TSTP Solution File: SCT071-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 14:11:58 EDT 2023
% Result : Unsatisfiable 1.82s 2.01s
% Output : Proof 1.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.21 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n013.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.42 % CPULimit : 300
% 0.20/0.42 % WCLimit : 300
% 0.20/0.42 % DateTime : Thu Aug 24 15:12:17 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.27/0.62 %----Proving TF0_NAR, FOF, or CNF
% 0.27/0.62 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PSoYYboapU/cvc5---1.0.5_6311.p...
% 0.27/0.77 ------- get file name : TPTP file name is SCT071-1
% 0.27/0.77 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6311.smt2...
% 0.27/0.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.82/2.01 % SZS status Unsatisfiable for SCT071-1
% 1.82/2.01 % SZS output start Proof for SCT071-1
% 1.82/2.02 (
% 1.82/2.02 (let ((_let_1 (not tptp.v_thesis____))) (let ((_let_2 (forall ((V_h $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oimage V_h _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_nat))) (not (tptp.c_Fun_Oinj__on V_h _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat)) tptp.v_thesis____))))) (let ((_let_3 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)))) (let ((_let_4 (tptp.c_Finite__Set_Ofinite _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi))) (let ((_let_5 (forall ((V_M $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 V_M T_a) V_M (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_M T_a) tptp.tc_nat) T_a tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_M T_a)))))) (let ((_let_6 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))))) (let ((_let_7 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (= (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))))) (let ((_let_8 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_9 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_10 (forall ((V_h $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oimage V_h _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_nat))) (not (tptp.c_Fun_Oinj__on V_h _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat))))))) (let ((_let_11 (tptp.c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi))) (let ((_let_12 (tptp.c_Fun_Oinj__on _let_11 _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_8 (tptp.c_Finite__Set_Ocard _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_nat))) (let ((_let_15 (= _let_14 (tptp.c_Set_Oimage _let_11 _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat)))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_13))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.c_Fun_Obij__betw _let_11 _let_3 _let_14 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_12 _let_20))) (let ((_let_22 (_let_6))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (not _let_4))) (let ((_let_25 (or _let_19 _let_24))) (let ((_let_26 (_let_5))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_19 (not _let_25)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Finite__Set_Ofinite V_M T_a) false))))) :args _let_26)) _let_27 :args (_let_25 false _let_5)) :args (_let_19 false _let_4 false _let_25)))) (let ((_let_29 (or _let_15 _let_20))) (let ((_let_30 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (= V_B (tptp.c_Set_Oimage V_f V_A T_a T_b)) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Set_Oimage V_h _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat)))) :args _let_32))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_13 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_20 _let_15 (not _let_29)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_11 _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b) false))))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_15 false _let_19 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_12 (not _let_21)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_11 _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b) false))))) :args _let_22)) _let_23 :args (_let_21 false _let_6)) :args (_let_12 false _let_19 false _let_21)) :args (_let_18 false _let_15 false _let_12)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_1)) :args (_let_10 true tptp.v_thesis____)) :args (false true _let_17 false _let_10)) :args ((forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Fun_Ocomp V_f (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_a T_b T_b) (tptp.c_Fun_Oid T_b)) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_f (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_a T_b T_b) (tptp.c_Fun_Oid T_b))) (tptp.c_Fun_Osurj V_f T_a T_b))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a _let_1 T_a) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc _let_1) tptp.tc_nat))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (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 ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1 V_A V_f V_g T_a T_b) V_A T_a)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_g V_A T_c T_a))) (or (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A (tptp.c_Fun_Ocomp V_f V_g T_a T_b T_c) T_c T_b) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp (tptp.c_Hilbert__Choice_Oinv__into V_A V_g T_c T_a) (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) T_a T_c T_b) V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_g V_A T_c T_a)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Obij (tptp.c_Fun_Ocomp V_g V_f T_b T_c T_a) T_a T_c) (not (tptp.c_Fun_Obij V_g T_b T_c)) (not (tptp.c_Fun_Obij V_f 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_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 (tptp.c_Suc V_n) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (or (tptp.c_lessequals (tptp.hAPP _let_2 V_B) (tptp.hAPP _let_2 V_A) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (or (tptp.c_lessequals V_B V_A _let_1) (not (tptp.c_lessequals (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (or (tptp.c_lessequals (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.c_lessequals V_B V_A _let_1)))))) (forall ((V_Abs $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_Rep $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_Abs V_x) (tptp.hAPP V_Abs V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)) (= V_x V_y))) (forall ((V_Rep $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_Abs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_Rep V_x) (tptp.hAPP V_Rep V_y))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)) (= V_x