TSTP Solution File: SWV844-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV844-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:53:31 EDT 2023
% Result : Unsatisfiable 1.34s 1.54s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.23 % Problem : SWV844-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.24 % Command : do_cvc5 %s %d
% 0.24/0.45 % Computer : n028.cluster.edu
% 0.24/0.45 % Model : x86_64 x86_64
% 0.24/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.45 % Memory : 8042.1875MB
% 0.24/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.45 % CPULimit : 300
% 0.24/0.45 % WCLimit : 300
% 0.24/0.45 % DateTime : Tue Aug 29 06:55:10 EDT 2023
% 0.24/0.45 % CPUTime :
% 0.41/0.68 %----Proving TF0_NAR, FOF, or CNF
% 0.52/0.69 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QtjZN2ifVP/cvc5---1.0.5_18561.p...
% 0.52/0.88 ------- get file name : TPTP file name is SWV844-1
% 0.52/0.88 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18561.smt2...
% 0.52/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.34/1.54 % SZS status Unsatisfiable for SWV844-1
% 1.34/1.54 % SZS output start Proof for SWV844-1
% 1.38/1.58 (
% 1.38/1.58 (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_b))) (let ((_let_2 (tptp.tc_fun tptp.t_b (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun _let_2 _let_1))) (let ((_let_4 (tptp.tc_fun tptp.tc_Com_Ocom _let_3))) (let ((_let_5 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_b))) (let ((_let_6 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB _let_5 tptp.v_P_H _let_2 _let_4 tptp.t_a) tptp.v_c0 tptp.t_a tptp.tc_Com_Ocom _let_3) tptp.v_Q_H tptp.t_a _let_2 _let_1) tptp.v_F tptp.t_a _let_1) tptp.t_b))) (let ((_let_7 (forall ((V_p $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_b))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP tptp.v_c0 V_p))) (let ((_let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_b))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP tptp.v_P V_p)) _let_3) (tptp.hAPP tptp.v_Q V_p)) _let_2 _let_1) tptp.t_b) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP tptp.v_P_H V_p)) _let_3) (tptp.hAPP tptp.v_Q_H V_p)) _let_2 _let_1) tptp.t_b)))))))))) (let ((_let_8 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_9 (tptp.hAPP tptp.v_c0 tptp.v_x))) (let ((_let_10 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP tptp.v_P tptp.v_x)) _let_9) (tptp.hAPP tptp.v_Q tptp.v_x)) _let_8 _let_1) tptp.t_b))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP tptp.v_P_H tptp.v_x)) _let_9) (tptp.hAPP tptp.v_Q_H tptp.v_x)) _let_8 _let_1) tptp.t_b))) (let ((_let_13 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_14 (tptp.hAPP tptp.v_Q tptp.v_R))) (let ((_let_15 (tptp.hAPP tptp.v_P tptp.v_R))) (let ((_let_16 (not _let_12))) (let ((_let_17 (or _let_10 _let_16))) (let ((_let_18 (_let_7))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (not _let_17))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.v_x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P V_p)))) :args _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_10 _let_16 _let_20))) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) :args (_let_20 true _let_10 false _let_12)) _let_19 :args (false true _let_17 false _let_7)) :args ((forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.c_Finite__Set_Osetsum V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Orderings_Oord__class_Omax T_a) T_a))) (forall ((V_m $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_a V_b T_a T_b) V_c V_d T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_c V_d T_a T_b) V_a V_b T_a T_b)) (= V_a V_c))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Oord__class_Omax T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_a)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_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))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))))))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_n)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_x V_z T_a T_b) (tptp.c_Fun_Ofun__upd V_f V_x V_z T_a T_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)) (tptp.hAPP _let_3 V_B)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_m V_u T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_x) V_x)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g) V_f)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f) V_g))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y))) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((V_times $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (= (tptp.hAPP _let_1 _let_2) _let_2) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))))) (forall ((V_times $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_times V_x) V_x) V_x) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (= V_m V_n)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_f) V_g)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) V_y)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b))) (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Orderings_Oord__class_Omin T_a) T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_b))) (= V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (= V_a V_b)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (let ((_let_3 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_l))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_n)) (tptp.hAPP _let_3 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_l))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_n)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Finite__Set_Ofold__image V_f V_g T_a T_b) (tptp.c_Finite__Set_Ofold (tptp.c_COMBB V_f V_g T_a (tptp.tc_fun T_a T_a) T_b) T_b T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n) (tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_m)) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_m)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_x) V_x) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (or (= (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP _let_1 V_y)) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) (tptp.hAPP (tptp.hAPP V_inf V_y) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (= (tptp.hAPP _let_1 _let_2) _let_2) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (let ((_let_2 (tptp.hAPP V_inf V_y))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_a)))))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B) T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) T_a T_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_g V_B T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c))))))) (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_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A)) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (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_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x)) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x)) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_k V_l T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_k) V_l))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_k V_l T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_k) V_l)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_b) V_d) T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_b) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) T_a))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_Suc V_n)))))) (forall ((V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) (tptp.c_Suc V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) (tptp.c_Suc V_m)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_B) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_B) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Oord__class_Omin T_a)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Suc V_n)))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) (tptp.c_Suc V_x)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_i)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oring T_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_b T_a) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_a