%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV880-1 : 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 21:53:38 EDT 2023

% Result   : Unsatisfiable 0.51s 0.95s
% Output   : Proof 0.51s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17  % Problem    : SWV880-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.18  % Command    : do_cvc5 %s %d
% 0.17/0.39  % Computer : n028.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Tue Aug 29 10:55:55 EDT 2023
% 0.17/0.39  % CPUTime    : 
% 0.24/0.57  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.58  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.jMbvW1O3vT/cvc5---1.0.5_32224.p...
% 0.45/0.67  ------- get file name : TPTP file name is SWV880-1
% 0.45/0.68  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32224.smt2...
% 0.45/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.51/0.95  % SZS status Unsatisfiable for SWV880-1
% 0.51/0.95  % SZS output start Proof for SWV880-1
% 0.51/0.96  (
% 0.51/0.96  (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage tptp.v_mgt__call tptp.v_U tptp.tc_Com_Opname tptp.t_a))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_4 (tptp.hAPP tptp.v_mgt__call tptp.v_pn))) (let ((_let_5 (tptp.c_lessequals (tptp.c_Set_Oinsert _let_4 _let_3 tptp.t_a) _let_2 _let_1))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.c_in tptp.v_pn tptp.v_U tptp.tc_Com_Opname))) (let ((_let_8 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a))))) (let ((_let_9 (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))))) (let ((_let_10 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))))) (let ((_let_11 (tptp.c_in _let_4 _let_2 tptp.t_a))) (let ((_let_12 (not _let_7))) (let ((_let_13 (or _let_12 _let_11))) (let ((_let_14 (_let_8))) (let ((_let_15 (ASSUME :args _let_14))) (let ((_let_16 (not _let_11))) (let ((_let_17 (tptp.c_lessequals _let_3 _let_2 _let_1))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_5 _let_18 _let_16))) (let ((_let_20 (_let_10))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (_let_9))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (tptp.tc_fun T_a tptp.tc_bool))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_12 _let_11 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_5 _let_18 _let_16 (not _let_19)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.t_a _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_24) V_A _let_24) true))))) :args _let_22)) _let_23 :args (_let_17 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_4 _let_3 tptp.t_a _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) true))))) :args _let_20)) _let_21 :args (_let_19 false _let_10)) :args (_let_16 true _let_5 false _let_17 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (tptp.v_pn tptp.v_U tptp.tc_Com_Opname tptp.v_mgt__call tptp.t_a QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a) true))))) :args _let_14)) _let_15 :args (_let_13 false _let_8)) (ASSUME :args (_let_7)) :args (false true _let_11 false _let_13 false _let_7)) :args ((forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a)) V_x) (tptp.c_Orderings_Oord__class_Omax (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x) T_a))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_i V_k T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.c_HOL_Oord__class_Oless V_i V_k T_a) (not (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_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_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_z T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a)) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_b T_a) T_b) (not (tptp.c_Fun_Oinj__on V_h (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Oord__class_Omin T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omax (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$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.c_Orderings_Oord__class_Omax V_x V_y T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_a) V_b) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)))) (forall ((V_g $$unsorted) (V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b))) (or (not (= (tptp.hAPP V_g _let_2) (tptp.hAPP V_g _let_1))) (not (= (tptp.hAPP V_g (tptp.hAPP V_f _let_2)) (tptp.hAPP V_g (tptp.hAPP V_f _let_1)))) (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)))))) (forall ((V_g $$unsorted) (V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b))) (or (not (= (tptp.hAPP V_g _let_2) (tptp.hAPP V_g _let_1))) (not (= (tptp.hAPP V_g (tptp.hAPP V_f _let_2)) (tptp.hAPP V_g (tptp.hAPP V_f _let_1)))) (tptp.c_Fun_Oinj__on V_g V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)))))) (forall ((V_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b))) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (= (tptp.hAPP V_g _let_2) (tptp.hAPP V_g _let_1)) (= (tptp.hAPP V_g (tptp.hAPP V_f _let_2)) (tptp.hAPP V_g (tptp.hAPP V_f _let_1))))))) (forall ((V_g $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b))) (or (tptp.c_Fun_Oinj__on V_g V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (= (tptp.hAPP V_g _let_2) (tptp.hAPP V_g _let_1)) (= (tptp.hAPP V_g (tptp.hAPP V_f _let_2)) (tptp.hAPP V_g (tptp.hAPP V_f _let_1))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into _let_1 V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard _let_1 T_a))) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omax V_y V_x T_a)))) (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.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.c_Set_Oimage V_f V_X T_a T_b) T_b T_a) V_X) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into _let_1 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 _let_1 T_a T_b))))) (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))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z) T_a) (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omax V_y (tptp.c_Orderings_Oord__class_Omax V_x V_z T_a) T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_f $$unsorted) (V_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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x _let_1 T_a) _let_1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_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_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (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.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (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.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c (tptp.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.c_in V_c V_A T_a) (not (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_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a)) (tptp.c_Orderings_Oord__class_Omax (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z) T_a))))) (forall ((V_f $$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 ((V_m $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_a V_b T_a T_b) V_c V_d T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_c V_d T_a T_b) V_a V_b T_a T_b)) (= V_a V_c))) (forall ((V_f $$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 ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_y T_a) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_z T_a) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) V_y) V_z T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$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 $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_C))) (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) V_C) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1))))) (forall ((V_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 ((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_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_3 V_B _let_1)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (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)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((V_f $$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 $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_aa T_a) V_f)) (forall ((T_a $$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 ((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 $$unsorted) (V_f $$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_Hilbert__Choice_Oinv__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 ((V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.c_Fun_Oinj__on V_f _let_1 T_aa T_a)) (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_aa T_a) (tptp.hAPP V_f V_x)) 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.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_B) V_C _let_1) (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((T_a $$unsorted) (V_A $$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.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_x (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a)) (tptp.c_Orderings_Oord__class_Omax V_x V_z T_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_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_in V_c V_A T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) V_x T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_y V_x T_a)) (tptp.c_Orderings_Oord__class_Omax V_z V_x T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a)) (tptp.c_Orderings_Oord__class_Omax V_x V_z T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A _let_1) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_in V_x V_A T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_x $$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.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.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.c_in V_a V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((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.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.