V_y))) (forall ((V_Rep $$unsorted) (V_Abs $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_Rep (tptp.hAPP V_Abs V_y)) V_y) (not (tptp.hBOOL (tptp.c_in V_y V_A T_b))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (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 ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a)))) (forall ((T_a $$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.hBOOL (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_HOL_Oord T_a)) (tptp.hBOOL (tptp.c_in V_i (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i V_k T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_A) V_B _let_1))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_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_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a T_b) _let_1) (not (tptp.c_Fun_Osurj V_f T_a T_b))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a) T_aa))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Osurj (tptp.c_Fun_Ocomp V_g V_f T_b T_c T_a) T_a T_c) (not (tptp.c_Fun_Osurj V_g T_b T_c)) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (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_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) _let_2) _let_1)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_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.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (not (tptp.c_lessequals V_x V_x tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Oid T_a) T_a T_b T_a) V_f)) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ocomp (tptp.c_Fun_Oid T_b) V_g T_b T_b T_a) V_g)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.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))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Fun_Oid T_a))) (= (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) _let_1 T_a T_a) _let_1))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.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_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_FuncSet_Orestrict V_f V_A T_a T_b) V_A V_B T_a T_b) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b) (not (tptp.c_Fun_Obij__betw (tptp.c_FuncSet_Orestrict V_f V_A T_a T_b) V_A V_B T_a T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (let ((_let_2 (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b))) (or (not (= (tptp.hAPP _let_2 V_x) (tptp.hAPP _let_2 V_y))) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in V_y _let_1 T_b))) (not (tptp.hBOOL (tptp.c_in V_x _let_1 T_b))))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard V_A T_a))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$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 ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.c_in V_x _let_1 T_a)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) V_B V_A T_b T_a) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_xs $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Omap V_g V_xs T_c T_b) T_b T_a) (tptp.c_List_Omap (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_xs T_c T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((V_A $$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 $$unsorted) (V_A $$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_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Orderings_Otop__class_Otop T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Orderings_Obot__class_Obot T_a))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_y))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted)) (tptp.c_Fun_Obij (tptp.c_Fun_Oid T_a) T_a T_a)) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) V_A _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_c V_a T_a) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_b V_d T_a) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_c V_d T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) V_A) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))) (forall ((V_B $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A (tptp.tc_fun T_a tptp.tc_bool)) (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_Obij V_f T_a T_b)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (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_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__Xex__nat__less__eq__1__2 V_P V_n) V_n tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_F $$unsorted) (T_b $$unsorted) (V_h $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_b) (not (tptp.c_Fun_Osurj V_h T_a T_b)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_a T_b) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Fun_Ocomp (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) V_f T_b T_a T_a) (tptp.c_Fun_Oid T_a)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Fun_Ocomp (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) V_f T_b T_a T_a) (tptp.c_Fun_Oid T_a))) (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) _let_1))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))) (tptp.c_lessequals V_C V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_p tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat) tptp.tc_nat T_a) T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_p tptp.tc_nat) tptp.tc_nat T_a)) (not (tptp.c_lessequals V_n V_p tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Otop__class_Otop _let_1) V_A _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a T_b) V_A) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (tptp.c_HOL_Oord__class_Oless _let_8 (tptp.c_Suc _let_8) tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (not (tptp.c_lessequals V_m V_u T_a)) (not (tptp.c_lessequals V_l V_m T_a)))) (= (tptp.hAPP (tptp.c_Fun_Oid tptp.t_a) tptp.v_x) tptp.v_x) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_a) T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((T_c $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_c tptp.tc_bool)))) (or (= (tptp.c_Hilbert__Choice_Oinv__into _let_1 (tptp.c_Fun_Ocomp V_f V_g T_a T_b T_c) T_c T_b) (tptp.c_Fun_Ocomp (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_g T_c T_a) (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_a T_c T_b)) (not (tptp.c_Fun_Obij V_g T_c T_a)) (not (tptp.c_Fun_Obij V_f T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) _let_1)) (= V_a _let_1)))) (= (tptp.c_SetInterval_Oord__class_OlessThan _let_8 tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_B T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_B _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Osurj V_f T_a