T_b) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_aa) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_aa T_a) V_f)) (forall ((V_inf $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (or (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_inf T_a) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_b) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_inf $$unsorted) (V_z $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_inf $$unsorted) (V_b $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_b) V_x))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Lattices_Olower__semilattice (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) (tptp.c_Orderings_Oord__class_Omax T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_B)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b) (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_HOL_Ouminus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun tptp.t_a T_b)) V_A) tptp.v_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_b) (tptp.hAPP V_A tptp.v_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b)) V_b)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_3 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))))) (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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_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_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_m V_u T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_n))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_j))))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_1 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP _let_1 V_c))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_k V_l T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_k) V_l)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_l $$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_OgreaterThanAtMost V_k V_l T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_k) V_l))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_OrderedGroup_Oab__semigroup__idem__mult (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (= (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))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Suc V_m)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)) V_r) (tptp.c_Finite__Set_Osetsum (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_1 V_f T_a (tptp.tc_fun T_a T_a) T_b) T_b T_a T_a) V_r) V_A T_b T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_g) V_f))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_f) V_g)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_l))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) (tptp.hAPP _let_2 V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_l)) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_k))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_3 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_m)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_k))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_3 V_n) V_k)))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_m)))))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (= V_m V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetsum (tptp.c_COMBB _let_1 V_f T_a T_a T_b) V_A T_b T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_x) V_y)) V_y)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP V_inf V_x) V_y)) V_x)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_e)) V_c)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) V_m))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_3 (tptp.hAPP _let_2 V_m))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_k)) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)) (tptp.hAPP _let_3 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_k)) V_j))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_b) V_d) T_a)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_c) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) V_A) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc V_m))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_n)) (= _let_2 V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) V_m)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_Lattices_Olower__semilattice (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) T_a))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)) (tptp.c_Suc V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) V_k)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_m V_u T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_b) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (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_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) V_y)) (= V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_z))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_c V_d T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_b) V_d) T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc V_m))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (V_z $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Ofold__image _let_1 V_g T_b T_a) V_z))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_g V_a)) (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_F $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Set_Oinsert V_a V_F T_a) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetsum V_f V_F T_a T_b))) (tptp.hBOOL (tptp.c_in V_a V_F T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (V_z $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Ofold__image _let_1 V_g T_b T_a) V_z))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_b)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_g V_a)) (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) (tptp.c_Orderings_Otop__class_Otop T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) (tptp.c_Orderings_Obot__class_Obot T_a))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_y))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (tptp.c_Finite__Set_Osetsum V_f V_B T_a tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A))) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard _let_2 T_a))) (not (tptp.c_Finite__Set_Ofinite _let_2 T_a)))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_times T_a) (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold V_times T_a T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (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 $$unsorted) (V_k $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_k V_l T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_l) V_k))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A V_y T_a T_b)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) V_C) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) V_C) (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.c_Set_Oinsert V_a (tptp.hAPP _let_1 V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_b))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_d)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_A T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_b)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_m V_u T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_l) V_m)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_l) V_m)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) _let_2) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) _let_2)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_Finite__Set_Ofold__graph _let_1 V_a (tptp.c_Set_Oinsert V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_2) T_a)) T_a) V_x T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A V_x T_a T_a)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (tptp.hAPP V_f V_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (tptp.c_Finite__Set_Ofold__graph _let_1 V_a (tptp.c_Set_Oinsert V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_2) T_a)) T_a) V_x T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A V_x T_a T_a)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Fun_Oinj__on V_f V_A T_aa T_a)) (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_aa T_a) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_m T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_n T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_m T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_i) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_x))) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_a) V_A)) (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_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 _let_1 T_a) (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_a) V_A)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_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.