%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV875-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 21:53:36 EDT 2023

% Result   : Unsatisfiable 0.53s 1.32s
% Output   : Proof 1.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWV875-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.24  % Command    : do_cvc5 %s %d
% 0.25/0.44  % Computer : n028.cluster.edu
% 0.25/0.44  % Model    : x86_64 x86_64
% 0.25/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.44  % Memory   : 8042.1875MB
% 0.25/0.44  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.44  % CPULimit   : 300
% 0.25/0.44  % WCLimit    : 300
% 0.25/0.44  % DateTime   : Tue Aug 29 10:35:26 EDT 2023
% 0.25/0.44  % CPUTime    : 
% 0.41/0.68  %----Proving TF0_NAR, FOF, or CNF
% 0.41/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.WdPih1ASu4/cvc5---1.0.5_10932.p...
% 0.53/0.85  ------- get file name : TPTP file name is SWV875-1
% 0.53/0.85  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10932.smt2...
% 0.53/0.85  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.53/1.32  % SZS status Unsatisfiable for SWV875-1
% 0.53/1.32  % SZS output start Proof for SWV875-1
% 1.17/1.36  (
% 1.17/1.36  (let ((_let_1 (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 tptp.v_x) tptp.v_x)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((V_s $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP) V_s) V_s))))) (let ((_let_5 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_6 (_let_4))) (let ((_let_7 (ASSUME :args _let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_7 :args (tptp.v_x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP _let_1 V_s)))) :args _let_6)) :args ((or _let_2 (not _let_4)))) (ASSUME :args (_let_3)) _let_7 :args (false true _let_2 false _let_4)) :args ((forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Orderings_Oord__class_Omin T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_b))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Finite__Set_Ofold__image _let_3 V_g _let_2 V_A T_b T_a)) (tptp.c_Finite__Set_Ofold__image _let_3 V_g _let_2 V_B T_b T_a)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Finite__Set_Ofold__image _let_3 V_g _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_b T_a)) (tptp.c_Finite__Set_Ofold__image _let_3 V_g _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_b T_a))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) V_a)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold V_f V_z V_A T_b T_a) (tptp.c_The (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_b T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c)) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c)) V_d)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d))))))))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP V_m V_x) _let_2)) (= V_x V_a) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2)) (= (tptp.hAPP V_m V_x) _let_2) (= V_b V_y))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2)) (= (tptp.hAPP V_m V_x) _let_2) (= V_x V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)))))) (forall ((V_t $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (not (= (tptp.c_Fun_Ofun__upd V_t V_k (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_x) T_a _let_1) (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_i) V_k))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a)))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (or (tptp.c_Map_Omap__le (tptp.c_Fun_Ofun__upd V_f V_a V_b T_a _let_1) (tptp.c_Fun_Ofun__upd V_g V_a V_b T_a _let_1) T_a T_b) (not (tptp.c_Map_Omap__le V_f V_g T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c)) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.c_Finite__Set_Osetsum V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Orderings_Oord__class_Omax T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_a V_b T_a T_b) V_c V_d T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_c V_d T_a T_b) V_a V_b T_a T_b)) (= V_a V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.t_b) V_a) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_a))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.t_b) V_xa) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_xa))))) (forall ((V_m $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_D $$unsorted)) (or (= (tptp.c_Map_Orestrict__map (tptp.c_Fun_Ofun__upd V_m V_x V_y T_a (tptp.tc_Option_Ooption T_b)) V_D T_a T_b) (tptp.c_Map_Orestrict__map V_m V_D T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_D)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y))) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Oord__class_Omax T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((V_m $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (= (tptp.c_Map_Orestrict__map (tptp.c_Map_Orestrict__map V_m V_A T_a T_b) V_B T_a T_b) (tptp.c_Map_Orestrict__map V_m (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2)) _let_1)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_b $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_b))) (= (tptp.hAPP (tptp.c_Map_Orestrict__map (tptp.c_COMBK _let_1 (tptp.tc_Option_Ooption T_b) tptp.t_a) V_D tptp.t_a T_b) tptp.v_x) _let_1))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Orestrict__map V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_f V_A T_a T_b) V_a (tptp.hAPP V_f V_a) T_a (tptp.tc_Option_Ooption T_b)))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Olinorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_C))) (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_C) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Finite__Set_Ofold _let_1 V_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_Finite__Set_Ofold _let_1 V_b V_A T_a T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_x V_z T_a T_b) (tptp.c_Fun_Ofun__upd V_f V_x V_z T_a T_b))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_D) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_3 V_B _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_x) V_x)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g) V_f)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f) V_g))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_COMBC (tptp.c_in T_a) T_a _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_R) V_S)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_R)) (tptp.hAPP _let_2 V_S))))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_COMBC (tptp.c_in T_a) T_a _let_1 tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_R)) (tptp.hAPP _let_3 V_S))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_R) V_S)))))))) (forall ((V_times $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (= (tptp.hAPP _let_1 _let_2) _let_2) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))))) (forall ((V_times $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_times V_x) V_x) V_x) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBK _let_1 T_a T_b) V_A T_b T_a) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_m $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_Map_Orestrict__map V_m V_A T_a T_b) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Map_Odom V_m T_a T_b)) V_A))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_x) V_x) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (or (= (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP _let_1 V_y)) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) (tptp.hAPP (tptp.hAPP V_inf V_y) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (= (tptp.hAPP _let_1 _let_2) _let_2) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (let ((_let_2 (tptp.hAPP V_inf V_y))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B) T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) T_a T_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g V_B T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_3 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_2) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c))))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_a) T_a T_b) (tptp.hAPP V_f2 V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_z T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a)) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((V_inf $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold V_inf V_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.c_Finite__Set_Ofold V_inf V_b V_A T_a T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (let ((_let_2 (tptp.hAPP V_f V_y))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_a T_b))) (or (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x))) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a) (tptp.c_Finite__Set_Ofold__image (tptp.c_HOL_Oplus__class_Oplus T_a) V_f (tptp.c_HOL_Ozero__class_Ozero T_a) V_A T_a T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_b) V_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Finite__Set_Olattice__class_OInf__fin T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_z $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_a T_b) V_x))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) T_a))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) _let_1))))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_B) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a)) (tptp.c_Finite__Set_Ofold _let_1 V_B V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_b $$unsorted) (V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_aa))) (or (= V_b V_y) (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_x (tptp.hAPP _let_1 V_b) T_a (tptp.tc_Option_Ooption T_aa)) V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (tptp.c_Finite__Set_Ofun__left__comm (tptp.c_HOL_Otimes__class_Otimes T_a) T_a T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_Finite__Set_Ofun__left__comm (tptp.c_HOL_Oplus__class_Oplus T_a) T_a T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Olinorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Oord__class_Omin T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_z T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a)) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a)))))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_g) V_f))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.c_Option_Ooption_ONone tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P V_f1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (= V_m V_n)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetprod V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B) T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) T_a T_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetprod V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g V_B T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_x) V_x))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.c_Finite__Set_Osetprod V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_f) V_g)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))))) (forall ((V_m_092_060_094isub_0621 $$unsorted) (V_m_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Osko__Map__Xmap__le__def__1__1 V_m_092_060_094isub_0621 V_m_092_060_094isub_0622 T_a T_b))) (or (not (= (tptp.hAPP V_m_092_060_094isub_0621 _let_1) (tptp.hAPP V_m_092_060_094isub_0622 _let_1))) (tptp.c_Map_Omap__le V_m_092_060_094isub_0621 V_m_092_060_094isub_0622 T_a T_b)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.c_Option_Ooption_ONone T_b) T_a T_b) V_f1)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b)) (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) T_b)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Suc V_n)))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) (tptp.c_Suc V_x)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_i)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP 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$$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL 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$$unsorted) (V_a $$unsorted) (V_inf $$unsorted) (V_b $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq 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_let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_4 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_4 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_4 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_3) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_4 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_4 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_4 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_3) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_B)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP 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((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_x))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a)) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a)) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_x) V_y)) V_y)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_x) V_y)) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_e)) V_c)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y))) _let_1))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y))) _let_1))))))) (forall ((V_m $$unsorted) (V_D $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Map_Orestrict__map V_m V_D T_a T_b))) (or (= (tptp.c_Fun_Ofun__upd _let_1 V_x (tptp.c_Option_Ooption_ONone T_b) T_a (tptp.tc_Option_Ooption T_b)) _let_1) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_D))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_b) V_d) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold V_f V_z V_A T_a T_b) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_a T_b) V_y))) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc V_m))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_n)) (= _let_2 V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))) (= V_b V_c)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_b T_a)) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_Lattices_Olower__semilattice (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) T_a))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Ofold _let_1 V_b V_A T_a T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_b)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.hAPP V_f V_x) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) _let_1)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.hAPP V_f V_x) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_x _let_1))))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_B) (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a)) (tptp.c_Finite__Set_Ofold _let_1 V_B V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_1 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_1 V_c))))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_B) V_C _let_1) (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1)))))) (forall ((V_m $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_xa _let_1 T_aa (tptp.tc_Option_Ooption T_a)) V_xa) _let_1))) (forall ((V_t $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_t V_k) _let_1)) (= (tptp.c_Fun_Ofun__upd V_t V_k _let_1 T_b (tptp.tc_Option_Ooption T_a)) V_t)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_3 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_b))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_3) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_3))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Ofold__image _let_2 V_g _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3) V_A) V_B) T_b T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Finite__Set_Ofold__image _let_2 V_g _let_1 V_A T_b T_a)) (tptp.c_Finite__Set_Ofold__image _let_2 V_g _let_1 V_B T_b T_a)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (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.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (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.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (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.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_times $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofun__left__comm V_times T_a T_a) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.c_Option_Ooption_OSome T_b))) (or (not (= (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_2 V_x) T_a _let_1) (tptp.c_Fun_Ofun__upd V_n V_a (tptp.hAPP _let_2 V_y) T_a _let_1))) (= V_x V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_x)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_3 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_3 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_f)) (= (tptp.hAPP V_f V_x) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_m)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.c_Finite__Set_Ofold V_inf V_b V_A T_a T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (or (= (tptp.hAPP _let_1 (tptp.c_Finite__Set_Ofold V_f V_z V_A T_a T_b)) (tptp.c_Finite__Set_Ofold V_f (tptp.hAPP _let_1 V_z) V_A T_a T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_x)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_g V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a T_b)) V_f) V_g))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_t $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_t))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B)))))) (forall ((V_m $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Orestrict__map V_m V_A T_a T_b) V_x) (tptp.hAPP V_m V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A T_a T_a) V_y)))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_aa T_a) V_xa))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_aa T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_aa) V_x) V_A) T_aa T_a) (tptp.hAPP (tptp.hAPP V_f V_x) V_xa))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_2) V_A) V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (tptp.hBOOL (tptp.hAPP _let_2 V_A)) (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B)))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A T_a T_a) V_y)))))) (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.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) _let_1) V_x) _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.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_z $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold__image V_f V_g V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) V_z)) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) V_z)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) _let_2) _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))) (or (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_2))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) V_z))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_z T_a T_b)) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_in tptp.t_a))) (let ((_let_4 (tptp.c_COMBC _let_3 tptp.t_a _let_1 tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R)) (tptp.hAPP _let_4 V_S)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 V_R) V_S)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_C)) (tptp.hAPP _let_2 V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_C) V_D))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Ofold__image _let_1 V_g V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_g V_a)) (tptp.c_Finite__Set_Ofold__image _let_1 V_g V_z V_A T_b T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a T_b) (tptp.c_Finite__Set_Ofold V_f (tptp.hAPP (tptp.hAPP V_f V_x) V_z) V_A T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a T_b) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_Finite__Set_Ofold V_f V_z V_A T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard V_A T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_F $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_F) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetsum V_f V_F T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_F)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_b)) (= (tptp.c_Finite__Set_Ofold__image _let_1 V_g V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_g V_a)) (tptp.c_Finite__Set_Ofold__image _let_1 V_g V_z V_A T_b T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.c_Finite__Set_Ofold _let_1 V_b V_A T_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) _let_1)) (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) _let_1) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) (tptp.c_Finite__Set_Ofold (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a) V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum 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_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b) T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (let ((_let_4 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_4 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_3 V_B))))))))) (forall ((V_m $$unsorted) (V_D $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m V_D T_a T_b) V_x V_y T_a _let_1) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m (tptp.c_HOL_Ominus__class_Ominus V_D (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2) T_a T_b) V_x V_y T_a _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a) V_A)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_times T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.c_Finite__Set_Ofold V_times V_a V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.c_Finite__Set_Ofold _let_1 V_a V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 V_A V_x T_a)) V_x))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_M)) (tptp.hAPP _let_2 V_N))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N))))))) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_N)) (tptp.hAPP _let_2 V_M))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a T_b) (tptp.hAPP (tptp.hAPP V_f V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_a T_b) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) _let_2))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_3)))))))) (forall ((V_m $$unsorted) (V_D $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m V_D T_a T_b) V_x V_y T_a _let_1) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m (tptp.c_HOL_Ominus__class_Ominus V_D (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2) T_a T_b) V_x V_y T_a _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_D))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_in T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_a (tptp.hAPP (tptp.hAPP _let_4 V_b) (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP _let_4 V_a) (tptp.c_Orderings_Obot__class_Obot _let_3)) _let_3)) T_a T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A T_a T_a) V_x))))))))) (forall ((V_m $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Map_Orestrict__map (tptp.c_Fun_Ofun__upd V_m V_x V_y T_a _let_1) V_D T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m (tptp.c_HOL_Ominus__class_Ominus V_D (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2) T_a T_b) V_x V_y T_a _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_D))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_in T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_a (tptp.hAPP (tptp.hAPP _let_4 V_b) (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP _let_4 V_a) (tptp.c_Orderings_Obot__class_Obot _let_3)) _let_3)) T_a T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A T_a T_a) V_x))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.c_Finite__Set_Ofold V_f V_z (tptp.hAPP _let_2 V_A) T_a T_b) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_Finite__Set_Ofold V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP _let_2 V_A) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.c_Finite__Set_Ofold _let_1 V_a V_A T_a T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.c_Finite__Set_Ofold _let_1 V_a V_A T_a T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_xo $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (= V_xo (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Option_Oset V_xo T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Option_Oset (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((V_m $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Orestrict__map V_m V_A T_a T_b) V_x) (tptp.c_Option_Ooption_ONone T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Orderings_Obot__class_Obot _let_3))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_3) V_A) V_B) _let_4)) (= V_B _let_4) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_4) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Orderings_Obot__class_Obot _let_3))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_3) V_A) V_B) _let_4)) (= V_B _let_4) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_4) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B) V_C) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1))))) (forall ((T_a $$unsorted)) (= (tptp.c_Option_Oset (tptp.c_Option_Ooption_ONone T_a) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_xo $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Option_Oset V_xo T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_xo (tptp.c_Option_Ooption_ONone T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_sup $$unsorted) (V_B $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_sup V_B) (tptp.hAPP V_Sup V_A)) (tptp.c_Finite__Set_Ofold V_sup V_B V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_inf $$unsorted) (V_B $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_B) (tptp.hAPP V_Inf V_A)) (tptp.c_Finite__Set_Ofold V_inf V_B V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (V_A $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup V_A) (tptp.c_Finite__Set_Ofold V_sup V_bot V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_A $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf V_A) (tptp.c_Finite__Set_Ofold V_inf V_top V_A T_a T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_y))) (= (tptp.c_Map_Omap__add V_f (tptp.c_Fun_Ofun__upd V_g V_x _let_2 T_a _let_1) T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Omap__add V_f V_g T_a T_b) V_x _let_2 T_a _let_1))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_m $$unsorted)) (= (tptp.c_Map_Omap__add (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) V_m T_a T_b) V_m)) (forall ((V_m $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Omap__add V_m (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) T_a T_b) V_m)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Map_Omap__le (tptp.c_Fun_Ofun__upd V_f V_x (tptp.c_Option_Ooption_ONone T_b) T_a (tptp.tc_Option_Ooption T_b)) V_f T_a T_b)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted)) (tptp.c_Map_Omap__le (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) V_g T_a T_b)) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Map_Odom V_f T_a T_b)) (tptp.c_Map_Odom V_g T_a T_b))) (not (tptp.c_Map_Omap__le V_f V_g T_a T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omax T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin 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_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((T_a $$unsorted) (V_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))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_B _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_A _let_2))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a))) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP _let_1 V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b))))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Map_Odom V_f T_b T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.c_Option_Ooption_ONone T_a))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x) V_A) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1)))))) (forall ((V_pname_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_G $$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_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OSemi V_c0 V_c1)) V_s0) V_s2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c1) V_s1) V_s2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c0) V_s0) V_s1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) V_B _let_1) (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_times $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) _let_3)) (= V_B _let_3) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_3) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B)) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B)))))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_times T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.c_Finite__Set_Ofold V_times V_a V_A T_a T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((V_times $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Set_Oinsert T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_times V_a (tptp.hAPP (tptp.hAPP _let_3 V_b) (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP _let_3 V_a) (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) T_a T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_times V_b V_A T_a T_a) V_x))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Map_Odom (tptp.c_Fun_Ofun__upd V_f V_x (tptp.c_Option_Ooption_ONone T_b) T_a (tptp.tc_Option_Ooption T_b)) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Map_Odom V_f T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool))) (let ((_let_4 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_COMBK (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal tptp.tc_Com_Ostate) tptp.tc_Com_Ostate tptp.tc_Com_Ostate tptp.tc_bool) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)) _let_3 tptp.t_a) V_c (tptp.c_COMBK (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) _let_3 tptp.t_a) tptp.t_a)) _let_2) tptp.t_a)))))))) (forall ((V_e1 $$unsorted) (V_m $$unsorted) (T_b $$unsorted) (V_u1 $$unsorted) (T_a $$unsorted) (V_e2 $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_u1))) (or (= (tptp.c_Map_Omap__add (tptp.c_Fun_Ofun__upd V_e1 V_m _let_2 T_a _let_1) V_e2 T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Omap__add V_e1 V_e2 T_a T_b) V_m _let_2 T_a _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_m) (tptp.c_Map_Odom V_e2 T_a T_b))))))) (= (tptp.c_Hoare__Mirabelle_OMGT tptp.v_c) (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_fequal tptp.tc_Com_Ostate) tptp.v_c (tptp.c_Natural_Oevalc tptp.v_c) tptp.tc_Com_Ostate)) (forall ((T_a $$unsorted) (V_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))) (let ((_let_3 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) (tptp.hAPP _let_1 V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) (tptp.hAPP _let_1 V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_times $$unsorted) (V_g $$unsorted) (V_z $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold__image V_times V_g V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A) T_a T_b) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP V_g V_a)) (tptp.c_Finite__Set_Ofold__image V_times V_g V_z V_A T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_b)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.c_Finite__Set_Ofold1 _let_3 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_A)) (tptp.hAPP _let_4 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP V_times V_x) (tptp.hAPP _let_1 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_inf $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_inf T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A T_a T_b) (tptp.hAPP (tptp.hAPP V_f V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b) V_y)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (let ((_let_4 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_4 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_3 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_4 (tptp.c_HOL_Oord__class_Oless _let_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_A) (tptp.hAPP _let_3 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_3 (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2))) (let ((_let_4 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) V_B)) (not (tptp.hBOOL (tptp.hAPP _let_4 V_A))) (tptp.hBOOL (tptp.hAPP _let_4 V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_1 