T_b) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) T_a))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y))) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_y $$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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((V_A $$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_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) V_y)) V_y) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_k $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_SetInterval_Oord__class_OlessThan V_k tptp.tc_nat) tptp.tc_nat)) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x _let_2 T_a) _let_1) (tptp.c_Set_Oinsert V_y _let_2 T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_f $$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_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Oid T_b) V_c T_b T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c V_v)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) V_A T_b T_a)) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) V_B V_A T_b T_a) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_Fun_Oid T_a) V_A T_a T_a) V_A)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_a T_b) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_b)) (not (tptp.c_Fun_Obij V_h T_a T_b)))) (forall ((V_F $$unsorted) (T_b $$unsorted) (V_h $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_a T_b) T_a)) (not (tptp.c_Fun_Obij V_h T_a T_b)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_Fun_Ocomp V_g V_f T_c T_b T_a) V_x T_a T_b) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Ovimage V_g V_x T_c T_b) T_a T_c))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_b T_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_a V_b) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b) T_b)) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (tptp.c_Fun_Osurj (tptp.c_Fun_Oid T_a) T_a T_a)) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_1))) (= (tptp.hAPP _let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat) (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 ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_f $$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.hBOOL (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 ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a _let_2 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_2 T_a))) (= V_a V_b) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_k (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_SetInterval_Oord__class_OlessThan V_k T_a) _let_1) _let_2))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBB _let_1 V_f T_a T_a T_b) V_A T_b T_a) (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_B) _let_1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) V_x) V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_x $$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.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Oid T_a) V_x) V_x)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_A)) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_a)) V_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_x)) V_x)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_b)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (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_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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$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 ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Fun_Oinj__on V_f V_A T_aa T_a)) (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_aa T_a) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) V_A))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OlessThan V_u T_a)) (not (tptp.c_lessequals V_l V_u T_a)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_Fun_Ocomp V_g V_f T_b T_c T_a) V_A V_C T_a T_c) (not (tptp.c_Fun_Obij__betw V_g V_B V_C T_b T_c)) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))) (= (tptp.hAPP _let_9 tptp.v_x) (tptp.c_in tptp.v_x _let_9 tptp.t_a)) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__Xall__nat__less__eq__1__1 V_P V_n) V_n tptp.tc_nat))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop _let_1) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_Abs $$unsorted) (V_Rep $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_Abs (tptp.hAPP V_Rep V_x)) V_x) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((V_Rep $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_Abs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_Rep V_x) V_A T_b)) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (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 ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a _let_1 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_y)) V_y) (not (tptp.hBOOL (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_b T_a) V_f) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_HOL_Ouminus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun tptp.t_a T_b)) V_A) tptp.v_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_b) (tptp.hAPP V_A tptp.v_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_c T_b tptp.t_a) tptp.v_x) (tptp.hAPP V_f (tptp.hAPP V_g tptp.v_x)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_B $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (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_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_b)) V_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_b (tptp.hAPP _let_1 V_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_b) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_b) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP _let_1 V_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) _let_1) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.c_lessequals _let_8 _let_8 tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_8 _let_8 tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat)))) (forall ((T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) tptp.tc_nat))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$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 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Ocomp V_f V_g T_c T_a T_b) V_r T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_r T_b T_c) T_c T_a))) _let_7 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_f $$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_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_FuncSet_Orestrict V_f V_A