%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV841-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 21:53:30 EDT 2023

% Result   : Unsatisfiable 1.61s 1.80s
% Output   : Proof 1.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : SWV841-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19  % Command    : do_cvc5 %s %d
% 0.18/0.40  % Computer : n005.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit   : 300
% 0.18/0.40  % WCLimit    : 300
% 0.18/0.40  % DateTime   : Tue Aug 29 06:53:08 EDT 2023
% 0.18/0.40  % CPUTime    : 
% 0.26/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.59  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PcPPIrHi0D/cvc5---1.0.5_18491.p...
% 0.26/0.71  ------- get file name : TPTP file name is SWV841-1
% 0.26/0.72  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18491.smt2...
% 0.26/0.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.61/1.80  % SZS status Unsatisfiable for SWV841-1
% 1.61/1.80  % SZS output start Proof for SWV841-1
% 1.61/1.82  (
% 1.61/1.82  (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert _let_1) tptp.v_t))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.c_Orderings_Obot__class_Obot _let_2)))) (let ((_let_5 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G _let_4 tptp.t_a))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G tptp.v_ts tptp.t_a))) (let ((_let_8 (or (not _let_7) _let_6))) (let ((_let_9 (tptp.hAPP _let_3 tptp.v_ts))) (let ((_let_10 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G _let_9 tptp.t_a))) (let ((_let_11 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A))))))) (let ((_let_12 (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_ts_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_ts_H (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts_H T_a)))))) (let ((_let_13 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (tptp.c_lessequals V_B (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))))) (let ((_let_14 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_15 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_1))))) (let ((_let_16 (not _let_10))) (let ((_let_17 (tptp.c_lessequals _let_4 _let_9 _let_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_5 _let_18 _let_16))) (let ((_let_20 (_let_12))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (not _let_19))) (let ((_let_23 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) _let_4) tptp.v_ts))) (let ((_let_24 (tptp.c_lessequals _let_4 _let_23 _let_2))) (let ((_let_25 (= _let_9 _let_23))) (let ((_let_26 (_let_15))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (_let_11))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (and _let_25 _let_24))) (let ((_let_31 (ASSUME :args (_let_24)))) (let ((_let_32 (ASSUME :args (_let_25)))) (let ((_let_33 (ASSUME :args (_let_10)))) (let ((_let_34 (tptp.c_lessequals tptp.v_ts _let_9 _let_2))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_7 _let_35 _let_16))) (let ((_let_37 ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) true)) (not (= (tptp.c_lessequals V_ts V_ts_H (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool)) false))))) (let ((_let_38 (_let_13))) (let ((_let_39 (ASSUME :args _let_38))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (tptp.v_G _let_4 tptp.t_a _let_9 QUANTIFIERS_INST_E_MATCHING _let_37)) :args _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_5 _let_16 _let_18 _let_22))) (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_7 _let_16 _let_35 (not _let_36)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.v_ts _let_1 tptp.v_t QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)))) :args _let_38)) _let_39 :args (_let_34 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (tptp.v_G tptp.v_ts tptp.t_a _let_9 QUANTIFIERS_INST_E_MATCHING _let_37)) :args _let_20)) _let_21 :args (_let_36 false _let_12)) :args (_let_7 false _let_10 false _let_34 false _let_36)) :args (_let_6 false _let_7)) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_30)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_31 _let_32) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_4)) (SYMM (SYMM _let_32)) (REFL :args (_let_2)) :args (APPLY_UF tptp.c_lessequals)) (TRUE_INTRO _let_31))) :args (_let_24 _let_25))) :args (_let_25 _let_24))) :args (true _let_30)) :args ((or (not _let_25) _let_17 (not _let_24)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_1 tptp.v_t tptp.v_ts QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)))) :args _let_28)) _let_29 :args (_let_25 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_4 _let_1 tptp.v_ts QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B)))) :args _let_26)) _let_27 :args (_let_24 false _let_15)) :args (_let_17 false _let_25 false _let_24)) :args (_let_22 true _let_5 false _let_10 false _let_17)) _let_21 :args (false true _let_19 false _let_12)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_xa T_a) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.c_lessequals V_x (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A T_a) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.hAPP V_M V_i) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_a T_b) T_b) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 V_f V_A T_a) (tptp.c_The (tptp.c_Finite__Set_Ofold1Set V_f V_A T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$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))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.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_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))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.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_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))) (or (tptp.c_lessequals (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) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_f T_a T_b))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) T_a T_b) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((T_b $$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 ((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 ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a))))) (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_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_x) V_x))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$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_a))) (or (tptp.c_Fun_Oinj__on V_f (tptp.hAPP _let_2 V_A) T_a T_b) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 V_A T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 V_A T_a) T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_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_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Set_Oimage V_f T_a T_b))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1))) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Set_Oimage V_f T_a T_b))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (tptp.hAPP _let_3 (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1))) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b))))))) (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_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_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_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMax V_M T_a) (tptp.c_Finite__Set_Olinorder__class_OMax V_N T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_f T_b T_a))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1) (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool))) _let_1)))) (forall ((T_a $$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_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_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_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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$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_A))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$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.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_1))) _let_15 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_y) V_z) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) T_a))) (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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$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.