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_in V_a (tptp.c_Inductive_Ocomplete__lattice__class_Ogfp V_f _let_1) T_a) (not (tptp.c_lessequals V_X (tptp.hAPP V_f V_X) _let_1)) (not (tptp.c_in V_a V_X T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a)) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_in (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_x) V_A T_b) (not (tptp.c_in V_x (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (let ((_let_2 (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b))) (or (not (= (tptp.hAPP _let_2 V_x) (tptp.hAPP _let_2 V_y))) (= V_x V_y) (not (tptp.c_in V_y _let_1 T_b)) (not (tptp.c_in V_x _let_1 T_b)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_y)) V_y) (not (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_b T_a) 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.c_in V_x V_A T_b))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (not (tptp.c_Fun_Oinj__on V_f V_A T_aa T_a)) (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_aa T_a) (tptp.hAPP V_f V_x)) V_x))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$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.c_in V_x V_A T_aa)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)) _let_1))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_a) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$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 ((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 ((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_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a) T_aa)) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_X (tptp.c_Inductive_Ocomplete__lattice__class_Ogfp V_f T_a) T_a) (not (tptp.c_lessequals V_X (tptp.hAPP V_f V_X) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not 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V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_y) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_y)) 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(tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_A $$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) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1)))) (forall ((V_x $$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 $$unsorted) (V_a $$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_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals V_f V_g _let_1) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1) (tptp.c_lessequals V_g V_f _let_1) (not (tptp.c_lessequals V_f V_g _let_1))))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (not (tptp.c_lessequals V_g V_f _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (= V_A V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_D) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B _let_1))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_A T_b T_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.c_Finite__Set_Ofinite (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 V_A V_B V_f T_a T_b) V_A T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 V_A V_B V_f T_b T_a)) V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 V_A V_B V_f T_b T_a) V_A T_b))) (forall ((V_g $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_X $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_g V_X T_a T_b))) (or (tptp.c_in (tptp.hAPP V_g V_a) (tptp.c_Inductive_Ocomplete__lattice__class_Ogfp V_f _let_1) T_b) (not (tptp.c_lessequals _let_2 (tptp.hAPP V_f _let_2) _let_1)) (not (tptp.c_in V_a V_X T_a)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 V_A V_B V_f T_a T_b)) V_B T_b)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_in V_c V_A T_b))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (not (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$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.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 $$unsorted) (V_x $$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.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_g $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b) V_A T_a))) (forall ((V_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b) V_A T_a))) (forall ((V_g $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b) V_A T_a))) (forall ((V_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b) V_A T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_k (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) _let_1) _let_2))))) (forall ((V_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 $$unsorted) (T_b $$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_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_S $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) (tptp.c_Set_Oimage V_f V_S T_a T_b) T_b T_a) V_S) (not (tptp.c_lessequals V_S V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_B T_a T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_x) (not (tptp.c_in V_x V_A T_a)) (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 ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_x) (not (tptp.c_in V_x V_A T_a)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a) V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Nitpick_Ofold__graph_H V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_y T_a T_b)) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_y T_a T_b))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b) T_b)) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (or (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.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (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 ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$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.c_lessequals (tptp.c_Set_Oimage V_g V_B T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_g V_B T_b T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_x) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 V_A V_x T_a) V_x T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_x) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_x (tptp.c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 V_A V_x T_a) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Omin T_a) V_x) (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.c_in V_a V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_in V_x V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((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.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_b) _let_1) T_b T_a) T_a)) (not (tptp.c_in V_x V_A T_b))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (not (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Set_Oinsert (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.c_in V_x V_A T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_A T_a) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_A T_a) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_x T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (T_b $$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_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a)) (tptp.c_in V_x V_B T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_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_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.c_in V_xa V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) V_A (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_B $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= V_B (tptp.c_Set_Oimage V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) T_b T_a)) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) V_A T_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_N T_a) (tptp.c_Finite__Set_Olinorder__class_OMin V_M T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (forall ((T_a $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMax V_M T_a) (tptp.c_Finite__Set_Olinorder__class_OMax V_N T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.c_in V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (forall ((V_f $$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 $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a) (not (tptp.c_in V_a V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_t V_B T_a) (not (tptp.c_in V_t V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) _let_10 (forall ((V_x $$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 $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((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)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (= V_a V_b) (not (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((T_a $$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_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$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_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) _let_9 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a) (not (tptp.c_in V_x V_A T_b)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a)) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (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 $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_f $$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.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 $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_in V_x V_xa T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.c_in V_x V_B T_a) (tptp.c_in V_x V_A T_a) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.c_in V_a V_A T_a)))) (forall ((T_a $$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))) _let_8 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_b)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a) (not (tptp.c_in V_x V_A T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_x V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (tptp.c_Finite__Set_Ofinite tptp.v_U tptp.tc_Com_Opname) (= tptp.v_G _let_2) _let_7 _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_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_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))
% 0.51/0.96  )
% 0.51/0.96  % SZS output end Proof for SWV880-1
% 0.51/0.97  % cvc5---1.0.5 exiting
% 0.51/0.97  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------