T_b T_a) V_A T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Oid T_a) V_Y T_a T_a) V_Y)) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) V_A T_b T_a) T_a T_b) V_A) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_a T_c T_b) _let_1 T_b T_c) T_c) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_g _let_1 T_b T_a) T_a))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (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)) (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_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop _let_1) V_B _let_1) V_B))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_f $$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_lessequals (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) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_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_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 V_A V_f V_g T_a T_b) V_A T_a)))) (forall ((V_g $$unsorted) (V_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.hBOOL (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 $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_a) T_a T_b) (not (tptp.c_Fun_Oinj__on V_g V_A T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 V_A V_f V_g T_a T_b) V_A T_a)))) (forall ((V_g $$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.hBOOL (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_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A V_f T_a T_b) V_y)) V_y) (not (tptp.hBOOL (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b) (tptp.c_Finite__Set_Osetsum (tptp.c_Fun_Oid T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) T_b T_b)) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_A $$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) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_A $$unsorted) (V_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_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_a $$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.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_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_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_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((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 $$unsorted) (V_x $$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 ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_FuncSet_Orestrict V_f V_A T_b T_a) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ocard V_xa T_a))) (or (tptp.hBOOL (tptp.c_in V_x V_xa T_a)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_xa T_a) T_a) (tptp.c_Suc _let_1)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_g V_A T_c T_a))) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into V_A (tptp.c_Fun_Ocomp V_f V_g T_a T_b T_c) T_c T_b) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp (tptp.c_Fun_Othe__inv__into V_A V_g T_c T_a) (tptp.c_Fun_Othe__inv__into _let_1 V_f T_a T_b) T_a T_c T_b) V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_g V_A T_c T_a)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_n T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_m T_a)) (not (tptp.c_lessequals V_i V_n T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (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.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((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 $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) 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 ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OlessThan V_l T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((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_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 ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (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_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 $$unsorted) (V_a $$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_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 $$unsorted) (V_x $$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_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 $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_b T_a) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$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 ((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_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_c $$unsorted) (V_h $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_c)) (= (tptp.c_Finite__Set_Osetsum V_h (tptp.c_Set_Oimage V_f V_B T_a T_b) T_b T_c) (tptp.c_Finite__Set_Osetsum (tptp.c_Fun_Ocomp V_h V_f T_b T_c T_a) V_B T_a T_c)) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (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 ((V_g $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_g (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) T_a T_c T_b) V_f T_b T_c T_a) V_g) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 V_P V_f T_a T_b))))) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_List_Omap V_f (tptp.c_List_OremoveAll V_x V_xs T_a) T_a T_b) (tptp.c_List_OremoveAll (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xs T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 V_f V_g T_a T_b))) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g _let_2)) _let_2)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b)) (= (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) V_g))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Osurj (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) T_b T_a) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_ATP__Linkup_Osko__Fun__XinjI__1__1 V_f T_a T_b) (tptp.c_ATP__Linkup_Osko__Fun__XinjI__1__2 V_f T_a T_b))) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (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) (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 V_f T_a T_b)) (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 V_f T_a T_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 V_f T_a T_b) (tptp.c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 V_f T_a T_b))) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Ovimage V_h V_F T_b T_a) T_b) (not (tptp.c_Fun_Oinj__on V_h (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (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) (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__XinjI__1__1 V_f T_a T_b)) (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__XinjI__1__2 V_f T_a