V_B)))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_lessequals _let_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_1 V_B))))))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Nitpick_Ofold__graph_H V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_y T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((V_m1 $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_m2 $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (or (tptp.c_Map_Omap__le (tptp.c_Fun_Ofun__upd V_m1 V_x (tptp.c_Option_Ooption_ONone T_b) T_a _let_1) (tptp.c_Fun_Ofun__upd V_m2 V_x (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_y) T_a _let_1) T_a T_b) (not (tptp.c_Map_Omap__le V_m1 V_m2 T_a T_b))))) (forall ((V_m_092_060_094isub_0621 $$unsorted) (V_m_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Map_Omap__le V_m_092_060_094isub_0621 V_m_092_060_094isub_0622 T_a T_b) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_Map_Osko__Map__Xmap__le__def__1__1 V_m_092_060_094isub_0621 V_m_092_060_094isub_0622 T_a T_b)) (tptp.c_Map_Odom V_m_092_060_094isub_0621 T_a T_b))))) (forall ((T_a $$unsorted) (V_m1 $$unsorted) (T_b $$unsorted) (V_m2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Map_Odom V_m1 T_a T_b)) (tptp.c_Map_Odom V_m2 T_a T_b)) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Map_Omap__add V_m1 V_m2 T_a T_b) (tptp.c_Map_Omap__add V_m2 V_m1 T_a T_b))))) (forall ((V_m1 $$unsorted) (V_m2 $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m1 V_m2 tptp.t_a T_b) tptp.v_x) (tptp.c_Option_Ooption_Ooption__case (tptp.hAPP V_m1 tptp.v_x) (tptp.c_Option_Ooption_OSome T_b) (tptp.hAPP V_m2 tptp.v_x) (tptp.tc_Option_Ooption T_b) T_b))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f V_A T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1 V_A V_f T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_times $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_times V_z (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP V_times V_z) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_times V_b V_A T_a T_a) V_y))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Map_Odom (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a (tptp.tc_Option_Ooption T_b)) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Map_Odom V_f T_a T_b))) (= V_y (tptp.c_Option_Ooption_ONone T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold__graph V_f V_a V_A T_a T_a) V_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Map_Odom V_f T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_f (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a)) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 V_A V_x T_a)) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_m V_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) (tptp.c_Map_Osko__Map__XdomD__1__1 V_a V_m T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Map_Odom V_m T_a T_b)))))) (forall ((T_a $$unsorted) (V_times $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 V_times T_a))) (let ((_let_3 (tptp.c_Set_Oinsert T_a))) (let ((_let_4 (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 V_times T_a))) (let ((_let_5 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_times T_a) V_A)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP V_times _let_4) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 _let_4) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1))))) (= V_A _let_1) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))))))) (forall ((V_m $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Map_Orestrict__map V_m (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)) tptp.t_a T_b) tptp.v_x) (tptp.c_Option_Ooption_ONone T_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))) (forall ((V_sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.c_Finite__Set_Olattice_OSup__fin V_sup V_A T_a) (tptp.hAPP V_Sup V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_inf $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.c_Finite__Set_Olattice_OInf__fin V_inf V_A T_a) (tptp.hAPP V_Inf V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olattice__class_OInf__fin T_a) V_A) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_f T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Option_Oset (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A)))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_inf T_a) V_A)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_k) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (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 ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_4 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_B))))))))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_in tptp.t_a))) (let ((_let_4 (tptp.c_COMBC _let_3 tptp.t_a _let_1 tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R)) (tptp.hAPP _let_4 V_S)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 V_R) V_S)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) (tptp.c_Finite__Set_Ofold (tptp.c_Set_Oinsert T_a) V_B V_A T_a _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Finite__Set_Ofold _let_1 V_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_Finite__Set_Ofold _let_1 V_b V_A T_a T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) (tptp.hAPP (tptp.c_Finite__Set_Olattice__class_OInf__fin T_a) V_A)) V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (= (tptp.c_Map_Odom (tptp.c_Fun_Ofun__upd (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) _let_1 T_a) V_x (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_xa) T_a _let_1) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_m $$unsorted) (V_D $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Map_Orestrict__map V_m V_D T_a T_b) V_x (tptp.c_Option_Ooption_ONone T_b) T_a (tptp.tc_Option_Ooption T_b)) (tptp.c_Map_Orestrict__map V_m (tptp.c_HOL_Ominus__class_Ominus V_D (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_D)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Ofield T_b)) (= (tptp.c_Finite__Set_Osetprod V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (= (tptp.hAPP V_f V_a) (tptp.c_HOL_Ozero__class_Ozero T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ofold V_f V_z V_A T_a T_b) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_Finite__Set_Ofold V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofun__left__comm V_f T_a T_b))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (let ((_let_4 (tptp.c_Set_Oinsert T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_3) _let_2) (tptp.hAPP (tptp.hAPP _let_4 V_y) _let_3) _let_2) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) V_x)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) _let_2) _let_2) _let_2)))) (forall ((V_f $$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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x) V_x))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) (tptp.hAPP (tptp.hAPP V_times V_x) (tptp.hAPP _let_1 V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A)) V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A)) V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_Map_Omap__add V_f V_g T_a T_b))) (or (tptp.c_Map_Omap__le _let_1 V_h T_a T_b) (not (tptp.c_Map_Omap__le V_f _let_1 T_a T_b)) (not (tptp.c_Map_Omap__le V_g V_h T_a T_b)) (not (tptp.c_Map_Omap__le V_f V_h T_a T_b))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Map_Omap__le V_f (tptp.c_Map_Omap__add V_g V_f T_a T_b) T_a T_b)) (forall ((V_n $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_m $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_n $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_xx $$unsorted) (V_m $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_xx))) (or (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP V_m V_k) _let_1)) (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) V_C _let_1) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1)) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) (tptp.hAPP _let_2 V_B))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) V_A) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_n V_k) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_m V_k) _let_1)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_m V_k) _let_1)) (not (= (tptp.hAPP V_n V_k) (tptp.c_Option_Ooption_ONone T_a))) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_m V_k) _let_1) (= (tptp.hAPP V_n V_k) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_a_H $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_a_H)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y)))) (forall ((V_A $$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 ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_f T_a) V_A) (tptp.c_The (tptp.c_Finite__Set_Ofold1Set V_f V_A T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$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_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_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_g $$unsorted) (V_h $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.c_Map_Omap__le V_g V_h T_a T_b) (not (tptp.c_Map_Omap__le (tptp.c_Map_Omap__add V_f V_g T_a T_b) V_h T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Map_Omap__le V_f V_f T_a T_b)) (forall ((V_m1 $$unsorted) (V_m3 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m2 $$unsorted)) (or (tptp.c_Map_Omap__le V_m1 V_m3 T_a T_b) (not (tptp.c_Map_Omap__le V_m2 V_m3 T_a T_b)) (not (tptp.c_Map_Omap__le V_m1 V_m2 T_a T_b)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_Map_Omap__add V_m V_n T_a T_b) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Map_Odom V_n T_a T_b)) (tptp.c_Map_Odom V_m T_a T_b)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted)) (not (= (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_a_H) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted)) (not (= (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_xa) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (or (not (= (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_a_H))) (= V_a V_a_H)))) (forall ((V_m1 $$unsorted) (V_m2 $$unsorted) (V_m3 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Omap__add V_m1 (tptp.c_Map_Omap__add V_m2 V_m3 T_a T_b) T_a T_b) (tptp.c_Map_Omap__add (tptp.c_Map_Omap__add V_m1 V_m2 T_a T_b) V_m3 T_a T_b))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_a))) (or (= (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_times V_b) V_c))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_a))) (let ((_let_2 (tptp.hAPP V_times V_b))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_times V_a) V_b) (tptp.hAPP (tptp.hAPP V_times V_b) V_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Omap__add V_f V_g T_a T_b))) (or (= _let_1 (tptp.c_Map_Omap__add V_g V_f T_a T_b)) (not (tptp.c_Map_Omap__le V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Omap__add V_f V_g T_a T_b))) (or (not (= _let_1 (tptp.c_Map_Omap__add V_g V_f T_a T_b))) (tptp.c_Map_Omap__le V_f _let_1 T_a T_b)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_f V_g) (not (tptp.c_Map_Omap__le V_g V_f T_a T_b)) (not (tptp.c_Map_Omap__le V_f V_g T_a T_b)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (let ((_let_2 (tptp.hAPP V_n V_k))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= _let_2 (tptp.c_Option_Ooption_ONone T_a)) (= _let_2 _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) _let_1) T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_A $$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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_fequal T_a) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Option_Othe (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x) T_a) V_x)) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x)) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 V_B) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 V_B) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Set_Ocontents (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x)) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (or (= V_y (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_f T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) (tptp.hAPP _let_1 V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l1 V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_m) (tptp.c_Map_Odom V_l2 T_a T_b))))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l2 V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_m) (tptp.c_Map_Odom V_l1 T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Map_Odom V_m T_a T_b))) (= (tptp.hAPP V_m V_a) (tptp.c_Option_Ooption_ONone T_b)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_m V_a) (tptp.c_Option_Ooption_ONone T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Map_Odom V_m T_a T_b)))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_m V_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Map_Odom V_m T_b T_a))))) (forall ((V_m_092_060_094isub_0621 $$unsorted) (V_x $$unsorted) (V_m_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_m_092_060_094isub_0621 V_x) (tptp.hAPP V_m_092_060_094isub_0622 V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Map_Odom V_m_092_060_094isub_0621 T_a T_b)))) (not (tptp.c_Map_Omap__le V_m_092_060_094isub_0621 V_m_092_060_094isub_0622 T_a T_b)))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l2 V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_m) (tptp.c_Map_Odom V_l2 T_a T_b)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Odom V_f T_b T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x) _let_1) _let_1)))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted) (V_Z_H $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)))))) (forall ((V_c $$unsorted)) (= (tptp.c_Hoare__Mirabelle_OMGT V_c) (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_fequal tptp.tc_Com_Ostate) V_c (tptp.c_Natural_Oevalc V_c) tptp.tc_Com_Ostate))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) T_a T_b)))))) (forall ((T_aa $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_a) (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.hAPP V_f V_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_aa T_a)))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_times $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_xa)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_A) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.tc_Com_Ostate)) _let_2))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_2 _let_4 tptp.tc_Com_Ostate) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids _let_2 _let_4 tptp.tc_Com_Ostate)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_2 (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_OMGT V_c)) _let_2) tptp.tc_Com_Ostate)))))))) (forall ((V_pn $$unsorted) (V_s0 $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OBODY V_pn)) V_s0) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Option_Othe (tptp.hAPP tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom)) V_s0) V_s1))))) (forall ((V_P $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Option_Othe (tptp.hAPP tptp.c_Com_Obody V_P) tptp.tc_Com_Ocom)) V_s) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OBODY V_P)) V_s) V_s1))))) (tptp.c_Finite__Set_Ofinite (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom) tptp.tc_Com_Opname) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OSemi V_c V_d) V_R T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_Q V_d V_R T_a)) _let_2) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q T_a)) _let_2) T_a))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OBODY V_pn) V_Q T_a)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_4 _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.hAPP _let_4 V_G) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Option_Othe (tptp.hAPP tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom) V_Q T_a)) _let_2) T_a)))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OBODY V_pn) V_Q T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Option_Othe (tptp.hAPP tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom) V_Q T_a)) _let_2) T_a))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert _let_1) V_t))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_2 V_ts) 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.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) 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.hAPP (tptp.hAPP (tptp.c_Set_Oinsert (tptp.tc_Hoare__Mirabelle_Otriple T_a)) V_t) V_ts) T_a)))) (forall ((V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_x))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P tptp.c_Com_Ocom_OSKIP V_P T_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) T_a))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_G_H T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_com V_com_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun1 V_fun1_H))) (= (tptp.hAPP _let_5 tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) tptp.v_x) _let_5)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_b V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_b V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_a V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_a V_c))))) (forall ((V_u $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Natural_Oevalc V_c) V_s))) (or (= V_u V_t) (not (tptp.hBOOL (tptp.hAPP _let_1 V_u))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_t)))))) _let_4 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_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_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_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.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_xa))) (let ((_let_4 (tptp.hAPP _let_2 V_x))) (= (tptp.hAPP _let_3 (tptp.hAPP _let_4 _let_1)) (tptp.hAPP _let_4 (tptp.hAPP _let_3 _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (= V_a V_b))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert _let_1) V_t))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_2 V_ts) T_a)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (not (= (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_A V_B))))) (forall ((V_pname $$unsorted) (V_pname_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OBODY V_pname_H))) (= V_pname V_pname_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_pname_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (or (= V_t V_s) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP) V_s) V_t))))) _let_3 (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Com_Ocom_OBODY V_x))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_fequal tptp.tc_Com_Ostate) _let_2 (tptp.c_Natural_Oevalc _let_2) tptp.tc_Com_Ostate)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.tc_Com_Ostate) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Com_Opname) V_x) (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom)))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_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_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice 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_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_Option_Ooption T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y)))))))))))))))
% 1.17/1.36  )
% 1.17/1.37  % SZS output end Proof for SWV875-1
% 1.17/1.37  % cvc5---1.0.5 exiting
% 1.17/1.37  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------