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x)) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x)) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Orderings_Obot__class_Obot _let_3))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_3) V_A) V_B) _let_4)) (= V_B _let_4) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_4) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.c_Orderings_Obot__class_Obot _let_3))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_3) V_A) V_B) _let_4)) (= V_B _let_4) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_4) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (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.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (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) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A)) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_a) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_a) V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 V_A)) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B) V_C)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into _let_1 V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omax T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_i)) V_i) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m))) (or (= V_m _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_x)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Omax T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_f)) (= (tptp.hAPP V_f V_x) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_m)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBB _let_1 V_f T_a T_a T_b) V_A T_b T_a) (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_b) V_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_A)) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_a)) V_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_x)) V_x)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_b)) V_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_x)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) (tptp.hAPP _let_1 V_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) (tptp.hAPP _let_1 V_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) V_a))))))) (forall ((V_c $$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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_c $$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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold V_inf T_a T_a) V_b) V_A)) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (tptp.c_Finite__Set_Ofold__graph _let_1 V_z (tptp.c_Set_Oinsert V_b V_A T_a) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_y) T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A V_y T_a T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_Finite__Set_Ofold__graph _let_1 V_z (tptp.c_Set_Oinsert V_b V_A T_a) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_y) T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.c_Finite__Set_Ofold__graph _let_1 V_b V_A V_y T_a T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A V_x T_a T_b)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((T_a $$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_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 ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold__image V_f V_g T_a T_b) V_z) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_z)) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold V_f T_b T_a) V_z) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_z)) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_x V_z) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x T_a T_b)))) (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 ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_z T_a T_b)) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_z T_a T_b)) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBS (tptp.c_COMBB _let_1 V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a) V_A T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetsum V_g V_A T_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_b))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_inf $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold V_inf T_a T_a) V_b))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP _let_1 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((T_a $$unsorted) (V_a $$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 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBS (tptp.c_COMBB _let_1 V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a) V_A T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetsum V_g V_A T_b T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1) V_A) (tptp.c_Set_Oinsert V_x V_B T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_b))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_m V_u T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_l) V_m)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_m T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_m V_u T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_l) V_m)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_A T_a T_b) (tptp.hBOOL (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) V_y)) V_y) (not (tptp.hBOOL (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_B T_a)) (tptp.c_Finite__Set_Ocard V_A T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_less__eq $$unsorted) (V_inf $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_less $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_inf T_a) V_A)) V_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a) V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 V_A V_x T_a) V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_times $$unsorted) (V_z $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (tptp.c_Finite__Set_Ofold__graph V_times V_z (tptp.c_Set_Oinsert V_b V_A T_a) (tptp.hAPP (tptp.hAPP V_times V_z) V_y) T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.c_Finite__Set_Ofold__graph V_times V_b V_A V_y T_a T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.v_P tptp.t_a tptp.t_b tptp.t_c) tptp.v_Q) tptp.v_R) (tptp.hAPP _let_15 tptp.v_Q)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold _let_1 T_a T_a) V_b) V_A))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((V_f $$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 $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun tptp.t_a T_b)) V_A) V_B) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP V_A tptp.v_x)) (tptp.hAPP V_B tptp.v_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) (tptp.hAPP _let_2 V_B))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) V_A) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard _let_1 T_a))) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a)) (= V_A _let_1)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_b T_a)) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.c_Set_Oinsert V_x _let_2 T_a))) (tptp.c_Set_Oinsert V_y _let_2 T_a)) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a)) (tptp.c_Finite__Set_Ocard V_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 ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.hAPP V_f V_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_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.hAPP V_f V_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_times $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) _let_3)) (= V_B _let_3) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_3) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B)) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B)))))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_times T_a) (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Ofold V_times T_a T_a) V_a) V_A)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofold__graph V_times V_a (tptp.c_Set_Oinsert V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) V_x T_a T_a) (tptp.hBOOL (tptp.c_in V_b V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofold__graph V_times V_b V_A V_x T_a T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))) (forall ((T_b $$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_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b)) (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 ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b)) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) V_B))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_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))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_A T_b T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_b)) T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Set_Oinsert V_l (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost V_l V_u T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_l) V_u)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (tptp.c_Set_Oinsert V_u (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_l) V_u)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Orderings_Oord__class_Omin T_a) T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_x))) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool))) (let ((_let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_COMBK (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal tptp.tc_Com_Ostate) tptp.tc_Com_Ostate tptp.tc_Com_Ostate tptp.tc_bool) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)) _let_3 tptp.t_a)) V_c) (tptp.c_COMBK (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) _let_3 tptp.t_a)) _let_2 _let_1) tptp.t_a)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omax T_a) V_x) (tptp.hAPP _let_1 V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) (tptp.hAPP _let_1 V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_times $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold__image V_times V_g T_a T_b) V_z))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_A T_b)) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP V_g V_a)) (tptp.hAPP _let_1 V_A))) (tptp.hBOOL (tptp.c_in V_a V_A T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_b)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 V_A V_x T_a)) V_x))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_2) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a T_b)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_2) (tptp.c_Set_Oimage V_f V_A T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b)))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.c_Finite__Set_Ofold1 _let_3 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_A)) (tptp.hAPP _let_4 V_B))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_Finite__Set_Ocard V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A))) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP V_times V_x) (tptp.hAPP _let_1 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_OrderedGroup_Oab__semigroup__idem__mult V_times T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Ofold1 _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_2 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_2 V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Set_Oimage V_f _let_2 T_aa T_a) T_a)) (= _let_1 (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_1 V_f V_x T_a T_aa))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 V_P V_f T_a T_b) (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP V_f V_x))) (or (not (= (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_2 V_f V_x T_a T_aa) V_x)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_aa T_a)) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Set_Oimage V_f _let_1 T_aa T_a) T_a)))))) (forall ((V_b $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_b (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 V_b V_f T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_y $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_y))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Set_Oimage V_f _let_2 T_aa T_a) T_a))) (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (= V_y (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 _let_1 V_f T_a T_aa)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_3 V_B)))))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_inf T_a) V_A)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Olower__semilattice V_less__eq V_less V_inf T_a))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) V_x) V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a) V_A)) V_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Nitpick_Ofold__graph_H V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_y T_a T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_3 V_B)))))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_y T_a T_b))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.c_in V_x _let_1 T_a)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard _let_1 T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard V_A T_a))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Set_Ovimage V_f V_B T_a T_b)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) V_B) (tptp.c_Set_Oimage V_f V_A T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_C))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_g V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a T_b)) V_f) V_g))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$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) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_f $$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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_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) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_b T_a) 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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_A))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in V_c V_A T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((T_a $$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)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (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)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((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 $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted)) (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 ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) _let_2) _let_2))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_2))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((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_HOL_Ominus__class_Ominus _let_1) _let_2) V_A) _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 ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_B _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_A _let_2))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B)))))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) _let_1) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Set_Oimage V_f V_A T_a T_a)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_C T_a)) (tptp.c_Set_Oinsert V_a V_D T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_C) V_D)))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Set_Oinsert V_a V_B T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.c_Set_Oinsert V_a (tptp.hAPP _let_1 V_B) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) V_C) (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_x T_b T_a)) (tptp.c_Set_Oimage V_f V_A T_b