T_b))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij V_f T_a T_b) (not (tptp.c_Fun_Osurj V_f T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij V_f T_a T_b) (not (tptp.c_Fun_Osurj V_f 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)))) (forall ((V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_a) (not (tptp.c_Fun_Osurj V_f T_a T_a)) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Osurj V_f T_a T_a) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_a)) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b)) (not (tptp.c_Fun_Obij__betw V_f V_A V_B T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_FuncSet_Orestrict V_f V_A T_a T_b) V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on (tptp.c_FuncSet_Orestrict V_f V_A T_a T_b) V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_COMBI T_a) V_A T_a T_a)) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_Fun_Oid T_a) V_A T_a T_a)) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1 V_A V_f V_g T_a T_b))) (or (not (= (tptp.hAPP V_g (tptp.hAPP V_f _let_1)) _let_1)) (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) _let_6 _let_5 (forall ((V_M $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Obij__betw (tptp.c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1 V_M T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_M T_a) tptp.tc_nat) V_M tptp.tc_nat T_a) (not (tptp.c_Finite__Set_Ofinite V_M T_a)))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (not (tptp.hBOOL (tptp.c_in V_xa (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xall__nat__less__eq__1__1 V_P V_n)))))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xex__nat__less__eq__1__2 V_P V_n))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u tptp.tc_nat) tptp.tc_nat)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard _let_1 T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (not (= (tptp.hAPP V_f _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_Suc _let_1) V_k tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat) tptp.tc_nat T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_1) V_A) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus _let_2) (tptp.c_Set_Oimage V_f V_A T_a T_b)) _let_2) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b)))))) (forall ((V_f $$unsorted) (V_y $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_y))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Set_Oimage V_f _let_2 T_aa T_a) T_a))) (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (= V_y (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 _let_1 V_f T_a T_aa)))))) (forall ((V_b $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_b (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 V_b V_f T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP V_f V_x))) (or (not (= (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_2 V_f V_x T_a T_aa) V_x)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_aa T_a)) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Set_Oimage V_f _let_1 T_aa T_a) T_a)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 V_P V_f T_a T_b) (tptp.c_Set_Oimage V_f _let_1 T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Set_Oimage V_f _let_2 T_aa T_a) T_a)) (= _let_1 (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_1 V_f V_x T_a T_aa))))))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_B T_a T_b) V_A _let_1) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_g V_B T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_g V_B T_b T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) _let_4 (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_Rep $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_Abs $$unsorted)) (or (= (tptp.c_Set_Oimage V_Rep (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) V_A) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((V_Abs $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_Rep $$unsorted)) (or (= (tptp.c_Set_Oimage V_Abs V_A T_b T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_A $$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 $$unsorted)) (or (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Obij__betw V_f V_A (tptp.c_Set_Oimage V_f V_A T_a T_b) T_a T_b))) (forall ((V_f $$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_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_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_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_c) T_c T_b) (not (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ocomp V_g V_f T_c T_b T_a) V_A T_a T_b)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ocomp V_g V_f T_b T_c T_a) V_A T_a T_c) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_c)) (not (tptp.c_Fun_Oinj__on V_f V_A 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 ((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 $$unsorted) (V_f $$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 $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_a T_b) (tptp.c_List_Omap V_f V_ys T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_xs V_ys))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_xs V_ys) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.c_Fun_Othe__inv__into _let_1 V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_m $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)))) (forall ((V_n $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OlessThan V_n tptp.tc_nat))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_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) (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_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) (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_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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_a) V_A) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) _let_2 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((V_f $$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_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) _let_1 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ouminus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ouminus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ouminus tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$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)))))))))))))))))))))))))))))))))))))))
% 1.82/2.02 )
% 1.82/2.03 % SZS output end Proof for SCT071-1
% 1.86/2.15 % cvc5---1.0.5 exiting
% 1.86/2.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------