsorted) (V_Q $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.hAPP V_Q (tptp.c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 V_P V_Q T_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$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 ((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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_A $$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_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 (= (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$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_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_A _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (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_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_B V_A _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 ((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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_A T_b T_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a) (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_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 V_P V_Q T_a))))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_t $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts (tptp.tc_Hoare__Mirabelle_Otriple T_a)) T_a)))) (forall ((V_G $$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) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)))) (forall ((V_c1 $$unsorted) (V_b $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_c2 $$unsorted) (V_b 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(not (tptp.c_lessequals (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1) T_b))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 V_f V_g T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b)) (not (tptp.c_lessequals (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1) T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeast V_x T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_y T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeast V_x T_a) (tptp.c_SetInterval_Oord__class_OatLeast V_y T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$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 ((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_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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatMost V_x T_a) (tptp.c_SetInterval_Oord__class_OatMost V_y T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals 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tptp.tc_bool)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_c V_a T_a) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_b V_d T_a) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals 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(tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_Option_Ooption T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))
% 0.53/0.97  )
% 0.53/0.97  % SZS output end Proof for SWV889-1
% 0.53/0.97  % cvc5---1.0.5 exiting
% 0.53/0.98  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------