T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.c_Set_Oinsert V_x V_B T_a)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_x V_A T_a)) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_B T_a)))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B) (tptp.c_Set_Oinsert V_x (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) (tptp.c_Finite__Set_Ocard 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))))) (forall ((V_times $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ofold1 V_times T_a))) (or (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.hAPP (tptp.hAPP V_times V_x) (tptp.hAPP _let_1 V_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 $$unsorted) (V_x $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a)) V_B))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_B) T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_B) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_a V_B T_a)) T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_3)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) (tptp.c_Set_Oinsert 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 $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (= (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (= (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a))) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a))))) (forall ((T_a $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Olinorder__class_OMax T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_M)) (tptp.hAPP _let_2 V_N))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (= V_x_H V_y_H)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x))) (= V_xa V_y)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_B) _let_2)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_b T_a) T_b) (not (tptp.c_Fun_Oinj__on V_h (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_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_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a)) V_A))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oimage V_f V_A T_a T_b) T_a T_b) V_A) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _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))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) _let_2) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)) (= V_A V_B))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((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 $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.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 $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_D) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Olinorder__class_OMin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_2 V_N)) (tptp.hAPP _let_2 V_M))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Complete__Lattice_OInf__class_OInf V_A T_a)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_g V_B T_b T_a)) V_A))) (not (tptp.c_Fun_Oinj__on V_g V_B T_b T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) V_B))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$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_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((V_f $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_b))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.hAPP (tptp.hAPP _let_3 V_B) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H))))))) (forall ((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 $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (or (= V_y (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.c_Finite__Set_Ofold1 V_f T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_a T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_A)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OInf__class_OInf (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) V_B) (tptp.c_Set_Oimage V_f V_A T_a T_b)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted) (V_Z_H $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_x) V_c) V_xa) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P) V_c) V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_P_H) V_c) V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q) _let_2 _let_1) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP _let_3 V_Q_H) _let_2 _let_1) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple tptp.t_a) V_P) V_c) V_Q) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)))))) (= (tptp.hAPP (tptp.c_COMBK tptp.v_P tptp.t_a tptp.t_b) tptp.v_Q) tptp.v_P) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMin T_a) V_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_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Finite__Set_Olinorder__class_OMax T_a) V_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 $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a) T_aa))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (V_times $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_b) (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 $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_a T_c T_b) _let_1 T_b T_c) T_c) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_g _let_1 T_b T_a) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (= (tptp.hAPP (tptp.c_COMBB tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP tptp.v_P _let_14)) (= (tptp.hAPP (tptp.c_COMBS tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP _let_15 _let_14)) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a) V_P) tptp.c_Com_Ocom_OSKIP) V_P) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (let ((_let_4 (tptp.hAPP _let_3 V_P))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Com_Ocom_OSemi V_c V_d)) V_R) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_3 V_Q) V_d) V_R) _let_2 _let_1) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP (tptp.hAPP _let_4 V_c) V_Q) _let_2 _let_1) T_a)))))))) (forall ((V_G $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_t $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts (tptp.tc_Hoare__Mirabelle_Otriple T_a)) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_G_H T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((V_x $$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 $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_fun2 V_fun2_H)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_com V_com_H)))) (forall ((T_a $$unsorted) (V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (let ((_let_1 (tptp.c_Hoare__Mirabelle_Otriple_Otriple T_a))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1) V_com) V_fun2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_fun1_H) V_com_H) V_fun2_H))) (= V_fun1 V_fun1_H)))) (= (tptp.hAPP _let_13 tptp.v_x) (tptp.c_in tptp.v_x _let_13 tptp.t_a)) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) (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 ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_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_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 $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_G $$unsorted) (V_t $$unsorted) (T_a $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (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_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (tptp.c_Finite__Set_Ofinite tptp.v_F tptp.t_a) (not (tptp.hBOOL (tptp.c_in tptp.v_x tptp.v_F tptp.t_a))) _let_12 _let_6 _let_11 _let_7 (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.c_Set_Oimage (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB _let_5 tptp.v_P _let_2 _let_4 tptp.t_a) tptp.v_c0 tptp.t_a tptp.tc_Com_Ocom _let_3) tptp.v_Q tptp.t_a _let_2 _let_1) tptp.v_F tptp.t_a _let_1) tptp.t_b) (not _let_6)) (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_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ouminus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ouminus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ouminus tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))
% 1.38/1.58 )
% 1.38/1.58 % SZS output end Proof for SWV844-1
% 1.38/1.59 % cvc5---1.0.5 exiting
% 1.38/1.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------