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _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_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 ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (= (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq 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 V_less V_b) V_a))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_a $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) (tptp.hAPP V_f V_x)) _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Ovimage V_f T_b T_a))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((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.c_in V_a V_A T_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.c_in V_a V_C T_a))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) V_A) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A))))) (forall ((T_a $$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 ((V_A $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_a) T_a _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a _let_1))) (not (tptp.hBOOL (tptp.c_in V_u V_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_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$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) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Ovimage V_f T_a T_b))) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Finite__Set_Ofold1 V_times (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a) (tptp.hAPP (tptp.hAPP V_times V_x) (tptp.c_Finite__Set_Ofold1 V_times V_A T_a))) (tptp.hBOOL (tptp.c_in V_x V_A T_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 ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.hAPP (tptp.c_Set_Ovimage V_f T_b T_a) V_A)) V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.c_Collect V_P T_a) V_P)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_Finite__Set_Ofun__left__comm__idem (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) T_a T_a))) (forall ((V_com1 $$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 $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((T_a $$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 ((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 ((T_a $$unsorted) (V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less $$unsorted)) (or (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b)) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP V_B V_x) T_b) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_a T_b))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)) (= V_A V_B)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_A V_x) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_I T_b))) (not (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_b _let_1) V_B _let_1))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_a _let_1))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_A V_k)) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_f T_b T_a))) (tptp.c_lessequals (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)) _let_1)))) (forall ((T_a $$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 $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_b V_d T_a)) (not (tptp.c_lessequals V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_b V_d T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_c V_a T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((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.c_lessequals V_C V_A _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_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.c_lessequals V_C V_A _let_1))))))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_lessequals V_a V_b T_a))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((T_a $$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 $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_a) V_A))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (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 ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB V_B V_f T_c _let_1 T_b) T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_c) V_A) V_B T_c _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_F $$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 $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_C))) (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_C) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_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 ((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.c_lessequals (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)) T_a))))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) 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_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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$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)) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$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_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_h $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage V_h T_a T_b) V_F) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (= (tptp.hAPP _let_14 tptp.v_x) (tptp.c_in tptp.v_x _let_14 tptp.t_a)) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_N T_a) (tptp.c_Finite__Set_Olinorder__class_OMin V_M T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$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 (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_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq 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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A) V_B T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_B V_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) T_a T_b) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in V_c V_A T_b)))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_less $$unsorted)) (or (tptp.c_lessequals (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_c) V_a))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_less $$unsorted)) (or (tptp.c_lessequals (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b)) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_d $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_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 $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun1 V_fun1_H))) (forall ((V_fun1 $$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 $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A T_a) V_a T_a) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a) V_x T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a))) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a))))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_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 ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_b T_a) V_A) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_b T_a) V_B) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) V_B) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) V_A) T_a))))) (forall ((V_less__eq $$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.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_l $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u)) (not (tptp.hBOOL (tptp.c_in V_i (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a) T_a))))) (forall ((V_less__eq $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i)) (not (tptp.hBOOL (tptp.c_in V_i (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a) T_a))))) (forall ((T_a $$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 $$unsorted) (V_x $$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_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 $$unsorted) (V_B $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B))) (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I (tptp.c_COMBB _let_2 V_A _let_1 _let_1 T_b) T_b _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$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_A))) (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1))))) (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.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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (= V_a V_b) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$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 $$unsorted) (V_times $$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_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_2)) (= 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__mult V_times T_a)) (= (tptp.c_Finite__Set_Ofold1 V_times (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a) (tptp.hAPP (tptp.hAPP V_times (tptp.c_Finite__Set_Ofold1 V_times V_A T_a)) (tptp.c_Finite__Set_Ofold1 V_times V_B T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Ovimage V_f T_a T_b))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$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))) (or (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)) _let_2)) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP _let_1 V_A) T_a T_b)))))) (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 $$unsorted) (V_x $$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.c_in V_x V_B T_a)))))) (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 $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Set_Oimage V_f T_aa T_a) V_A) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C) _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C) _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Ovimage V_f T_a T_b))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_Finite__Set_Ofun__left__comm__idem (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a T_a))) (forall ((T_a $$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_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.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.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 ((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)) (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.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_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 ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$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 $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Collect V_P T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) V_x)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((T_a $$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_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_B) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted)) (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)) (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.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (= V_P (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__2 V_P T_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__1 V_P V_xa T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Ovimage V_f T_a T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1)) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (forall ((V_f $$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.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) (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))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (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.c_in V_a V_A T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_D) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A _let_1))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B _let_1))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (= (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq 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 V_less__eq V_a) V_b)) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (not (= (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$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_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.hAPP (tptp.c_Set_Oimage V_g T_c T_b) V_A)) (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) T_c T_a) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf 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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (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 ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Set_Oimage V_f T_b T_a))) (= (tptp.hAPP _let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_c _let_2)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB _let_3 V_B _let_2 _let_1 T_c) T_c _let_1)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (= (tptp.hAPP _let_1 _let_2) _let_2) (not (tptp.c_Finite__Set_Ofun__left__comm__idem V_f T_a T_b)))))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Set_Ovimage V_f T_a T_b))) (= (tptp.hAPP _let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_c _let_2)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB _let_3 V_B _let_2 _let_1 T_c) T_c _let_1)))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.c_Finite__Set_Ofun__left__comm__idem (tptp.c_COMBB V_f V_g T_a (tptp.tc_fun T_b T_b) T_c) T_c T_b) (not (tptp.c_Finite__Set_Ofun__left__comm__idem V_f T_a T_b)))) (forall ((V_i $$unsorted) (V_less__eq $$unsorted) (V_l $$unsorted) (V_u $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_i (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_C _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$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)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_f $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.c_Set_Oimage V_f T_c T_b) V_A) V_B T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB V_B V_f T_b _let_1 T_c) T_c _let_1)))) (forall ((T_a $$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_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_D) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((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_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$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_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_f T_a T_b))) (or (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B) V_C) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_M T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_B V_M T_b _let_1))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) V_A) V_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Ovimage V_f T_a T_b) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_The (tptp.c_fequal V_x T_a) T_a) V_x)) (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_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_x T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_a T_b))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_A) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.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_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (or (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1)) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__1 V_P V_xa T_a) V_xa)) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (= V_P (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__2 V_P T_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) T_b T_a) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (forall ((V_less__eq $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (= (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_a V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 V_A T_a)) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 V_A T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Ovimage V_f T_aa T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.hAPP V_f V_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_aa))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C V_B T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1)) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_times $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_b)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.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 ((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.c_Finite__Set_Ofold1 V_f (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))) T_b) V_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 ((V_A $$unsorted) (T_a $$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))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_B _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((T_a $$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_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 ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_D $$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.c_lessequals (tptp.hAPP _let_2 V_C) (tptp.hAPP _let_2 V_D) _let_1) (not (tptp.c_lessequals V_C V_D _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.hAPP V_f V_a)) (tptp.hAPP _let_1 V_B))))) (forall ((V_Inf $$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 $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a))))) (forall ((T_a $$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 $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a)))) _let_13 (forall ((T_a $$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 $$unsorted) (V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_b)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) T_a))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofun__left__comm__idem (tptp.c_Set_Oinsert T_a) T_a (tptp.tc_fun T_a tptp.tc_bool))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) _let_12 (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_G_H V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))))) (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 $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$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 $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OSemi V_c V_d) V_R T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_Q V_d V_R T_a)) _let_2) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q T_a)) _let_2) T_a))))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Collect (tptp.c_fequal V_a T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$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.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in 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))) T_a))) (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 $$unsorted) (V_a $$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 ((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_a $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$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.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((T_a $$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_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 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_a)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (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 ((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_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.c_in V_x V_xa T_a)))) _let_11 (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_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 ((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) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_G_H T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)))) (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 ((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_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 $$unsorted) (V_xa $$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 ((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))))) _let_10 _let_8 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_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_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 ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x T_a) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_X T_a) V_Y)))))))))))))))))))))))))))))))))))))))))))))))
% 1.61/1.82  )
% 1.61/1.82  % SZS output end Proof for SWV841-1
% 1.61/1.83  % cvc5---1.0.5 exiting
% 1.61/1.83  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------